WorldWideScience

Sample records for non-commutative potential scattering

  1. Scattering theory of space-time non-commutative abelian gauge field theory

    International Nuclear Information System (INIS)

    Rim, Chaiho; Yee, Jaehyung

    2005-01-01

    The unitary S-matrix for space-time non-commutative quantum electrodynamics is constructed using the *-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, we formulate the perturbation theory and present the Feynman rule. We then apply this perturbation analysis to the Compton scattering process to the lowest order and check the gauge invariance of the scattering amplitude at this order.

  2. Coulomb Scattering in the Massless Nelson Model III: Ground State Wave Functions and Non-commutative Recurrence Relations

    Science.gov (United States)

    Dybalski, Wojciech; Pizzo, Alessandro

    2018-02-01

    Let $H_{P,\\sigma}$ be the single-electron fiber Hamiltonians of the massless Nelson model at total momentum $P$ and infrared cut-off $\\sigma>0$. We establish detailed regularity properties of the corresponding $n$-particle ground state wave functions $f^n_{P,\\sigma}$ as functions of $P$ and $\\sigma$. In particular, we show that \\[ |\\partial_{P^j}f^{n}_{P,\\sigma}(k_1,\\ldots, k_n)|, \\ \\ |\\partial_{P^j} \\partial_{P^{j'}} f^{n}_{P,\\sigma}(k_1,\\ldots, k_n)| \\leq \\frac{1}{\\sqrt{n!}} \\frac{(c\\lambda_0)^n}{\\sigma^{\\delta_{\\lambda_0}}} \\prod_{i=1}^n\\frac{ \\chi_{[\\sigma,\\kappa)}(k_i)}{|k_i|^{3/2}}, \\] where $c$ is a numerical constant, $\\lambda_0\\mapsto \\delta_{\\lambda_0}$ is a positive function of the maximal admissible coupling constant which satisfies $\\lim_{\\lambda_0\\to 0}\\delta_{\\lambda_0}=0$ and $\\chi_{[\\sigma,\\kappa)}$ is the (approximate) characteristic function of the energy region between the infrared cut-off $\\sigma$ and the ultraviolet cut-off $\\kappa$. While the analysis of the first derivative is relatively straightforward, the second derivative requires a new strategy. By solving a non-commutative recurrence relation we derive a novel formula for $f^n_{P,\\sigma}$ with improved infrared properties. In this representation $\\partial_{P^{j'}}\\partial_{P^{j}}f^n_{P,\\sigma}$ is amenable to sharp estimates obtained by iterative analytic perturbation theory in part II of this series of papers. The bounds stated above are instrumental for scattering theory of two electrons in the Nelson model, as explained in part I of this series.

  3. Chiral effective potential in N = {1/2} non-commutative Wess-Zumino model

    International Nuclear Information System (INIS)

    Banin, A.T.; Buchbinder, I.L.; Pletnev, N.G.

    2004-01-01

    We study a structure of holomorphic quantum contributions to the effective action for N = {1/2} noncommutative Wess-Zumino model. Using the symbol operator techniques we present the one-loop chiral effective potential in a form of integral over proper time of the appropriate heat kernel. We prove that this kernel can be exactly found. As a result we obtain the exact integral representation of the one-loop effective potential. Also we study the expansion of the effective potential in a series in powers of the chiral superfield φ and derivative D 2 φ and construct a procedure for systematic calculation of the coefficients in the series. We show that all terms in the series without derivatives can be summed up in an explicit form. (author)

  4. Non-commutative analysis

    CERN Document Server

    Jorgensen, Palle

    2017-01-01

    The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret 'non-commutative analysis' broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.

  5. Testing Non-commutative QED, Constructing Non-commutative MHD

    OpenAIRE

    Guralnik, Z.; Jackiw, R.; Pi, S. Y.; Polychronakos, A. P.

    2001-01-01

    The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In principle, this allows a test by the Michelson-Morley interference method. We also study non-commutativity in another context, by constructing the theory describing a charged fluid in a strong magnetic field, which forces the fluid particles into ...

  6. Non-commutative Nash inequalities

    International Nuclear Information System (INIS)

    Kastoryano, Michael; Temme, Kristan

    2016-01-01

    A set of functional inequalities—called Nash inequalities—are introduced and analyzed in the context of quantum Markov process mixing. The basic theory of Nash inequalities is extended to the setting of non-commutative L p spaces, where their relationship to Poincaré and log-Sobolev inequalities is fleshed out. We prove Nash inequalities for a number of unital reversible semigroups

  7. Covariant non-commutative space–time

    Directory of Open Access Journals (Sweden)

    Jonathan J. Heckman

    2015-05-01

    Full Text Available We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation introduces a short-distance scale ℓp, and thus breaks scale invariance, but preserves all space–time isometries. The non-commutative algebra is defined on space–times with non-zero constant curvature, i.e. dS4 or AdS4. The construction makes essential use of the representation of CFT tensor operators as polynomials in an auxiliary polarization tensor. The polarization tensor takes active part in the non-commutative algebra, which for dS4 takes the form of so(5,1, while for AdS4 it assembles into so(4,2. The structure of the non-commutative correlation functions hints that the deformed theory contains gravitational interactions and a Regge-like trajectory of higher spin excitations.

  8. Non-commutative tomography and signal processing

    International Nuclear Information System (INIS)

    Mendes, R Vilela

    2015-01-01

    Non-commutative tomography is a technique originally developed and extensively used by Professors M A Man’ko and V I Man’ko in quantum mechanics. Because signal processing deals with operators that, in general, do not commute with time, the same technique has a natural extension to this domain. Here, a review is presented of the theory and some applications of non-commutative tomography for time series as well as some new results on signal processing on graphs. (paper)

  9. Non-commutative standard model: model building

    CERN Document Server

    Chaichian, Masud; Presnajder, P

    2003-01-01

    A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by U sub * (n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just 0,+-1. We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the U sub * (3) x U sub * (2) x U sub * (1) gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherentCP violation and new neutrino interactions. (orig.)

  10. Stability of a non-commutative Jackiw-Teitelboim gravity

    Energy Technology Data Exchange (ETDEWEB)

    Vassilevich, D.V. [Universitaet Leipzig, Institut fuer Theoretische Physik, Postfach 100 920, Leipzig (Germany); St. Petersburg University, V.A. Fock Institute of Physics, St. Petersburg (Russian Federation); Fresneda, R.; Gitman, D.M. [Sao Paulo Univ. (Brazil). Inst. de Fisica

    2006-07-15

    We start with a non-commutative version of the Jackiw-Teitelboim gravity in two dimensions which has a linear potential for the dilaton fields. We study whether it is possible to deform this model by adding quadratic terms to the potential but preserving the number of gauge symmetries. We find that no such deformation exists (provided one does not twist the gauge symmetries). (orig.)

  11. Non-commutativity in polar coordinates

    Energy Technology Data Exchange (ETDEWEB)

    Edwards, James P. [Universidad Michoacana de San Nicolas de Hidalgo, Ciudad Universitaria, Instituto de Fisica y Matematicas, Morelia, Michoacan (Mexico)

    2017-05-15

    We reconsider the fundamental commutation relations for non-commutative R{sup 2} described in polar coordinates with non-commutativity parameter θ. Previous analysis found that the natural transition from Cartesian coordinates to the traditional polar system led to a representation of [r, φ] as an everywhere diverging series. In this article we compute the Borel resummation of this series, showing that it can subsequently be extended throughout parameter space and hence provide an interpretation of this commutator. Our analysis provides a complete solution for arbitrary r and θ that reproduces the earlier calculations at lowest order and benefits from being generally applicable to problems in a two-dimensional non-commutative space. We compare our results to previous literature in the (pseudo-)commuting limit, finding a surprising spatial dependence for the coordinate commutator when θ >> r{sup 2}. Finally, we raise some questions for future study in light of this progress. (orig.)

  12. Non-commutative arithmetic circuits with division

    Czech Academy of Sciences Publication Activity Database

    Hrubeš, Pavel; Wigderson, A.

    2015-01-01

    Roč. 11, Article 14 (2015), s. 357-393 ISSN 1557-2862 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : arithmetic circuits * non-commutative rational function * skew field Subject RIV: BA - General Mathematics http://theoryofcomputing.org/articles/v011a014/

  13. Non-commutative geometry and supersymmetry 2

    International Nuclear Information System (INIS)

    Hussain, F.; Thompson, G.

    1991-05-01

    Following the general construction of supersymmetric models, the model based on the idea of non-commutative geometry is formulated as a Yang-Mills theory of the graded Lie algebra U(2/1) over a graded space-time manifold. 4 refs

  14. Two-dimensional black holes and non-commutative spaces

    International Nuclear Information System (INIS)

    Sadeghi, J.

    2008-01-01

    We study the effects of non-commutative spaces on two-dimensional black hole. The event horizon of two-dimensional black hole is obtained in non-commutative space up to second order of perturbative calculations. A lower limit for the non-commutativity parameter is also obtained. The observer in that limit in contrast to commutative case see two horizon

  15. Non-commutative tools for topological insulators

    International Nuclear Information System (INIS)

    Prodan, Emil

    2010-01-01

    This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic limit and in the presence of disorder, whose robustness is shown to have nontrivial physical consequences for the bulk states. The set of tools also includes a general relation between the current of an observable and its edge index, a relation that can be used to investigate the robustness of the edge states against disorder. The paper focuses on the motivations behind creating such tools and on how to use them.

  16. Classical mechanics in non-commutative phase space

    International Nuclear Information System (INIS)

    Wei Gaofeng; Long Chaoyun; Long Zhengwen; Qin Shuijie

    2008-01-01

    In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys. Rev. D, 2005, 72: 025010). The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative. (authors)

  17. On tea, donuts and non-commutative geometry

    Directory of Open Access Journals (Sweden)

    Igor V. Nikolaev

    2018-03-01

    Full Text Available As many will agree, it feels good to complement a cup of tea by a donut or two. This sweet relationship is also a guiding principle of non-commutative geometry known as Serre Theorem. We explain the algebra behind this theorem and prove that elliptic curves are complementary to the so-called non-commutative tori.

  18. Linearization of non-commuting operators in the partition function

    International Nuclear Information System (INIS)

    Ahmed, M.

    1983-06-01

    A generalization of the Stratonovich-Hubbard scheme for evaluating the grand canonical partition function is given. The scheme involves linearization of products of non-commuting operators using the functional integral method. The non-commutivity of the operators leads to an additional term which can be absorbed in the single-particle Hamiltonian. (author)

  19. Geometry of time-spaces non-commutative algebraic geometry, applied to quantum theory

    CERN Document Server

    Landau, Olav Arnfinn

    2011-01-01

    This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory o

  20. Introduction to Dubois-Violette's non-commutative differential geometry

    International Nuclear Information System (INIS)

    Djemai, A.E.F.

    1994-07-01

    In this work, one presents a detailed review of Dubois-Violette et al. approach to non-commutative differential calculus. The non-commutative differential geometry of matrix algebras and the non-commutative Poisson structures are treated in some details. We also present the analog of the Maxwell's theory and the new models of Yang-Mills-Higgs theories that can be constructed in this framework. In particular, some simple models are compared with the standard model. Finally, we discuss some perspectives and open questions. (author). 32 refs

  1. Non-Commutative Mechanics in Mathematical & in Condensed Matter Physics

    Directory of Open Access Journals (Sweden)

    Peter A. Horváthy

    2006-12-01

    Full Text Available Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table 1. Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ''exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.

  2. Computational commutative and non-commutative algebraic geometry

    CERN Document Server

    Cojocaru, S; Ufnarovski, V

    2005-01-01

    This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The topic is looked at from different perspectives in over 20 lecture reports. It emphasizes the current trends in commutative and non-commutative algebraic geometry and algebra. The contributors to this publication present the most recent and state-of-the-art progresses which reflect the topic discussed in this publication. Both researchers and graduate students will find this book a good source of information on commutative and non-commutative algebraic geometry.

  3. Minimal length uncertainty and generalized non-commutative geometry

    International Nuclear Information System (INIS)

    Farmany, A.; Abbasi, S.; Darvishi, M.T.; Khani, F.; Naghipour, A.

    2009-01-01

    A generalized formulation of non-commutative geometry for the Bargmann-Fock space of quantum field theory is presented. The analysis is related to the symmetry of the simplistic space and a minimal length uncertainty.

  4. Vectors and covectors in non-commutative setting

    OpenAIRE

    Parfionov, G. N.; Romashev, Yu. A.; Zapatrine, R. R.

    1995-01-01

    Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors and covectors is carried out.

  5. Non-commutative geometry on quantum phase-space

    International Nuclear Information System (INIS)

    Reuter, M.

    1995-06-01

    A non-commutative analogue of the classical differential forms is constructed on the phase-space of an arbitrary quantum system. The non-commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. They are constructed by applying the Weyl-Wigner symbol map to the differential envelope of the linear operators on the quantum mechanical Hilbert space. This leads to a representation of the non-commutative forms considered by A. Connes in terms of multiscalar functions on the classical phase-space. In an appropriate coincidence limit they define a quantum deformation of the classical tensor fields and both commutative and non-commutative forms can be studied in a unified framework. We interprete the quantum differential forms in physical terms and comment on possible applications. (orig.)

  6. Differential Galois obstructions for non-commutative integrability

    Energy Technology Data Exchange (ETDEWEB)

    Maciejewski, Andrzej J. [Institute of Astronomy, University of Zielona Gora, Podgorna 50, PL-65-246 Zielona Gora (Poland)], E-mail: maciejka@astro.ia.uz.zgora.pl; Przybylska, Maria [Torun Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87-100 Torun (Poland)], E-mail: mprzyb@astri.uni.torun.pl

    2008-08-11

    We show that if a holomorphic Hamiltonian system is holomorphically integrable in the non-commutative sense in a neighbourhood of a non-equilibrium phase curve which is located at a regular level of the first integrals, then the identity component of the differential Galois group of the variational equations along the phase curve is Abelian. Thus necessary conditions for the commutative and non-commutative integrability given by the differential Galois approach are the same.

  7. Trace Dynamics and a non-commutative special relativity

    International Nuclear Information System (INIS)

    Lochan, Kinjalk; Singh, T.P.

    2011-01-01

    Trace Dynamics is a classical dynamical theory of non-commuting matrices in which cyclic permutation inside a trace is used to define the derivative with respect to an operator. We use the methods of Trace Dynamics to construct a non-commutative special relativity. We define a line-element using the Trace over space-time coordinates which are assumed to be operators. The line-element is shown to be invariant under standard Lorentz transformations, and is used to construct a non-commutative relativistic dynamics. The eventual motivation for constructing such a non-commutative relativity is to relate the statistical thermodynamics of this classical theory to quantum mechanics. -- Highlights: → Classical time is external to quantum mechanics. → This implies need for a formulation of quantum theory without classical time. → A starting point could be a non-commutative special relativity. → Such a relativity is developed here using the theory of Trace Dynamics. → A line-element is defined using the Trace over non-commuting space-time operators.

  8. Non-commutative representation for quantum systems on Lie groups

    Energy Technology Data Exchange (ETDEWEB)

    Raasakka, Matti Tapio

    2014-01-27

    The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a {sup *}-algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R{sup d}, U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase

  9. Non-commutative representation for quantum systems on Lie groups

    International Nuclear Information System (INIS)

    Raasakka, Matti Tapio

    2014-01-01

    The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a * -algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R d , U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase space path

  10. The standard model on non-commutative space-time

    International Nuclear Information System (INIS)

    Calmet, X.; Jurco, B.; Schupp, P.; Wohlgenannt, M.; Wess, J.

    2002-01-01

    We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter θ μν . No new particles are introduced; the structure group is SU(3) x SU(2) x U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in θ μν we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. (orig.)

  11. The standard model on non-commutative space-time

    Energy Technology Data Exchange (ETDEWEB)

    Calmet, X.; Jurco, B.; Schupp, P.; Wohlgenannt, M. [Sektion Physik, Universitaet Muenchen (Germany); Wess, J. [Sektion Physik, Universitaet Muenchen (Germany); Max-Planck-Institut fuer Physik, Muenchen (Germany)

    2002-03-01

    We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter {theta}{sup {mu}}{sup {nu}}. No new particles are introduced; the structure group is SU(3) x SU(2) x U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in {theta}{sup {mu}}{sup {nu}} we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. (orig.)

  12. Optimization of polynomials in non-commuting variables

    CERN Document Server

    Burgdorf, Sabine; Povh, Janez

    2016-01-01

    This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.

  13. Non-commutative flux representation for loop quantum gravity

    Science.gov (United States)

    Baratin, A.; Dittrich, B.; Oriti, D.; Tambornino, J.

    2011-09-01

    The Hilbert space of loop quantum gravity is usually described in terms of cylindrical functionals of the gauge connection, the electric fluxes acting as non-commuting derivation operators. It has long been believed that this non-commutativity prevents a dual flux (or triad) representation of loop quantum gravity to exist. We show here, instead, that such a representation can be explicitly defined, by means of a non-commutative Fourier transform defined on the loop gravity state space. In this dual representation, flux operators act by sstarf-multiplication and holonomy operators act by translation. We describe the gauge invariant dual states and discuss their geometrical meaning. Finally, we apply the construction to the simpler case of a U(1) gauge group and compare the resulting flux representation with the triad representation used in loop quantum cosmology.

  14. Investigations on the renormalizability of a non-commutative u(1) gauge theory

    International Nuclear Information System (INIS)

    Rofner, A.

    2009-01-01

    standard model is formulated via gauge field theories. It is therefore crucial to find their non-commutative, renormalizable counterparts. Having said this we have already addressed the goal and content of this dissertation, which consists in finding a potentially renormalizable theta-deformed u(1) gauge theory. In a first step, we studied in detail a localized version of a model, which represents an extension of ordinary u(1) gauge theory (formulated on Euclidean space) to the non-commutative setting, and is based on adding a term similar to the one of Gurau et. al., leading to an IR-damped gauge boson propagator. In the course of one-loop calculations, we have shown that it implements additional degrees of freedom and hence modifies the original physical content of the theory. A way out was found by implementing the modification of the IR sector through the introduction of a soft breaking term similar to the approach of Gribov and Zwanziger known from commutative Yang Mills theory. However, when trying to show renormalizability at one-loop level, it turned out that the action does not contain the appropriate terms for absorbing the IR divergences. usually, in such cases one constructs an effective renormalizable action via application of renormalization schemes such as Algebraic Renormalization, which in this case fails, due to the inherent non-locality of the star product. As a consequence, some ideas regarding the applicability and possible extension of traditional renormalization schemes to non-commutative GFTs have been discussed. Finally a new action (the BRSW model) was constructed. It could be shown to be renormalizable to one-loop order. Although a rigorous proof is still missing, we expect it to be a very promising candidate for the first fully renormalizable non-commutative gauge field theory.(author) [de

  15. Modular Theory, Non-Commutative Geometry and Quantum Gravity

    Directory of Open Access Journals (Sweden)

    Wicharn Lewkeeratiyutkul

    2010-08-01

    Full Text Available This paper contains the first written exposition of some ideas (announced in a previous survey on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal.

  16. Non-commutative covering spaces and their symmetries

    DEFF Research Database (Denmark)

    Canlubo, Clarisson

    dened and its corresponding Galois theory. Using this and basic concepts from algebraic geometryand spectral theory, we will give a full description of the general structure of non-centralcoverings. Examples of coverings of the rational and irrational non-commutative tori will alsobe studied. Using...... will explain this and relate it to bi-Galois theory.Using the OZ-transform, we will show that non-commutative covering spaces come in pairs.Several categories of covering spaces will be dened and studied. Appealing to Tannaka duality,we will explain how this lead to a notion of an etale fundamental group...

  17. The M5-brane and non-commutative open strings

    NARCIS (Netherlands)

    Bergshoeff, E.; Berman, D.S.; Schaar, J.P. van der; Sundell, P.

    2001-01-01

    The M-theory origin of non-commutative open-string theory is examined by investigating the M-theory 5-brane at near critical field strength. In particular, it is argued that the open-membrane metric provides the appropriate moduli when calculating the duality relations between M and II

  18. On Subgroups of Non-Commutative General Rhotrix Group ...

    African Journals Online (AJOL)

    This paper considers the pair (GRn(F),o) consisting of the set of all invertible rhotrices of size n over an arbitrary field F; and together with the binary operation of row-column based method for rhotrix multiplication; 'o' , in order to introduce it as the concept of “non commutative general rhotrix group”. We identify a number of ...

  19. Notes on algebraic invariants for non-commutative dynamical systems

    Energy Technology Data Exchange (ETDEWEB)

    Longo, R [Rome Univ. (Italy). Istituto di Matematica

    1979-11-01

    We consider an algebraic invariant for non-commutative dynamical systems naturally arising as the spectrum of the modular operator associated to an invariant state, provided certain conditions of mixing type are present. This invariant turns out to be exactly the annihilator of the invariant T of Connes. Further comments are included, in particular on the type of certain algebras of local observables

  20. Newton's second law in a non-commutative space

    International Nuclear Information System (INIS)

    Romero, Juan M.; Santiago, J.A.; Vergara, J. David

    2003-01-01

    In this Letter we show that corrections to Newton's second law appear if we assume a symplectic structure consistent with the commutation rules of the non-commutative quantum mechanics. For central field we find that the correction term breaks the rotational symmetry. For the Kepler problem, this term is similar to a Coriolis force

  1. Limit algebras of differential forms in non-commutative geometry

    Indian Academy of Sciences (India)

    The holomorphic functional calculus closure of Connes' non- commutative de Rham algebra. ∗. D. (p. 549 of [C]) leads to a couple of operator algebras which are briefly discussed in this section. In §5, which contains the main contributions of the paper, quantized integrals are constructed on ∞A by using Dixmier trace ...

  2. quasi hyperrigidity and weak peak points for non-commutative ...

    Indian Academy of Sciences (India)

    7

    Abstract. In this article, we introduce the notions of weak boundary repre- sentation, quasi hyperrigidity and weak peak points in the non-commutative setting for operator systems in C∗-algebras. An analogue of Saskin's theorem relating quasi hyperrigidity and weak Choquet boundary for particular classes of C∗-algebras is ...

  3. The shear viscosity of the non-commutative plasma

    International Nuclear Information System (INIS)

    Landsteiner, Karl; Mas, Javier

    2007-01-01

    We compute the shear viscosity of the non-commutative N = 4 super Yang-Mills quantum field theory at strong coupling using the dual supergravity background. Special interest derives from the fact that the background presents an intrinsic anisotropy in space through the distinction of commutative and non-commutative directions. Despite this anisotropy the analysis exhibits the ubiquitous result η/s = 1/4π for two different shear channels. In order to derive this result, we show that the boundary energy momentum tensor must couple to the open string metric. As a byproduct we compute the renormalised holographic energy momentum tensor and show that it coincides with one in the commutative theory

  4. Space/time non-commutative field theories and causality

    International Nuclear Information System (INIS)

    Bozkaya, H.; Fischer, P.; Pitschmann, M.; Schweda, M.; Grosse, H.; Putz, V.; Wulkenhaar, R.

    2003-01-01

    As argued previously, amplitudes of quantum field theories on non-commutative space and time cannot be computed using naive path integral Feynman rules. One of the proposals is to use the Gell-Mann-Low formula with time-ordering applied before performing the integrations. We point out that the previously given prescription should rather be regarded as an interaction-point time-ordering. Causality is explicitly violated inside the region of interaction. It is nevertheless a consistent procedure, which seems to be related to the interaction picture of quantum mechanics. In this framework we compute the one-loop self-energy for a space/time non-commutative φ 4 theory. Although in all intermediate steps only three-momenta play a role, the final result is manifestly Lorentz covariant and agrees with the naive calculation. Deriving the Feynman rules for general graphs, we show, however, that such a picture holds for tadpole lines only. (orig.)

  5. Semiclassical and quantum motions on the non-commutative plane

    International Nuclear Information System (INIS)

    Baldiotti, M.C.; Gazeau, J.P.; Gitman, D.M.

    2009-01-01

    We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a θ-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man'ko states and circular squeezed states. The relation between these states and the 'classical' trajectories is investigated, and we present numerical explorations of some semiclassical quantities.

  6. Semiclassical and quantum motions on the non-commutative plane

    Energy Technology Data Exchange (ETDEWEB)

    Baldiotti, M.C., E-mail: baldiott@fma.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Gazeau, J.P., E-mail: gazeau@apc.univ-paris7.f [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Gitman, D.M., E-mail: gitman@dfn.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil)

    2009-10-19

    We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a theta-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man'ko states and circular squeezed states. The relation between these states and the 'classical' trajectories is investigated, and we present numerical explorations of some semiclassical quantities.

  7. Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach

    OpenAIRE

    Bertram, Wolfgang

    2013-01-01

    By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via exercises using dynamical software (such as geogebra), hopefully accessible to a wide mathematical audience, from undergraduate students and high school teachers to researchers, proceeding in three steps: (1) experimental geometry, (2) algebra (linear algebr...

  8. Euler Polynomials and Identities for Non-Commutative Operators

    OpenAIRE

    De Angelis, V.; Vignat, C.

    2015-01-01

    Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt, expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, due to J.-C. Pain, links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Fig...

  9. Non-topological non-commutativity in string theory

    International Nuclear Information System (INIS)

    Guttenberg, S.; Herbst, M.; Kreuzer, M.; Rashkov, R.

    2008-01-01

    Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum field theory. Appositely, open string diagrams provided the inspiration for Kontsevich's solution of the long-standing problem of quantization of Poisson geometry by virtue of his formality theorem. In the context of D-brane physics non-commutativity is not limited, however, to the topological sector. We show that non-commutative effective actions still make sense when associativity is lost and establish a generalized Connes-Flato-Sternheimer condition through second order in a derivative expansion. The measure in general curved backgrounds is naturally provided by the Born-Infeld action and reduces to the symplectic measure in the topological limit, but remains non-singular even for degenerate Poisson structures. Analogous superspace deformations by RR-fields are also discussed. (Abstract Copyright [2008], Wiley Periodicals, Inc.)

  10. Non-commutative and commutative vacua effects in a scalar torsion scenario

    Energy Technology Data Exchange (ETDEWEB)

    Sheikhahmadi, Haidar, E-mail: h.sh.ahmadi@gmail.com [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of); Aghamohammadi, Ali, E-mail: a.aghamohamadi@iausdj.ac.ir [Sanandaj Branch, Islamic Azad University, Sanandaj (Iran, Islamic Republic of); Saaidi, Khaled, E-mail: ksaaidi@uok.ac.ir [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)

    2015-10-07

    In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.

  11. Non-commutative and commutative vacua effects in a scalar torsion scenario

    International Nuclear Information System (INIS)

    Sheikhahmadi, Haidar; Aghamohammadi, Ali; Saaidi, Khaled

    2015-01-01

    In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.

  12. Non-commutative and commutative vacua effects in a scalar torsion scenario

    Directory of Open Access Journals (Sweden)

    Haidar Sheikhahmadi

    2015-10-01

    Full Text Available In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.

  13. Non-commutative geometry inspired charged black holes

    International Nuclear Information System (INIS)

    Ansoldi, Stefano; Nicolini, Piero; Smailagic, Anais; Spallucci, Euro

    2007-01-01

    We find a new, non-commutative geometry inspired, solution of the coupled Einstein-Maxwell field equations describing a variety of charged, self-gravitating objects, including extremal and non-extremal black holes. The metric smoothly interpolates between de Sitter geometry, at short distance, and Reissner-Nordstrom geometry far away from the origin. Contrary to the ordinary Reissner-Nordstrom spacetime there is no curvature singularity in the origin neither 'naked' nor shielded by horizons. We investigate both Hawking process and pair creation in this new scenario

  14. Can non-commutativity resolve the big-bang singularity?

    Energy Technology Data Exchange (ETDEWEB)

    Maceda, M.; Madore, J. [Laboratoire de Physique Theorique, Universite de Paris-Sud, Batiment 211, 91405, Orsay (France); Manousselis, P. [Department of Engineering Sciences, University of Patras, 26110, Patras (Greece); Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Zoupanos, G. [Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Theory Division, CERN, 1211, Geneva 23 (Switzerland)

    2004-08-01

    A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has non-commutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a modification of the Kasner metric is constructed which is commutative only at large time scales. At small time scales, near the singularity, the commutation relations among the space coordinates diverge. We interpret this result as meaning that the singularity has been completely delocalized. (orig.)

  15. Non-commutative field theory with twistor-like coordinates

    International Nuclear Information System (INIS)

    Taylor, Tomasz R.

    2007-01-01

    We consider quantum field theory in four-dimensional Minkowski spacetime, with the position coordinates represented by twistors instead of the usual world-vectors. Upon imposing canonical commutation relations between twistors and dual twistors, quantum theory of fields described by non-holomorphic functions of twistor variables becomes manifestly non-commutative, with Lorentz symmetry broken by a time-like vector. We discuss the free field propagation and its impact on the short- and long-distance behavior of physical amplitudes in perturbation theory. In the ultraviolet limit, quantum field theories in twistor space are generically less divergent than their commutative counterparts. Furthermore, there is no infrared-ultraviolet mixing problem

  16. Non-commutative multiple-valued logic algebras

    CERN Document Server

    Ciungu, Lavinia Corina

    2014-01-01

    This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects.   A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing.   Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.

  17. Bootstrapping non-commutative gauge theories from L∞ algebras

    Science.gov (United States)

    Blumenhagen, Ralph; Brunner, Ilka; Kupriyanov, Vladislav; Lüst, Dieter

    2018-05-01

    Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L∞ algebra, that governs not only the action of the symmetries but also the dynamics of the theory. Our approach is well motivated from string theory. We recall that such field theories arise in the context of branes in WZW models and briefly comment on its appearance for integrable deformations of AdS5 sigma models. For the SU(2) WZW model, we show that the earlier proposed matrix valued gauge theory on the fuzzy 2-sphere can be bootstrapped via an L∞ algebra. We then apply this approach to the construction of non-commutative Chern-Simons and Yang-Mills theories on flat and curved backgrounds with non-constant NC-structure. More concretely, up to the second order, we demonstrate how derivative and curvature corrections to the equations of motion can be bootstrapped in an algebraic way from the L∞ algebra. The appearance of a non-trivial A∞ algebra is discussed, as well.

  18. One-loop beta functions for the orientable non-commutative Gross Neveu model TH1"-->

    Science.gov (United States)

    Lakhoua, A.; Vignes-Tourneret, F.; Wallet, J.-C.

    2007-11-01

    We compute at the one-loop order the β-functions for a renormalisable non-commutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The β-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.

  19. Essay on physics and non-commutative geometry

    International Nuclear Information System (INIS)

    Connes, A.

    1990-01-01

    Our aim, in this article, is to try to discover what physics would be like if the space in which it took place was not a set of points, but a non-commutative space. We shall not go very far in this direction, and the consequences of this investigation are for the moment either mathematical or only applied to a commutative space-time. It is clear, however, that a tool as remarkable as the Dixmier trace for analyzing logarithmic divergences should be useful to physicists. Moreover we have been able to show that a small modification of our picture of space-time gives a conceptual explanation of the Higgs fields and of the way they appear in the Weinberg-Salam model. This should allow us to make at the classical level explicit predictions of the Higgs mass: a very crude one is discussed. (author)

  20. Non-commuting variations in mathematics and physics a survey

    CERN Document Server

    Preston, Serge

    2016-01-01

    This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equa...

  1. Non commutative geometry and super Yang-Mills theory

    International Nuclear Information System (INIS)

    Bigatti, D.

    1999-01-01

    We aim to connect the non commutative geometry 'quotient space' viewpoint with the standard super Yang Mills theory approach in the spirit of Connes-Douglas-Schwartz and Douglas-Hull description of application of noncommutative geometry to matrix theory. This will result in a relation between the parameters of a rational foliation of the torus and the dimension of the group U(N). Namely, we will be provided with a prescription which allows to study a noncommutative geometry with rational parameter p/N by means of a U(N) gauge theory on a torus of size Σ/N with the boundary conditions given by a system with p units of magnetic flux. The transition to irrational parameter can be obtained by letting N and p tend to infinity with fixed ratio. The precise meaning of the limiting process will presumably allow better clarification. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

  2. Euler polynomials and identities for non-commutative operators

    Science.gov (United States)

    De Angelis, Valerio; Vignat, Christophe

    2015-12-01

    Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.

  3. Wavepacket scattering in potential theory

    International Nuclear Information System (INIS)

    Weber, T.A.; Hammer, C.L.

    1977-01-01

    A contour integration technique is developed which enforces the initial conditions for wavepacket-potential scattering. The expansion coefficients for the exact energy eigenstate expansion are automatically expressed in terms of the plane wave expansion coefficients of the initial wavepacket, thereby simplifying what is usually a tedious, mathematical process. The method is applicable regardless of the initial spatial separation of the wavepacket from the scattering center

  4. Potential scattering of Dirac particles

    International Nuclear Information System (INIS)

    Thaller, B.

    1981-01-01

    A quantum mechanical interpretation of the Dirac equation for particles in external electromagnetic potentials is discussed. It is shown that a consequent development of the Stueckelberg-Feynman theory into a probabilistic interpretation of the Dirac equation corrects some prejudices concerning negative energy states, Zitterbewegung and bound states in repulsive potentials and yields the connection between propagator theory and scattering theory. Limits of the Dirac equation, considered as a wave mechanical equation, are considered. (U.K.)

  5. Strong coupling effects in non-commutative spaces from OM theory and supergravity

    International Nuclear Information System (INIS)

    Russo, J.G.; Sheikh-Jabbari, M.M.

    2000-11-01

    We show that a four-parameter class of 3+1 dimensional NCOS theories can be obtained by dimensional reduction on a general 2-torus from OM theory. Compactifying two spatial directions of NCOS theory on a 2-torus, we study the transformation properties under the SO(2,2; Z) T-duality group. We then discuss non-perturbative configurations of non-commutative super Yang-Mills theory. In particular, we calculate the tension for magnetic monopoles and (p,q) dyons and exhibit their six-dimensional origin, and construct a supergravity solution representing an instanton in the gauge theory. We also compute the potential for a monopole-antimonopole in the supergravity approximation. (author)

  6. Non-commutative solitons and strong-weak duality

    Energy Technology Data Exchange (ETDEWEB)

    Blas, Harold [Departamento de Matematica - ICET, Universidade Federal de Mato Grosso, Av. Fernando Correa, s/n, Coxipo, 78060-900, Cuiaba - MT (Brazil)]. E-mail: blas@cpd.ufmt.br; Carrion, Hector L. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro (Brazil); Rojas, Moises [Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud, 150 CEP 22290-180, Rio de Janeiro-RJ (Brazil)

    2005-03-01

    Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. The master lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) associated to the group GL(2), in which the Toda field belongs to certain representations of either U(1)xU(1) or U(1){sub C} corresponding to the Lechtenfeld et al. (NCSG{sub 1}) or Grisaru-Penati (NCSG{sub 2}) proposals for the NC versions of the sine-Gordon model, respectively. Besides, the relevant NCMT{sub 1,2} models are written for two (four) types of Dirac fields corresponding to the Moyal product extension of one (two) copy(ies) of the ordinary massive Thirring model. The NCATM{sub 1,2} models share the same one-soliton (real Toda field sector of model 2) exact solutions, which are found without expansion in the NC parameter {theta} for the corresponding Toda and matter fields describing the strong-weak phases, respectively. The correspondence NCSG{sub 1} {r_reversible} NCMT{sub 1} is promising since it is expected to hold on the quantum level. (author)

  7. Weinberg-Salam theory in non-commutative geometry

    International Nuclear Information System (INIS)

    Morita, Katsusada; Okumura, Yoshitaka.

    1994-01-01

    Ordinary differential calculus on smooth manifold is generalized so as to construct gauge theory coupled to fermions on discrete space M 4 xZ 2 which is an underlying space-time in the non-commutative geometry for the standard model. We can reproduce not only the bosonic sector but also the fermionic sector of the Weinberg-Salam theory without recourse to the Dirac operator at the outset. Treatment of the fermionic sector is based on the generalized spinor one-forms from which the Dirac lagrangian is derived through taking the inner product. Two model constructions are presented using our formalism, both giving the classical mass relation m H = √2m w . The first model leaves the Weinberg angle arbitrary as usual, while the second one predicts sin 2 θ w = 1/4 in the tree level. This prediction is the same as that of Connes but we obtain it from correct hypercharge assignment of 2x2 matrix-valued Higgs field and from vanishing photon mass, thereby dispensing with Connes' 0-trace condition or the equivalent. (author)

  8. Problem of quantifying quantum correlations with non-commutative discord

    Science.gov (United States)

    Majtey, A. P.; Bussandri, D. G.; Osán, T. M.; Lamberti, P. W.; Valdés-Hernández, A.

    2017-09-01

    In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Guo (Sci Rep 6:25241, 2016). By resorting to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt's is used. In order to avoid this basis-dependence feature, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt's. In addition, the resulting measure inherits the main properties of Guo's measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such an optimization. The results show that, in most cases of interest, the use of Guo's measure can result in an overestimation of quantum correlations. However, since Guo's measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.

  9. A non-commutative formula for the isotropic magneto-electric response

    International Nuclear Information System (INIS)

    Leung, Bryan; Prodan, Emil

    2013-01-01

    A non-commutative formula for the isotropic magneto-electric response of disordered insulators under magnetic fields is derived using the methods of non-commutative geometry. Our result follows from an explicit evaluation of the Ito derivative with respect to the magnetic field of the non-commutative formula for the electric polarization reported in Schulz-Baldes and Teufel (2012 arXiv:1201.4812v1). The quantization, topological invariance and connection to a second Chern number of the magneto-electric response are discussed in the context of three-dimensional, disordered, time-reversal or inversion symmetric topological insulators. (paper)

  10. On the classical dynamics of charges in non-commutative QED

    International Nuclear Information System (INIS)

    Fatollahi, A.H.; Mohammadzadeh, H.

    2004-01-01

    Following Wong's approach to formulating the classical dynamics of charged particles in non-Abelian gauge theories, we derive the classical equations of motion of a charged particle in U(1) gauge theory on non-commutative space, the so-called non-commutative QED. In the present use of the procedure, it is observed that the definition of the mechanical momenta should be modified. The derived equations of motion manifest the previous statement about the dipole behavior of the charges in non-commutative space. (orig.)

  11. Loop calculations for the non-commutative U*(1) gauge field model with oscillator term

    International Nuclear Information System (INIS)

    Blaschke, Daniel N.; Grosse, Harald; Kronberger, Erwin; Schweda, Manfred; Wohlgenannt, Michael

    2010-01-01

    Motivated by the success of the non-commutative scalar Grosse-Wulkenhaar model, a non-commutative U * (1) gauge field theory including an oscillator-like term in the action has been put forward in (Blaschke et al. in Europhys. Lett. 79:61002, 2007). The aim of the current work is to analyze whether that action can lead to a fully renormalizable gauge model on non-commutative Euclidean space. In a first step, explicit one-loop graph computations are hence presented, and their results as well as necessary modifications of the action are successively discussed. (orig.)

  12. Quantum groups, non-commutative differential geometry and applications

    International Nuclear Information System (INIS)

    Schupp, P.; California Univ., Berkeley, CA

    1993-01-01

    The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related sciences. A generalization of unitary time evolution is proposed and studied for a simple 2-level system, leading to non-conservation of microscopic entropy, a phenomenon new to quantum mechanics. A Cartan calculus that combines functions, forms, Lie derivatives and inner derivations along general vector fields into one big algebra is constructed for quantum groups and then extended to quantum planes. The construction of a tangent bundle on a quantum group manifold and an BRST type approach to quantum group gauge theory are given as further examples of applications. The material is organized in two parts: Part I studies vector fields on quantum groups, emphasizing Hopf algebraic structures, but also introducing a ''quantum geometric'' construction. Using a generalized semi-direct product construction we combine the dual Hopf algebras A of functions and U of left-invariant vector fields into one fully bicovariant algebra of differential operators. The pure braid group is introduced as the commutant of Δ(U). It provides invariant maps A → U and thereby bicovariant vector fields, casimirs and metrics. This construction allows the translation of undeformed matrix expressions into their less obvious quantum algebraic counter parts. We study this in detail for quasitriangular Hopf algebras, giving the determinant and orthogonality relation for the ''reflection'' matrix. Part II considers the additional structures of differential forms and finitely generated quantum Lie algebras -- it is devoted to the construction of the Cartan calculus, based on an undeformed Cartan identity

  13. On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

    Energy Technology Data Exchange (ETDEWEB)

    Amini, Nina H. [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States); CNRS, Laboratoire des Signaux et Systemes (L2S) CentraleSupelec, Gif-sur-Yvette (France); Miao, Zibo; Pan, Yu; James, Matthew R. [Australian National University, ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Canberra, ACT (Australia); Mabuchi, Hideo [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States)

    2015-12-15

    The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice. (orig.)

  14. On θ-commutators and the corresponding non-commuting graphs

    Directory of Open Access Journals (Sweden)

    Shalchi S.

    2017-12-01

    Full Text Available The θ-commutators of elements of a group with respect to an automorphism are introduced and their properties are investigated. Also, corresponding to θ-commutators, we define the θ-non-commuting graphs of groups and study their correlations with other notions. Furthermore, we study independent sets in θ-non-commuting graphs, which enable us to evaluate the chromatic number of such graphs.

  15. A new non-commutative representation of the Wiener and Poisson processes

    International Nuclear Information System (INIS)

    Privault, N.

    1996-01-01

    Using two different constructions of the chaotic and variational calculus on Poisson space, we show that the Wiener and Poisson processes have a non-commutative representation which is different from the one obtained by transfer of the Fock space creation and annihilation operators. We obtain in this way an extension of the non-commutative It calculus. The associated commutation relations show a link between the geometric and exponential distributions. (author). 11 refs

  16. A non-perturbative study of 4d U(1) non-commutative gauge theory - the fate of one-loop instability

    International Nuclear Information System (INIS)

    Bietenholz, Wolfgang; Nishimura, Jun; Susaki, Yoshiaki; Volkholz, Jan

    2006-01-01

    Recent perturbative studies show that in 4d non-commutative spaces, the trivial (classically stable) vacuum of gauge theories becomes unstable at the quantum level, unless one introduces sufficiently many fermionic degrees of freedom. This is due to a negative IR-singular term in the one-loop effective potential, which appears as a result of the UV/IR mixing. We study such a system non-perturbatively in the case of pure U(1) gauge theory in four dimensions, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d = 2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter θ, which provides evidence for a possible continuum theory. The extent of the dynamically generated space in the non-commutative directions becomes finite in the above limit, and its dependence on θ is evaluated explicitly. We also study the dispersion relation. In the weak coupling symmetric phase, it involves a negative IR-singular term, which is responsible for the observed phase transition. In the broken phase, it reveals the existence of the Nambu-Goldstone mode associated with the spontaneous symmetry breaking

  17. A non-perturbative study of 4d U(1) non-commutative gauge theory — the fate of one-loop instability

    Science.gov (United States)

    Bietenholz, Wolfgang; Nishimura, Jun; Susaki, Yoshiaki; Volkholz, Jan

    2006-10-01

    Recent perturbative studies show that in 4d non-commutative spaces, the trivial (classically stable) vacuum of gauge theories becomes unstable at the quantum level, unless one introduces sufficiently many fermionic degrees of freedom. This is due to a negative IR-singular term in the one-loop effective potential, which appears as a result of the UV/IR mixing. We study such a system non-perturbatively in the case of pure U(1) gauge theory in four dimensions, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d = 2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter θ, which provides evidence for a possible continuum theory. The extent of the dynamically generated space in the non-commutative directions becomes finite in the above limit, and its dependence on θ is evaluated explicitly. We also study the dispersion relation. In the weak coupling symmetric phase, it involves a negative IR-singular term, which is responsible for the observed phase transition. In the broken phase, it reveals the existence of the Nambu-Goldstone mode associated with the spontaneous symmetry breaking.

  18. Non-Commutative Integration, Zeta Functions and the Haar State for SU{sub q}(2)

    Energy Technology Data Exchange (ETDEWEB)

    Matassa, Marco, E-mail: marco.matassa@gmail.com [SISSA (Italy)

    2015-12-15

    We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group SU{sub q}(2). In particular we define the non-commutative integral as the residue at the spectral dimension of a zeta function, which is constructed using a Dirac operator and a weight. We consider the Dirac operator introduced by Kaad and Senior and a family of weights depending on two parameters, which are related to the diagonal automorphisms of SU{sub q}(2). We show that, after fixing one of the parameters, the non-commutative integral coincides with the Haar state of SU{sub q}(2). Moreover we can impose an additional condition on the zeta function, which also fixes the second parameter. For this unique choice the spectral dimension coincides with the classical dimension.

  19. Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry

    International Nuclear Information System (INIS)

    Alvarez, Pedro D.; Gomis, Joaquim; Kamimura, Kiyoshi; Plyushchay, Mikhail S.

    2008-01-01

    We investigate the planar anisotropic harmonic oscillator with explicit rotational symmetry as a particle model with non-commutative coordinates. It includes the exotic Newton-Hooke particle and the non-commutative Landau problem as special, isotropic and maximally anisotropic, cases. The system is described by the same (2+1)-dimensional exotic Newton-Hooke symmetry as in the isotropic case, and develops three different phases depending on the values of the two central charges. The special cases of the exotic Newton-Hooke particle and non-commutative Landau problem are shown to be characterized by additional, so(3) or so(2,1) Lie symmetry, which reflects their peculiar spectral properties

  20. Non-Commutative Integration, Zeta Functions and the Haar State for SUq(2)

    International Nuclear Information System (INIS)

    Matassa, Marco

    2015-01-01

    We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group SU q (2). In particular we define the non-commutative integral as the residue at the spectral dimension of a zeta function, which is constructed using a Dirac operator and a weight. We consider the Dirac operator introduced by Kaad and Senior and a family of weights depending on two parameters, which are related to the diagonal automorphisms of SU q (2). We show that, after fixing one of the parameters, the non-commutative integral coincides with the Haar state of SU q (2). Moreover we can impose an additional condition on the zeta function, which also fixes the second parameter. For this unique choice the spectral dimension coincides with the classical dimension

  1. An algebraic scheme associated with the non-commutative KP hierarchy and some of its extensions

    International Nuclear Information System (INIS)

    Dimakis, Aristophanes; Mueller-Hoissen, Folkert

    2005-01-01

    A well-known ansatz ('trace method') for soliton solutions turns the equations of the (non-commutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We develop an algebraic formalism, in particular involving a (mixable) shuffle product, to explore their structure. More precisely, we show that the equations of the non-commutative KP hierarchy and its extension (xncKP) in the case of a Moyal-deformed product, as derived in previous work, correspond to identities in this algebra. Furthermore, the Moyal product is replaced by a more general associative product. This leads to a new even more general extension of the non-commutative KP hierarchy. Relations with Rota-Baxter algebras are established

  2. Area-preserving diffeomorphisms in gauge theory on a non-commutative plane. A lattice study

    International Nuclear Information System (INIS)

    Bietenholz, W.; Bigarini, A.; INFN, Sezione di Perugia; Humboldt-Universitaet, Berlin; Torrielli, A.

    2007-06-01

    We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results confirm the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either. (orig.)

  3. Non-commutative phase space and its space-time symmetry

    International Nuclear Information System (INIS)

    Li Kang; Dulat Sayipjamal

    2010-01-01

    First a description of 2+1 dimensional non-commutative (NC) phase space is presented, and then we find that in this formulation the generalized Bopp's shift has a symmetric representation and one can easily and straightforwardly define the star product on NC phase space. Then we define non-commutative Lorentz transformations both on NC space and NC phase space. We also discuss the Poincare symmetry. Finally we point out that our NC phase space formulation and the NC Lorentz transformations are applicable to any even dimensional NC space and NC phase space. (authors)

  4. Some homological properties of skew PBW extensions arising in non-commutative algebraic geometry

    Directory of Open Access Journals (Sweden)

    Lezama Oswaldo

    2017-06-01

    Full Text Available In this short paper we study for the skew PBW (Poincar-Birkhoff-Witt extensions some homological properties arising in non-commutative algebraic geometry, namely, Auslander-Gorenstein regularity, Cohen-Macaulayness and strongly noetherianity. Skew PBW extensions include a considerable number of non-commutative rings of polynomial type such that classical PBW extensions, quantum polynomial rings, multiplicative analogue of the Weyl algebra, some Sklyanin algebras, operator algebras, diffusion algebras, quadratic algebras in 3 variables, among many others. Parametrization of the point modules of some examples is also presented.

  5. Unitary quantum physics with time-space non-commutativity

    International Nuclear Information System (INIS)

    Balachandran, A P; Govindarajan, T R; Martins, A G; Molina, C; Teotonio-Sobrinho, P

    2005-01-01

    In these lectures 4 quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. In the context of noncommutative quantum mechanics, some important points are explored, such as the formal construction of the theory, symmetries, causality, simultaneity and observables. The dynamics generated by a noncommutative Schroedinger equation is studied. The theory is further extended to certain noncommutative versions of the cylinder, R 3 and R x S 3 . In all these models, only discrete time translations are possible. One striking consequence of quantised time translations is that even though a time independent Hamiltonian is an observable, in scattering processes, it is conserved only modulo 2π/θ, where θ is the noncommutative parameter. Scattering theory is formulated and an approach to quantumfield theory is outlined

  6. Gravitational amplitudes in black hole evaporation: the effect of non-commutative geometry

    International Nuclear Information System (INIS)

    Grezia, Elisabetta Di; Esposito, Giampiero; Miele, Gennaro

    2006-01-01

    Recent work in the literature has studied the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat spacetime and weak radiation at a very late time. The relevant quantum amplitudes have been evaluated for bosonic and fermionic fields, showing that no information is lost in collapse to a black hole. On the other hand, recent developments in non-commutative geometry have shown that, in general relativity, the effects of non-commutativity can be taken into account by keeping the standard form of the Einstein tensor on the left-hand side of the field equations and introducing a modified energy-momentum tensor as a source on the right-hand side. The present paper, relying on the recently obtained non-commutativity effect on a static, spherically symmetric metric, considers from a new perspective the quantum amplitudes in black hole evaporation. The general relativity analysis of spin-2 amplitudes is shown to be modified by a multiplicative factor F depending on a constant non-commutativity parameter and on the upper limit R of the radial coordinate. Limiting forms of F are derived which are compatible with the adiabatic approximation here exploited. Approximate formulae for the particle emission rate are also obtained within this framework

  7. A Note on UV/IR Mixing and Non-Commutative Instanton Calculus

    CERN Document Server

    Bichl, A A

    2003-01-01

    We estimate the instanton-induced vacuum energy in non-commutative U(1) Yang-Mills theory in four dimensions. In the dilute gas approximation, it is found to be plagued by infrared divergences, as a result of UV/IR mixing.

  8. Determinants of self-employment among commuters and non-commuters

    DEFF Research Database (Denmark)

    Backman, M.; Karlsson, C.

    2016-01-01

    We analyse the determinants of self-employment and focus on the contextual environment. By distinguishing between commuters and non-commuters we are able to analyse the influence from the work and home environment, respectively. Our results indicate a significant difference between non...

  9. An introduction to quantum groups and non-commutative differential calculus

    International Nuclear Information System (INIS)

    Azcarraga, J.A. de; Rodenas, F.

    1995-01-01

    An introduction to quantum groups and quantum spaces is presented, and the non-commutative calculus on them is discussed. The case of q-Minkowski space is presented as an illustrative example. A set of useful expressions and formulae are collected in an appendix. 45 refs

  10. Matrix models as non-commutative field theories on R3

    International Nuclear Information System (INIS)

    Livine, Etera R

    2009-01-01

    In the context of spin foam models for quantum gravity, group field theories are a useful tool allowing on the one hand a non-perturbative formulation of the partition function and on the other hand admitting an interpretation as generalized matrix models. Focusing on 2d group field theories, we review their explicit relation to matrix models and show their link to a class of non-commutative field theories invariant under a quantum-deformed 3d Poincare symmetry. This provides a simple relation between matrix models and non-commutative geometry. Moreover, we review the derivation of effective 2d group field theories with non-trivial propagators from Boulatov's group field theory for 3d quantum gravity. Besides the fact that this gives a simple and direct derivation of non-commutative field theories for the matter dynamics coupled to (3d) quantum gravity, these effective field theories can be expressed as multi-matrix models with a non-trivial coupling between matrices of different sizes. It should be interesting to analyze this new class of theories, both from the point of view of matrix models as integrable systems and for the study of non-commutative field theories.

  11. On Some Isomorphisms between Bounded Linear Maps and Non-Commutative Lp-Spaces

    Directory of Open Access Journals (Sweden)

    E. J. Atto

    2014-04-01

    Full Text Available We define a particular space of bounded linear maps using a Von Neumann algebra and some operator spaces. By this, we prove some isomorphisms, and using interpolation in some particular cases, we get analogue of non-commutative Lp spaces.

  12. Energy Transfer in Scattering by Rotating Potentials

    Indian Academy of Sciences (India)

    Quantum mechanical scattering theory is studied for time-dependent Schrödinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at infinity we show uniform boundedness in time for the kinetic energy of scattering states, existence and completeness of wave ...

  13. Late time acceleration in a non-commutative model of modified cosmology

    Energy Technology Data Exchange (ETDEWEB)

    Malekolkalami, B., E-mail: b.malakolkalami@uok.ac.ir [Department of Physics, University of Kurdistan, Pasdaran St., Sanandaj (Iran, Islamic Republic of); Atazadeh, K., E-mail: atazadeh@azaruniv.ac.ir [Department of Physics, Azarbaijan Shahid Madani University, 53714-161, Tabriz (Iran, Islamic Republic of); Vakili, B., E-mail: b-vakili@iauc.ac.ir [Department of Physics, Central Tehran Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of)

    2014-12-12

    We investigate the effects of non-commutativity between the position–position, position–momentum and momentum–momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such non-commutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of an α-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables take the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution.

  14. Zeta functions for the spectrum of the non-commutative harmonic oscillators

    CERN Document Server

    Ichinose, T

    2004-01-01

    This paper investigates the spectral zeta function of the non-commutative harmonic oscillator studied in \\cite{PW1, 2}. It is shown, as one of the basic analytic properties, that the spectral zeta function is extended to a meromorphic function in the whole complex plane with a simple pole at $s=1$, and further that it has a zero at all non-positive even integers, i.e. at $s=0$ and at those negative even integers where the Riemann zeta function has the so-called trivial zeros. As a by-product of the study, both the upper and the lower bounds are also given for the first eigenvalue of the non-commutative harmonic oscillator.

  15. (Non-)commutative closed string on T-dual toroidal backgrounds

    CERN Document Server

    Andriot, David; Lust, Dieter; Patalong, Peter

    2013-01-01

    In this paper we investigate the connection between (non-)geometry and (non-)commutativity of the closed string. To this end, we solve the classical string on three T-dual toroidal backgrounds: a torus with H-flux, a twisted torus and a non-geometric background with Q-flux. In all three situations we work under the assumption of a dilute flux and consider quantities to linear order in the flux density. Furthermore, we perform the first steps of a canonical quantization for the twisted torus, to derive commutators of the string expansion modes. We use them as well as T-duality to determine, in the non-geometric background, a commutator of two string coordinates, which turns out to be non-vanishing. We relate this non-commutativity to the closed string boundary conditions, and the non-geometric Q-flux.

  16. Late time acceleration in a non-commutative model of modified cosmology

    International Nuclear Information System (INIS)

    Malekolkalami, B.; Atazadeh, K.; Vakili, B.

    2014-01-01

    We investigate the effects of non-commutativity between the position–position, position–momentum and momentum–momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such non-commutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of an α-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables take the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution

  17. Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory

    CERN Document Server

    Molina, Mercedes

    2016-01-01

    Presenting the collaborations of over thirty international experts in the latest developments in pure and applied mathematics, this volume serves as an anthology of research with a common basis in algebra, functional analysis and their applications. Special attention is devoted to non-commutative algebras, non-associative algebras, operator theory and ring and module theory. These themes are relevant in research and development in coding theory, cryptography and quantum mechanics. The topics in this volume were presented at the Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory, held May 23—25, 2014 at Cheikh Anta Diop University in Dakar, Senegal in honor of Professor Amin Kaidi. The workshop was hosted by the university's Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications, in cooperation with the University of Almería and the University of Málaga. Dr. Kaidi's work focuses on non-associative rings and algebras, operator theory and functional analysis, and he...

  18. Constraints on effective Lagrangian of D-branes from non-commutative gauge theory

    International Nuclear Information System (INIS)

    Okawa, Yuji; Terashima, Seiji

    2000-01-01

    It was argued that there are two different descriptions of the effective Lagrangian of gauge fields on D-branes by non-commutative gauge theory and by ordinary gauge theory in the presence of a constant B field background. In the case of bosonic string theory, however, it was found in the previous works that the two descriptions are incompatible under the field redefinition which relates the non-commutative gauge field to the ordinary one found by Seiberg and Witten. In this paper we resolve this puzzle to observe the necessity of gauge-invariant but B-dependent correction terms involving metric in the field redefinition which have not been considered before. With the problem resolved, we establish a systematic method under the α' expansion to derive the constraints on the effective Lagrangian imposed by the compatibility of the two descriptions where the form of the field redefinition is not assumed

  19. Non-commutative residue of projections in Boutet de Monvel's calculus

    DEFF Research Database (Denmark)

    Gaarde, Anders

    2007-01-01

    Using results by Melo, Nest, Schick, and Schrohe on the K-theory of Boutet de Monvel's calculus of boundary value problems, we show that the non-commutative residue introduced by Fedosov, Golse, Leichtnam, and Schrohe vanishes on projections in the calculus. This partially answers a question raised...... in a recent collaboration with Grubb, namely whether the residue is zero on sectorial projections for boundary value problems: This is confirmed to be true when the sectorial projections is in the calculus....

  20. An anthology of non-local QFT and QFT on non-commutative spacetime

    Science.gov (United States)

    Schroer, Bert

    2005-09-01

    Ever since the appearance of renormalization theory, there have been several differently motivated attempts at non-localized (in the sense of not generated by pointlike fields) relativistic particle theories, the most recent one being at QFT on non-commutative Minkowski spacetime. The often conceptually uncritical and historically forgetful contemporary approach to these problems calls for a critical review in the light of previous results on this subject.

  1. An anthology of non-local QFT and QFT on non-commutative spacetime

    International Nuclear Information System (INIS)

    Schroer, Bert

    2005-01-01

    Ever since the appearance of renormalization theory, there have been several differently motivated attempts at non-localized (in the sense of not generated by pointlike fields) relativistic particle theories, the most recent one being at QFT on non-commutative Minkowski spacetime. The often conceptually uncritical and historically forgetful contemporary approach to these problems calls for a critical review in the light of previous results on this subject

  2. Marginal and non-commutative deformations via non-abelian T-duality

    Energy Technology Data Exchange (ETDEWEB)

    Hoare, Ben [Institut für Theoretische Physik, ETH Zürich,Wolfgang-Pauli-Strasse 27, 8093 Zürich (Switzerland); Thompson, Daniel C. [Theoretische Natuurkunde, Vrije Universiteit Brussel & The International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium)

    2017-02-10

    In this short article we develop recent proposals to relate Yang-Baxter sigma-models and non-abelian T-duality. We demonstrate explicitly that the holographic space-times associated to both (multi-parameter)-β-deformations and non-commutative deformations of N=4 super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity.

  3. Effective exchange potentials for electronically inelastic scattering

    International Nuclear Information System (INIS)

    Schwenke, D.W.; Staszewska, G.; Truhlar, D.G.

    1983-01-01

    We propose new methods for solving the electron scattering close coupling equations employing equivalent local exchange potentials in place of the continuum-multiconfiguration-Hartree--Fock-type exchange kernels. The local exchange potentials are Hermitian. They have the correct symmetry for any symmetries of excited electronic states included in the close coupling expansion, and they have the same limit at very high energy as previously employed exchange potentials. Comparison of numerical calculations employing the new exchange potentials with the results obtained with the standard nonlocal exchange kernels shows that the new exchange potentials are more accurate than the local exchange approximations previously available for electronically inelastic scattering. We anticipate that the new approximations will be most useful for intermediate-energy electronically inelastic electron--molecule scattering

  4. Kohn condition and exotic Newton-Hooke symmetry in the non-commutative Landau problem

    International Nuclear Information System (INIS)

    Zhang, P.-M.; Horvathy, P.A.

    2012-01-01

    N “exotic” [alias non-commutative] particles with masses m a , charges e a and non-commutative parameters θ a , moving in a uniform magnetic field B, separate into center-of-mass and internal motions if Kohn's condition e a /m a =const is supplemented with e a θ a =const. Then the center-of-mass behaves as a single exotic particle carrying the total mass and charge of the system, M and e, and a suitably defined non-commutative parameter Θ. For vanishing electric field off the critical case eΘB≠1, the particles perform the usual cyclotronic motion with modified but equal frequency. The system is symmetric under suitable time-dependent translations which span a (4+2)-parameter centrally-extended subgroup of the “exotic” [i.e., two-parameter centrally-extended] Newton–Hooke group. In the critical case B=B c =(eΘ) −1 the system is frozen into a static “crystal” configuration. Adding a constant electric field, all particles perform, collectively, a cyclotronic motion combined with a drift perpendicular to the electric field when eΘB≠1. For B=B c the cyclotronic motion is eliminated and all particles move, collectively, following the Hall law. Our time-dependent symmetries are reduced to the (2+1)-parameter Heisenberg group of centrally-extended translations.

  5. Non-commutative algebra of functions of 4-dimensional quantum Hall droplet

    International Nuclear Information System (INIS)

    Chen Yixin; Hou Boyu; Hou Boyuan

    2002-01-01

    We develop the description of non-commutative geometry of the 4-dimensional quantum Hall fluid's theory proposed recently by Zhang and Hu. The non-commutative structure of fuzzy S 4 , which is the base of the bundle S 7 obtained by the second Hopf fibration, i.e., S 7 /S 3 =S 4 , appears naturally in this theory. The fuzzy monopole harmonics, which are the essential elements in the non-commutative algebra of functions on S 4 , are explicitly constructed and their obeying the matrix algebra is obtained. This matrix algebra is associative. We also propose a fusion scheme of the fuzzy monopole harmonics of the coupling system from those of the subsystems, and determine the fusion rule in such fusion scheme. By products, we provide some essential ingredients of the theory of SO(5) angular momentum. In particular, the explicit expression of the coupling coefficients, in the theory of SO(5) angular momentum, are given. We also discuss some possible applications of our results to the 4-dimensional quantum Hall system and the matrix brane construction in M-theory

  6. Theory of complex potential scattering

    International Nuclear Information System (INIS)

    Kok, L.P.; Haeringen, H.v.

    1981-01-01

    We study the effect of the addition of a complex potential lambdaV/sub sep/ to an arbitrary Schroedinger operator H = H 0 +V on the singularities of the S matrix, as a function of lambda. Here V/sub sep/ is a separable interaction, and lambda is a complex coupling parameter. The paths of these singularities are determined to a great extent by certain saddle points in the momentum (or energy) plane. We explain certain critical phenomena recently reported in the literature. Associated with these saddles are branch-type singularities in the complex lambda plane, which are dynamical in origin. Some examples are discussed in detail

  7. Semiempirical potentials for positron scattering by atoms

    Energy Technology Data Exchange (ETDEWEB)

    Assafrao, Denise; Walters, H. R. J.; Arretche, Felipe; Dutra, Adriano; Mohallem, J. R. [Departamento de Fisica, Universidade Federal do Espirito Santo, 29075-910, Vitoria, ES (Brazil); Department of Applied Mathematics and Theoretical Physics, Queen' s University, Belfast, BT7 1NN (United Kingdom); Departamento de Fisica, Universidade do Estado de Santa Catarina, 89223-100, Joinville, SC (Brazil); Laboratorio de Atomos e Moleculas Especiais, Departamento de Fisica, ICEx, Universidade Federal de Minas Gerais, PO Box 702, 30123-970, Belo Horizonte, MG (Brazil)

    2011-08-15

    We report calculations of differential and integral cross sections for positron scattering by noble gas and alkaline-earth atoms within the same methodology. The scattering potentials are constructed by scaling adiabatic potentials so that their minima coincide with the covalent radii of the target atoms. Elastic differential and integral cross sections are calculated for Ne, Ar, Be, and Mg, and the results are very close to experimental and best theoretical data. Particularly, elastic differential cross sections for Be and Mg at low energies are reported.

  8. Test of non-commutative QED in the process $e^{+}e^{-} \\to \\gamma \\gamma$ at LEP

    CERN Document Server

    Abbiendi, G.; Akesson, P.F.; Alexander, G.; Allison, John; Amaral, P.; Anagnostou, G.; Anderson, K.J.; Arcelli, S.; Asai, S.; Axen, D.; Azuelos, G.; Bailey, I.; Barberio, E.; Barlow, R.J.; Batley, R.J.; Bechtle, P.; Behnke, T.; Bell, Kenneth Watson; Bell, P.J.; Bella, G.; Bellerive, A.; Benelli, G.; Bethke, S.; Biebel, O.; Bloodworth, I.J.; Boeriu, O.; Bock, P.; Bonacorsi, D.; Boutemeur, M.; Braibant, S.; Brigliadori, L.; Brown, Robert M.; Buesser, K.; Burckhart, H.J.; Campana, S.; Carnegie, R.K.; Caron, B.; Carter, A.A.; Carter, J.R.; Chang, C.Y.; Charlton, David G.; Csilling, A.; Cuffiani, M.; Dado, S.; De Roeck, A.; De Wolf, E.A.; Desch, K.; Dienes, B.; Donkers, M.; Dubbert, J.; Duchovni, E.; Duckeck, G.; Duerdoth, I.P.; Elfgren, E.; Etzion, E.; Fabbri, F.; Feld, L.; Ferrari, P.; Fiedler, F.; Fleck, I.; Ford, M.; Frey, A.; Furtjes, A.; Gagnon, P.; Gary, John William; Gaycken, G.; Geich-Gimbel, C.; Giacomelli, G.; Giacomelli, P.; Giunta, Marina; Goldberg, J.; Gross, E.; Grunhaus, J.; Gruwe, M.; Gunther, P.O.; Gupta, A.; Hajdu, C.; Hamann, M.; Hanson, G.G.; Harder, K.; Harel, A.; Harin-Dirac, M.; Hauschild, M.; Hawkes, C.M.; Hawkings, R.; Hemingway, R.J.; Hensel, C.; Herten, G.; Heuer, R.D.; Hill, J.C.; Hoffman, Kara Dion; Homer, R.J.; Horvath, D.; Igo-Kemenes, P.; Ishii, K.; Jeremie, H.; Jovanovic, P.; Junk, T.R.; Kanaya, N.; Kanzaki, J.; Karapetian, G.; Karlen, D.; Kawagoe, K.; Kawamoto, T.; Keeler, R.K.; Kellogg, R.G.; Kennedy, B.W.; Kim, D.H.; Klein, K.; Klier, A.; Kluth, S.; Kobayashi, T.; Kobel, M.; Komamiya, S.; Kormos, Laura L.; Kramer, T.; Kress, T.; Krieger, P.; von Krogh, J.; Kruger, K.; Kuhl, T.; Kupper, M.; Lafferty, G.D.; Landsman, H.; Lanske, D.; Layter, J.G.; Leins, A.; Lellouch, D.; Lettso, J.; Levinson, L.; Lillich, J.; Lloyd, S.L.; Loebinger, F.K.; Lu, J.; Ludwig, J.; Macpherson, A.; Mader, W.; Marcellini, S.; Martin, A.J.; Masetti, G.; Mashimo, T.; Mattig, Peter; McDonald, W.J.; McKenna, J.; McMahon, T.J.; McPherson, R.A.; Meijers, F.; Menges, W.; Merritt, F.S.; Mes, H.; Michelini, A.; Mihara, S.; Mikenberg, G.; Miller, D.J.; Moed, S.; Mohr, W.; Mori, T.; Mutter, A.; Nagai, K.; Nakamura, I.; Neal, H.A.; Nisius, R.; O'Neale, S.W.; Oh, A.; Okpara, A.; Oreglia, M.J.; Orito, S.; Pahl, C.; Pasztor, G.; Pater, J.R.; Patrick, G.N.; Pilcher, J.E.; Pinfold, J.; Plane, David E.; Poli, B.; Polok, J.; Pooth, O.; Przybycien, M.; Quadt, A.; Rabbertz, K.; Rembser, C.; Renkel, P.; Rick, H.; Roney, J.M.; Rosati, S.; Rozen, Y.; Runge, K.; Sachs, K.; Saeki, T.; Sarkisyan, E.K.G.; Schaile, A.D.; Schaile, O.; Scharff-Hansen, P.; Schieck, J.; Schoerner-Sadenius, Thomas; Schroder, Matthias; Schumacher, M.; Schwick, C.; Scott, W.G.; Seuster, R.; Shears, T.G.; Shen, B.C.; Sherwood, P.; Siroli, G.; Skuja, A.; Smith, A.M.; Sobie, R.; Soldner-Rembold, S.; Spano, F.; Stahl, A.; Stephens, K.; Strom, David M.; Strohmer, R.; Tarem, S.; Tasevsky, M.; Taylor, R.J.; Teuscher, R.; Thomson, M.A.; Torrence, E.; Toya, D.; Tran, P.; Tricoli, A.; Trigger, I.; Trocsanyi, Z.; Tsur, E.; Turner-Watson, M.F.; Ueda, I.; Ujvari, B.; Vollmer, C.F.; Vannerem, P.; Vertesi, R.; Verzocchi, M.; Voss, H.; Vossebeld, J.; Waller, D.; Ward, C.P.; Ward, D.R.; Watkins, P.M.; Watson, A.T.; Watson, N.K.; Wells, P.S.; Wengler, T.; Wermes, N.; Wetterling, D.; Wilson, G.W.; Wilson, J.A.; Wolf, G.; Wyatt, T.R.; Yamashita, S.; Zer-Zion, D.; Zivkovic, Lidija

    2003-01-01

    Non-communicative QED would lead to deviations from the Standard Model depending on a new energy scale $\\Delta_{NC}$ and a unique direction in space defined by two angles $\\eta$ and $\\xi$. Here in this analysis $\\eta$ is defined as the angle between the unique direction and the rotation axis of the earth. The predictions of such a theory for the process $e^{+} e^{-} \\to \\gamma \\gamma$ are evalued for the specific orientation of the OPAL detector and compared to the measurements. Distributions of the polar and azimuthal scattering angles are used to extract limits on the energy scale $\\Delta_{NC}$ depending on the model parameter $\\eta$. At the 95% confidence level $\\Delta_{NC}$ is found to be larger than 141 GeV for all $\\eta$ and $\\xi$. It is shown that the time dependence of the total cross-section could be used to determine the model parameter $\\xi$ if there were a detectable signal. These are the first limits obtained on non-commutative QED from an $e^{+} e^{-}$ collider experiment.

  9. Some consequences of a non-commutative space-time structure

    International Nuclear Information System (INIS)

    Vilela Mendes, R.

    2005-01-01

    The existence of a fundamental length (or fundamental time) has been conjectured in many contexts. Here we discuss some consequences of a fundamental constant of this type, which emerges as a consequence of deformation-stability considerations leading to a non-commutative space-time structure. This mathematically well defined structure is sufficiently constrained to allow for unambiguous experimental predictions. In particular we discuss the phase-space volume modifications and their relevance for the calculation of the Greisen-Zatsepin-Kuz'min sphere. The (small) corrections to the spectrum of the Coulomb problem are also computed. (orig.)

  10. Non-commutative differential calculus and the axial anomaly in Abelian lattice gauge theories

    International Nuclear Information System (INIS)

    Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke

    2000-01-01

    The axial anomaly in lattice gauge theories has a topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological arguments. The crucial tool in our approach is the non-commutative differential calculus (NCDC) which makes the Leibniz rule of exterior derivatives valid on the lattice. The topological nature of the 'Chern character' on the lattice becomes manifest in the context of NCDC. Our result provides an algebraic proof of Luescher's theorem for a four-dimensional lattice and its generalization to arbitrary dimensions

  11. Asymptotic behaviour of a non-commutative rational series with a nonnegative linear representation

    Directory of Open Access Journals (Sweden)

    Philippe Dumas

    2007-01-01

    Full Text Available We analyse the asymptotic behaviour in the mean of a non-commutative rational series, which originates from differential cryptanalysis, using tools from probability theory, and from analytic number theory. We derive a Fourier representation of a first-order summation function obtained by interpreting this rational series as a non-classical rational sequence via the octal numeration system. The method is applicable to a wide class of sequences rational with respect to a numeration system essentially under the condition that they admit a linear representation with nonnegative coefficients.

  12. The non-commutative topology of two-dimensional dirty superconductors

    Science.gov (United States)

    De Nittis, Giuseppe; Schulz-Baldes, Hermann

    2018-01-01

    Non-commutative analysis tools have successfully been applied to the integer quantum Hall effect, in particular for a proof of the stability of the Hall conductance in an Anderson localization regime and of the bulk-boundary correspondence. In this work, these techniques are implemented to study two-dimensional dirty superconductors described by Bogoliubov-de Gennes Hamiltonians. After a thorough presentation of the basic framework and the topological invariants, Kubo formulas for the thermal, thermoelectric and spin Hall conductance are analyzed together with the corresponding edge currents.

  13. Model potential for electron scattering from rubidium

    Energy Technology Data Exchange (ETDEWEB)

    Gien, T.E. (Memorial Univ. of Newfoundland, St. John' s, NF (Canada). Dept. of Physics)

    1992-11-28

    An analytic model potential for the e[sup -]-Rb[sup +] system is generated from experimental data, using an iteration method. The potential obtained can reproduce rather accurately the energy levels of rubidium. We employed it in the calculation of elastic differential cross sections for electron (and positron) scatterings from rubidium in the conventional Glauber approximation. The differential cross sections calculated in the model potential approach are compared to those in the frozen-core approach, employing either the Clementi-Roetti or the Szasz-McGinn wavefunctions. The core correlation and polarization effects are found to significantly affect the cross section results. (author).

  14. Model potential for electron scattering from rubidium

    International Nuclear Information System (INIS)

    Gien, T.E.

    1992-01-01

    An analytic model potential for the e - -Rb + system is generated from experimental data, using an iteration method. The potential obtained can reproduce rather accurately the energy levels of rubidium. We employed it in the calculation of elastic differential cross sections for electron (and positron) scatterings from rubidium in the conventional Glauber approximation. The differential cross sections calculated in the model potential approach are compared to those in the frozen-core approach, employing either the Clementi-Roetti or the Szasz-McGinn wavefunctions. The core correlation and polarization effects are found to significantly affect the cross section results. (author)

  15. Existence of stable wormholes on a non-commutative-geometric background in modified gravity

    Energy Technology Data Exchange (ETDEWEB)

    Zubair, M.; Mustafa, G. [COMSATS, Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); Waheed, Saira [Prince Mohammad Bin Fahd University, Al Khobar (Saudi Arabia); Abbas, G. [The Islamia University of Bahawalpur, Department of Mathematics, Bahawalpur (Pakistan)

    2017-10-15

    In this paper, we discuss spherically symmetric wormhole solutions in f(R, T) modified theory of gravity by introducing well-known non-commutative geometry in terms of Gaussian and Lorentzian distributions of string theory. For analytic discussion, we consider an interesting model of f(R, T) gravity defined by f(R, T) = f{sub 1}(R) + λT. By taking two different choices for the function f{sub 1}(R), that is, f{sub 1}(R) = R and f{sub 1}(R) = R + αR{sup 2} + γR{sup n}, we discuss the possible existence of wormhole solutions. In the presence of non-commutative Gaussian and Lorentzian distributions, we get exact and numerical solutions for both these models. By taking appropriate values of the free parameters, we discuss different properties of these wormhole models analytically and graphically. Further, using an equilibrium condition, it is found that these solutions are stable. Also, we discuss the phenomenon of gravitational lensing for the exact wormhole model and it is found that the deflection angle diverges at the wormhole throat. (orig.)

  16. Construction of potentials using mixed scattering data

    International Nuclear Information System (INIS)

    Lassaut, M; Larsen, S Y; Sofianos, S A; Wallet, J C

    2008-01-01

    The long-standing problem of constructing a potential from mixed scattering data is discussed. We first consider the fixed l inverse scattering problem. We show that the zeros of the regular solution of the Schrödinger equation, r n (E) which are monotonic functions of the energy, determine a unique potential when the domain of energy is such that the r n (E)'s range from zero to infinity. The latter method is applied to the domain {E ≥ E 0 , l = l 0 } ∪ {E = E 0 , l ≥ l 0 } for which the zeros of the regular solution are monotonic in both parts of the domain and still range from zero to infinity. Our analysis suggests that a unique potential can be obtained from the mixed scattering data {δ(l 0 , k), k ≥ k 0 } ∪ {δ(l, k 0 ), l ≥ l 0 } provided that certain integrability conditions required for the fixed l problem, are fulfilled. The uniqueness is demonstrated using the JWKB approximation

  17. Multiple scattering theory for space filling potentials

    International Nuclear Information System (INIS)

    Butler, W.H.; Brown, R.G.; Nesbet, R.K.

    1990-01-01

    Multiple scattering theory (MST) provides an efficient technique for solving the wave equation for the special case of muffin-tin potentials. Here MST is extended to treat space filling non-muffin tin potentials and its validity, accuracy and efficiency are tested by application of the two dimensional empty lattice test. For this test it is found that the traditional formulation of MST does not coverage as the number of partial waves is increased. A simple modification of MST, however, allows this problem to be solved exactly and efficiently. 15 refs., 3 tabs

  18. Non-commutative cryptography and complexity of group-theoretic problems

    CERN Document Server

    Myasnikov, Alexei; Ushakov, Alexander

    2011-01-01

    This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public-key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research avenues within group theory. In particular, a lot of emphasis in the book is put on studying search problems, as compared to decision problems traditionally studied in combinatorial group theory. Then, complexity theory, notably generic-case complexity of algorithms, is employed for cryptanalysis of various cryptographic protocols based on infinite groups, and the ideas and machinery from the theory of generic-case complexity are used to study asymptotically dominant prop...

  19. On the development of non-commutative translation-invariant quantum gauge field models

    International Nuclear Information System (INIS)

    Sedmik, R.I.P.

    2009-01-01

    Aiming to understand the most fundamental principles of nature one has to approach the highest possible energy scales corresponding to the smallest possible distances - the Planck scale. Historically, three different theoretical fields have been developed to treat the problems appearing in this endeavor: string theory, quantum gravity, and non-commutative (NC) quantum field theory (QFT). The latter was originally motivated by the conjecture that the introduction of uncertainty relations between space-time coordinates introduces a natural energy cutoff, which should render the resulting computations well defined and finite. Despite failing to fulfill this expectation, NC physics is a challenging field of research, which has proved to be a fruitful source for new ideas and methods. Mathematically, non-commutativity is implemented by the so called Weyl quantization, giving rise to a modified product - the Groenewold-Moyal product. It realizes an operator ordering, and allows to work within the well established framework of QFT on non-commutative spaces. The main obstacle of NCQFT is the appearance of singularities being shifted from high to low energies. This effect, being referred to as 'uV/IR mixing', is a direct consequence of the deformation of the product, and inhibits or complicates the direct application of well approved renormalization schemes. In order to remedy this problem, several approaches have been worked out during the past decade which, unfortunately, all have shortcomings such as the breaking of translation invariance or an inappropriate alternation of degrees of freedom. Thence, the resulting theories are either being rendered 'unphysical', or considered a priori to be toy models. Nonetheless, these efforts have helped to analyze the mechanisms leading to uV/IR mixing and finally led to the insight that renormalizability can only be achieved by respecting the inherent connection of long and short distances (scales) of NCQFT in the construction of

  20. A computational non-commutative geometry program for disordered topological insulators

    CERN Document Server

    Prodan, Emil

    2017-01-01

    This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder. In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons’ dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the co...

  1. Enveloping algebra-valued gauge transformations for non-abelian gauge groups on non-commutative spaces

    Science.gov (United States)

    Jurco, B.; Schraml, S.; Schupp, P.; Wess, J.

    2000-11-01

    An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces.

  2. Enveloping algebra-valued gauge transformations for non-abelian gauge groups on non-commutative spaces

    International Nuclear Information System (INIS)

    Jurco, B.; Schraml, S.; Wess, J.; Schupp, P.

    2000-01-01

    An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces. (orig.)

  3. Enveloping algebra-valued gauge transformations for non-abelian gauge groups on non-commutative spaces

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, B. [Max-Planck-Institut fuer Mathematik, Bonn (Germany); Schraml, S.; Wess, J. [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany); Sektion Physik, Universitaet Muenchen, Theresienstrasse 37, 80333 Muenchen (Germany); Schupp, P. [Sektion Physik, Universitaet Muenchen, Theresienstrasse 37, 80333 Muenchen (Germany)

    2000-11-01

    An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces. (orig.)

  4. Renormalization of NN scattering: Contact potential

    International Nuclear Information System (INIS)

    Yang Jifeng; Huang Jianhua

    2005-01-01

    The renormalization of the T matrix for NN scattering with a contact potential is re-examined in a nonperturbative regime through rigorous nonperturbative solutions. Based on the underlying theory, it is shown that the ultraviolet divergences in the nonperturbative solutions of the T matrix should be subtracted through 'endogenous' counterterms, which in turn leads to a nontrivial prescription dependence. Moreover, employing the effective range expansion, the importance of imposing physical boundary conditions to remove the nontrivial prescription dependence, especially before making any physical claims, is discussed and highlighted. As by-products, some relations between the effective range expansion parameters are derived. We also discuss the power counting of the couplings for the nucleon-nucleon interactions and other subtle points related to the EFT framework beyond perturbative treatment

  5. Open branes in space-time non-commutative little string theory

    International Nuclear Information System (INIS)

    Harmark, T.

    2001-01-01

    We conjecture the existence of two new non-gravitational six-dimensional string theories, defined as the decoupling limit of NS5-branes in the background of near-critical electrical two- and three-form RR fields. These theories are space-time non-commutative Little String Theories with open branes. The theory with (2,0) supersymmetry has an open membrane in the spectrum and reduces to OM theory at low energies. The theory with (1,1) supersymmetry has an open string in the spectrum and reduces to (5+1)-dimensional NCOS theory for weak NCOS coupling and low energies. The theories are shown to be T-dual with the open membrane being T-dual to the open string. The theories therefore provide a connection between (5+1)-dimensional NCOS theory and OM theory. We study the supergravity duals of these theories and we consider a chain of dualities that shows how the T-duality between the two theories is connected with the S-duality between (4+1)-dimensional NCOS theory and OM theory

  6. Reconstruction of the spontaneously broken gauge theory in non-commutative geometry

    International Nuclear Information System (INIS)

    Okumura, Y.; Morita, K.

    1996-01-01

    The scheme previously proposed by the present authors is modified to incorporate the strong interaction by affording the direct product internal symmetry. The authors do not need to prepare the extra discrete space for the colour gauge group responsible for the strong interaction to reconstruct the standard model and the left-right symmetric gauge model (LRSM). The approach based on non-commutative geometry leads us to present many attractive points such as the unified picture of the gauge and Higgs field as the generalized connection on the discrete space M 4 x Z N . This approach leads to unified picture of gauge and Higgs fields as the generalized connection. The standard model needs N=2 discrete space for reconstruction in this formalism. LRSM is still alive as a model with the intermediate symmetry of the spontaneously broken SO(10) grand unified theory (GUT). N=3 discrete space is needed for the reconstruction of LRSM to include two Higgs φ and ξ bosons usual transformed as (2, 2 * , 0) and (1, 3, -2) under SU(2) L x SU(2) R x U(1) Y , respectively. ξ is responsible to make v R Majorana fermion and so well explains the seesaw mechanism. Up and down quarks have different masses through the vacuum expectation value of φ

  7. Scattering cross section for various potential systems

    Directory of Open Access Journals (Sweden)

    Myagmarjav Odsuren

    2017-08-01

    Full Text Available We discuss the problems of scattering in this framework, and show that the applied method is very useful in the investigation of the effect of the resonance in the observed scattering cross sections. In this study, not only the scattering cross sections but also the decomposition of the scattering cross sections was computed for the α–α system. To obtain the decomposition of scattering cross sections into resonance and residual continuum terms, the complex scaled orthogonality condition model and the extended completeness relation are used. Applying the present method to the α–α and α–n systems, we obtained good reproduction of the observed phase shifts and cross sections. The decomposition into resonance and continuum terms makes clear that resonance contributions are dominant but continuum terms and their interference are not negligible. To understand the behavior of observed phase shifts and the shape of the cross sections, both resonance and continuum terms are calculated.

  8. Scattering cross section for various potential systems

    Energy Technology Data Exchange (ETDEWEB)

    Odsuren, Myagmarjav; Khuukhenkhuu, Gonchigdorj; Davaa, Suren [Nuclear Research Center, School of Engineering and Applied Sciences, National University of Mongolia, Ulaanbaatar (Mongolia); Kato, Kiyoshi [Nuclear Reaction Data Centre, Faculty of Science, Hokkaido University, Sapporo (Japan)

    2017-08-15

    We discuss the problems of scattering in this framework, and show that the applied method is very useful in the investigation of the effect of the resonance in the observed scattering cross sections. In this study, not only the scattering cross sections but also the decomposition of the scattering cross sections was computed for the α–α system. To obtain the decomposition of scattering cross sections into resonance and residual continuum terms, the complex scaled orthogonality condition model and the extended completeness relation are used. Applying the present method to the α–α and α–n systems, we obtained good reproduction of the observed phase shifts and cross sections. The decomposition into resonance and continuum terms makes clear that resonance contributions are dominant but continuum terms and their interference are not negligible. To understand the behavior of observed phase shifts and the shape of the cross sections, both resonance and continuum terms are calculated.

  9. Finite energy sum rules in potential scattering

    International Nuclear Information System (INIS)

    Graham, N.; Jaffe, R.L.; Quandt, M.; Weige, H.

    2001-01-01

    We study scattering theory identities previously obtained as consistency conditions in the context of one-loop quantum field theory calculations. We prove the identities using Jost function techniques and study applications

  10. The non-commutative and discrete spatial structure of a 3D Wigner quantum oscillator

    International Nuclear Information System (INIS)

    King, R C; Palev, T D; Stoilova, N I; Jeugt, J Van der

    2003-01-01

    The properties of a non-canonical 3D Wigner quantum oscillator, whose position and momentum operators generate the Lie superalgebra sl(1|3), are further investigated. Within each state space W(p), p = 1, 2, ..., the energy E q , q = 0, 1, 2, 3, takes no more than four different values. If the oscillator is in a stationary state ψ q element of W(p) then measurements of the non-commuting Cartesian coordinates of the particle are such that their allowed values are consistent with it being found at a finite number of sites, called 'nests'. These lie on a sphere centred on the origin of fixed, finite radius ρ q . The nests themselves are at the vertices of a rectangular parallelepiped. In the typical cases (p > 2) the number of nests is 8 for q = 0 and 3, and varies from 8 to 24, depending on the state, for q = 1 and 2. The number of nests is less in the atypical cases (p = 1, 2), but it is never less than 2. In certain states in W(2) (respectively in W(1)) the oscillator is 'polarized' so that all the nests lie on a plane (respectively on a line). The particle cannot be localized in any one of the available nests alone since the coordinates do not commute. The probabilities of measuring particular values of the coordinates are discussed. The mean trajectories and the standard deviations of the coordinates and momenta are computed, and conclusions are drawn about uncertainty relations

  11. Scattering of charged particles by a multicenter potential

    International Nuclear Information System (INIS)

    Gerasimov, O.I.; Stienko, A.G.

    1994-01-01

    Exact expressions are obtained for the amplitude and elastic cross section in the case of scattering of charged particles by a multicenter pseudopotential that includes the Coulomb potential and an arbitrary number of short-range potentials (modeled by zero-range potentials). Asymptotic limits are calculated and explicit expressions are found for the amplitudes of scattering by few-nucleon complexes modeled by superpositions of the Coulomb potential and purely point potentials

  12. The Nonrelativistic Scattering States of the Deng-Fan Potential

    Directory of Open Access Journals (Sweden)

    Bentol Hoda Yazarloo

    2013-01-01

    Full Text Available The approximately analytical scattering state solution of the Schrodinger equation is obtained for the Deng-Fan potential by using an approximation scheme to the centrifugal term. Energy eigenvalues, normalized wave functions, and scattering phase shifts are calculated. We consider and verify two special cases: the l=0 and the s-wave Hulthén potential.

  13. On low energy scattering theory with Coulomb potentials

    International Nuclear Information System (INIS)

    Gibson, A.G.

    1985-09-01

    The scattering length is a very useful characteristic of the scattering phenomena. But in the presence of a combined potential (e.g. in nuclear physics, when Coulomb, the polarization and the strong potentials are to be added), the analytical definition of the scattering length in not unambigous and strictly defined. This problem is discussed in detail, the various alternatives are examined and compared. A practical suggestion is given for the proper choice of the definition and for the calculation of scattering length. Numerical solutions of the Schroedinger equation are compared with the results of different definitions. Some questions of application to nuclear physics are discussed. (D.Gy.)

  14. Simulation of isotropic scattering of charged particles by composed potentials

    CERN Document Server

    Gerasimov, O Y

    2003-01-01

    The analytical model of scattering of charged particles by a multicentered adiabatic potential which consists of the long-range Coulomb and short-range potentials is used for the parametrization of experiments of elastic low-energy proton-deuteron scattering. For the energies 2.26-13 MeV, the analytical expressions for the phase scattering function in terms of identical parameters which depend on the lengths and effective radii of proton-proton and proton-neutron scattering and on the effective size of deuteron are obtained. The results are in good qualitative accordance with experiments.

  15. Energy transfer in scattering by rotating potentials

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Quantum mechanical scattering theory is studied for time-dependent. Schrödinger ... the energy transferred to a particle by collision with a rotating blade. Keywords. ..... terms of the unitary group for some time-independent generator. This will ...

  16. Singularities of elastic scattering amplitude by long-range potentials

    International Nuclear Information System (INIS)

    Kvitsinsky, A.A.; Komarov, I.V.; Merkuriev, S.P.

    1982-01-01

    The angular peculiarities and the zero energy singularities of the elastic scattering amplitude by a long-range potential are described. The singularities of the elastic (2 → 2) scattering amplitude for a system of three Coulomb particles are considered [ru

  17. Resonances in the potential scattering and decay of metastable states

    International Nuclear Information System (INIS)

    Batsch, J.

    1975-04-01

    The analytic properties of the S-matrix in the complex energy plane are reviewed for potential scattering with particular attention to resonance scattering and decay of metastable states. For a one dimensional model potential with a potential barrier and a repulsive core exact formulas are derived for the energy and width of a resonance in terms of the scattering amplitudes of the barrier and the repulsive core alone. For narrow resonances simple and intuitive results are obtained, which are applied to semiclassical cases where the WKB approximation is valid. (orig.) [de

  18. Path integral approach to electron scattering in classical electromagnetic potential

    International Nuclear Information System (INIS)

    Xu Chuang; Feng Feng; Li Ying-Jun

    2016-01-01

    As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential. (paper)

  19. Dynamic polarization potentials in heavy ion scattering

    International Nuclear Information System (INIS)

    Wolf, R.

    1984-01-01

    In this thesis the polarization potential is calculated which is caused by several collective, strongly coupled states. In the framework of the considered model space the calculation of the polarization potential was exact, i.e. no approximations were made. For this purpose the Green function of the system had to be calculated. This led to a nonlocal polarization potential. For the better interpretation possibility and for the easier use in coupled-channel or optical-model calculations from the nonlocal potentials also equivalent potentials were constructed. The properties of the local and nonlocal potentials as shape, angular momentum, and energy dependence were discussed. Furthermore parametrizations were given, how polarization effects can be regarded in a simple way in optical-model or coupled-channel calculations. The calculations were performed for the systems 12 C+ 12 C and 16 O+ 16 O. To meet as realistic results as possible, parameters for the unperturbed potential were looked for which describe as many data as possible, like angular distributions, excitation functions, and alignment of the main channels. As unperturbed potential both folding potentials and phenomenological potentials were applied in order to study the differences in the polarization potential in the application of deep and flat potentials. (orig./HSI) [de

  20. T-duality with H-flux. Non-commutativity, T-folds and G x G structure

    International Nuclear Information System (INIS)

    Grange, P.

    2006-09-01

    Various approaches to T-duality with NSNS three-form flux are reconciled. Non-commutative torus fibrations are shown to be the open-string version of T-folds. The non-geometric T-dual of a three-torus with uniform flux is embedded into a generalized complex six-torus, and the non-geometry is probed by D0-branes regarded as generalized complex submanifolds. The non-commutativity scale, which is present in these compactifications, is given by a holomorphic Poisson bivector that also encodes the variation of the dimension of the world-volume of D-branes under monodromy. This bivector is shown to exist in SU(3) x SU(3) structure compactifications, which have been proposed as mirrors to NSNS-flux backgrounds. The two SU(3)-invariant spinors are generically not parallel, thereby giving rise to a non-trivial Poisson bivector. Furthermore we show that for non-geometric T-duals, the Poisson bivector may not be decomposable into the tensor product of vectors. (orig.)

  1. Bounds for phase-shifts and deductions in potential scattering

    International Nuclear Information System (INIS)

    Sidharth, B.G.

    1979-01-01

    Starting from the radial Schroedinger equation and using the Cauchy-Schwarz inequality, expressions have been derived for bounds for phase-shifts in potential scattering and the deductions are verified in special cases such as the spherically symmetric square-well potential, where exact solutions are already known. (K.B.)

  2. On the interaction potential in low energy ion scattering

    International Nuclear Information System (INIS)

    Chini, T.K.; Ghose, D.

    1989-01-01

    The shadow cones for 998 eV Li + → Ag and 2 keV Na + → Cu are calculated by classical scattering theory using Thomas-Fermi-Moliere potential, universal potential of Ziegler et al. and the Born-Mayer potential. It is found that the Born-Mayer potential with the parameters calculated by Andersen and Sigmund also predicts well the shape of the shadow cones. (orig.)

  3. Scattering theory for one-dimensional step potentials

    International Nuclear Information System (INIS)

    Ruijsenaars, S.N.M.; Bongaarts, P.J.M.

    1977-01-01

    The scattering theory is treated for the one-dimensional Dirac equation with potentials that are bounded, measurable, real-valued functions on the real line, having constant values, not necessarily the same, on the left and on the right side of a compact interval. Such potentials appear in the Klein paradox. It is shown that appropriately modified wave operators exist and that the corresponding S-operator is unitary. The connection between time-dependent scattering theory and time-independent scattering theory in terms of incoming and outgoing plane wave solutions is established and some further properties are proved. All results and their proofs have a straightforward translation to the one-dimensional Schroedinger equation with the same class of step potentials

  4. Optical-potential model for electron-atom scattering

    International Nuclear Information System (INIS)

    Callaway, J.; Oza, D.H.

    1985-01-01

    It is proposed that the addition of a matrix optical potential to a close-coupling calculation should lead to improved results in studies of electron-atom scattering. This procedure is described with use of a pseudostate expansion to evaluate the optical potential. The integro-differential equations are solved by a linear-algebraic method. As a test case, applications are made to electron-hydrogen scattering, and the results are compared with those obtained by other calculational procedures, and with experiment

  5. Nucleon-Nucleon Potentials and Computation of Scattering Phase Shifts

    Directory of Open Access Journals (Sweden)

    Jhasaketan Bhoi

    2015-12-01

    Full Text Available By judicious exploitation of supersymmetry formalism of quantum mechanics higher partial wave nucleon-nucleon potentials are generated from its ground state interactions. The nuclear Hulthen potential and the corresponding ground state wave function with the parameters of Arnold and MacKellar are used as the starting point of our calculation. We compute the scattering phase shifts for our constructed potentials through Phase Function Method to examine the merit of our approach to the problem.

  6. Closure approximation to the absorptive potential in heavy ion scattering

    International Nuclear Information System (INIS)

    Vinh Mau, N.

    1986-02-01

    We propose a simple model which is based on the Feshbach's theory of optical potential. The use of closure relation in both nuclei implies that we implicitly include all possible channels, in particular inelastic scattering and one nucleon transfer processes. The local absorptive potential is calculated at large distances and its energy dependence is studied. The results are compared to other theoretical works and to phenomenological potentials

  7. Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) non-commutative motives

    Science.gov (United States)

    Bernardara, M.; Tabuada, G.

    2016-06-01

    Conjectures of Beilinson-Bloch type predict that the low-degree rational Chow groups of intersections of quadrics are one-dimensional. This conjecture was proved by Otwinowska in [20]. By making use of homological projective duality and the recent theory of (Jacobians of) non-commutative motives, we give an alternative proof of this conjecture in the case of a complete intersection of either two quadrics or three odd-dimensional quadrics. Moreover, we prove that in these cases the unique non-trivial algebraic Jacobian is the middle one. As an application, we make use of Vial's work [26], [27] to describe the rational Chow motives of these complete intersections and show that smooth fibrations into such complete intersections over bases S of small dimension satisfy Murre's conjecture (when \\dim (S)≤ 1), Grothendieck's standard conjecture of Lefschetz type (when \\dim (S)≤ 2), and Hodge's conjecture (when \\dim(S)≤ 3).

  8. Special values of the spectral zeta function of the non-commutative harmonic oscillator and confluent Heun equations

    CERN Document Server

    Ichinose, T

    2004-01-01

    We study the special values at $s=2$ and $3$ of the spectral zeta function $\\zeta_Q(s)$ of the non-commutative harmonic oscillator $Q(x,D_x)$ introduced in \\cite{PW1, 2}. It is shown that the series defining $\\zeta_Q(s)$ converges absolutely for Re $s>1$ and further the respective values $\\zeta_Q(2)$ and $\\zeta_Q(3)$ are represented essentially by contour integrals of the solutions, respectively, of a singly confluent Heun's ordinary differential equation and of exactly the same but an inhomogeneous equation. As a by-product of these results, we obtain integral representations of the solutions of these equations by rational functions. \\par\

  9. Chiral-Yang-Mills theory, non commutative differential geometry, and the need for a Lie super-algebra

    International Nuclear Information System (INIS)

    Thierry-Mieg, Jean

    2006-01-01

    In Yang-Mills theory, the charges of the left and right massless Fermions are independent of each other. We propose a new paradigm where we remove this freedom and densify the algebraic structure of Yang-Mills theory by integrating the scalar Higgs field into a new gauge-chiral 1-form which connects Fermions of opposite chiralities. Using the Bianchi identity, we prove that the corresponding covariant differential is associative if and only if we gauge a Lie-Kac super-algebra. In this model, spontaneous symmetry breakdown naturally occurs along an odd generator of the super-algebra and induces a representation of the Connes-Lott non commutative differential geometry of the 2-point finite space

  10. Algebraic and coordinate space potentials from heavy ion scattering

    International Nuclear Information System (INIS)

    Amos, K.; Berge, L.; Allen, L.J.; Fiedeldey, H.

    1993-01-01

    An inversion scheme is presented to derive the potentials of algebraic scattering theory from the corresponding S-functions. Representative heavy ion scattering data of 12 C, 14 N and 16 O ions on 208 Pb, accurately fitted by McIntyre strong absorption type S-functions, are employed to obtain exact algebraic potentials and to generalize the analytical shapes proposed previously by Alhassid et al. The coordinate space potentials corresponding to a number of S-functions are also obtained via semiclassical inversion. The major advantage of the algebraic potentials is that, at a theoretical level they are more directly related to the S-functions than are coordinate space potentials. 16 refs., 1 tab., 9 figs

  11. Scattering at zero energy for attractive homogeneous potentials

    DEFF Research Database (Denmark)

    Derezinski, Jan; Skibsted, Erik

    2009-01-01

    We compute up to a compact term the zero-energy scattering matrix for a class of potentials asymptotically behaving as −γ|x|−μ with 0 < μ < 2 and γ > 0. It turns out to be the propagator for the wave equation on the sphere at time ....

  12. Reconstruction of atomic effective potentials from isotropic scattering factors

    International Nuclear Information System (INIS)

    Romera, E.; Angulo, J.C.; Torres, J.J.

    2002-01-01

    We present a method for the approximate determination of one-electron effective potentials of many-electron systems from a finite number of values of the isotropic scattering factor. The method is based on the minimum cross-entropy technique. An application to some neutral ground-state atomic systems has been done within a Hartree-Fock framework

  13. Information on pion-nucleus optical potentials from elastic scattering

    International Nuclear Information System (INIS)

    Friedman, E.

    1983-02-01

    Data on the elastic scattering of pions by nuclei between 20 and 230 MeV is analyzed in an almost model-independent fashion. The real part of the potential, which is described by a bias-free Fourier-Bessel series, is found to have the typical Kisslinger or Laplacian-like shape between 30 and 80 MeV

  14. Quasielastic electron scattering: effect of relativistic nuclear potentials

    International Nuclear Information System (INIS)

    Do Dang, G.; Nguyen Van Giai.

    1983-11-01

    It is shown that a solution to the difficulty encountered in reproducing simultaneously the experimental longitudinal and transverse response functions deduced from deep inelastic electron scattering may be found in a consistent treatment of the electromagnetic interaction in a Dirac equation in which Lorentz scalar and vector potentials are explicitly introduced. Results for 12 C and 40 Ca are given and compared with experiments

  15. Dirac potentials in a coupled channel approach to inelastic scattering

    International Nuclear Information System (INIS)

    Mishra, V.K.; Clark, B.C.; Cooper, E.D.; Mercer, R.L.

    1990-01-01

    It has been shown that there exist transformations that can be used to change the Lorentz transformation character of potentials, which appear in the Dirac equation for elastic scattering. We consider the situation for inelastic scattering described by coupled channel Dirac equations. We examine a two-level problem where both the ground and excited states are assumed to have zero spin. Even in this simple case we have not found an appropriate transformation. However, if the excited state has zero excitation energy it is possible to find a transformation

  16. On deformed tensor potential for inelastic deuteron scattering

    International Nuclear Information System (INIS)

    Raynal, Jacques.

    1980-08-01

    Tensor analysing powers for inelastic deuteron scattering have been measured around 12 to 15 MeV. There is no problem to use such a tensor potential for the excited states in coupled channel calculations. However, for transition potentials, form factors are very different. A fit has been done with the first order vibrational model for 64 Ni(d,d') 64 Ni*, 2 + at 1,344 MeV

  17. Obtaining the crystal potential by inversion from electron scattering intensities

    International Nuclear Information System (INIS)

    Allen, L.T.; Josefsson, T.W.; Leeb, H.

    1998-01-01

    A method to obtain the crystal potential from the intensities of the diffracted beams in high energy electron diffraction is proposed. It is based on a series of measurements for specific well determined orientations of the incident beam which determine the moduli of all elements of the scattering matrix. Using unitarity and the specific form of the scattering matrix (including symmetries) an overdetermined set of non-linear equations is obtained from these data. Solution of these equations yields the required phase information and allows the determination of a (projected) crystal potential by inversion which is unique up to an arbitrary shift of the origin. The reconstruction of potentials from intensities is illustrated for two realistic examples, a [111] systematic row case in ZnS and a [110] zone axis orientation in GaAs (both noncentrosymmetric crystals)

  18. s -wave scattering length of a Gaussian potential

    Science.gov (United States)

    Jeszenszki, Peter; Cherny, Alexander Yu.; Brand, Joachim

    2018-04-01

    We provide accurate expressions for the s -wave scattering length for a Gaussian potential well in one, two, and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of ultracold-atomic gases, where the s -wave scattering length is a physically relevant parameter. We first describe a numerical procedure to compute the value of the s -wave scattering length from the parameters of the Gaussian, but find that its accuracy is limited in the vicinity of singularities that result from the formation of new bound states. We then derive simple analytical expressions that capture the correct asymptotic behavior of the s -wave scattering length near the bound states. Expressions that are increasingly accurate in wide parameter regimes are found by a hierarchy of approximations that capture an increasing number of bound states. The small number of numerical coefficients that enter these expressions is determined from accurate numerical calculations. The approximate formulas combine the advantages of the numerical and approximate expressions, yielding an accurate and simple description from the weakly to the strongly interacting limit.

  19. Classical and quantum chaotic scattering in a muffin tin potential

    International Nuclear Information System (INIS)

    Brandis, S.

    1995-05-01

    In this paper, we study the classical mechanics, the quantum mechanics and the semi-classical approximation of the 2-dimensional scattering from a muffin tin potential. The classical dynamical system for Coulombic muffin tins is proven to be chaotic by explicit construction of the exponentially increasing number of periodic orbits. These are all shown to be completely unstable (hyperbolic). By methods of the thermodynamic formalism we can determine the Hausdorff dimension, escape rate and Kolmogorov-Sinai-entropy of the system. An extended KKR-method is developed to determine the quantum mechanical S-matrix. We compare a few integrable scattering examples with the results of the muffin tin scattering. Characteristic features of the spectrum of eigenphases turn out to be the level repulsion and long range rigidity as compared to a completely random spectrum. In the semiclassical analysis we can rederive the regularized Gutzwiller trace formula directly from the exact KKR-determinant to prove that no further terms contribute in the case of the muffin tin potential. The periodic orbit sum allows to draw some qualitative conclusions about the effects of classical chaos on the quantum mechanics. In the context of scaling systems the theory of almost periodic functions is discussed as a possible mathematical foundation for the semiclassical periodic orbit sums. Some results that can be obtained from this analysis are developed in the context of autocorrelation functions and distribution functions for chaotic scattering systems. (orig.)

  20. One-dimensional scattering problem for inverse square potential

    International Nuclear Information System (INIS)

    Mineev, V.S.

    1990-01-01

    Analytical continuation of the solution for the Schroedinger equation of inverse square potential, together with the modified method for variation of constants makes it possible to construct admittable self-adjoint extensions and to completely analyze the respective scattering problem along the entire line. In this case, the current density conservation and the wave function continuity when passing through the singular point x=0 require, that a 8-shaped induced potential should be introduced in the Schroedinger equation. The relevant calculations have shown that the potential x -2 can be either absolutely penetrable or absolutely impenetrable. 16 refs

  1. Multiple Scattering Approach to Continuum State with Generally Shaped Potential

    International Nuclear Information System (INIS)

    Hatada, Keisuke; Hayakawa, Kuniko; Tenore, Antonio; Benfatto, Maurizio; Natoli, Calogero

    2007-01-01

    We present a new scheme for solving the scattering problem for an arbitrarily shaped potential cell that avoids the well known convergence problems in the angular momentum expansion of the cell shape function. Tests of the method against analytically soluble separable model potentials, with and without shape truncation, have been performed with success. By a judicious choice of the shape of the cells partitioning the whole molecular space and use of empty cells when necessary, we set up a multiple scattering scheme that leads to a straightforward generalization of the same equations in the muffin-tin approximation. For example lmax in the angular momentum expansion can still be chosen according to the rule lmax ∼ kR, where R is the radius of the bounding sphere of the cell and all the matrices appearing in the theory are square matrices

  2. Optical potential study of electron scattering by rubidium

    Energy Technology Data Exchange (ETDEWEB)

    Chin, J. H.; Ratnavelu, K. [University of Malaya, Kuala Lumpur (Malaysia); Zhou, Y. [Harbin Institute of Technology, Harbin (China)

    2011-10-15

    The coupled-channel optical method (CCOM) has been implemented in a study of electronrubidium scattering. This method includes the continuum effect in the calculation via an ab-initio optical potential. Eight atomic states (5s, 5p, 4d, 6s, 6p, 5d, 7s, 7p) were used together with the continuum optical potential in the 5s-5s, 5s-5p, and 5p-5p coupling. The elastic, inelastic and total cross sections for electron-rubidium scattering at low and intermediate energies, ranging from 10 eV to 100 eV, are reported. The results are compared with available experimental and theoretical data.

  3. Determinantal method for complex angular momenta in potential scattering

    Energy Technology Data Exchange (ETDEWEB)

    Lee, B. W. [University of Pennsylvania, Philadelphia, PA (United States)

    1963-01-15

    In this paper I would like do describe a formulation of the complex angular momenta in potential scattering based on the Lippmann-Schwinger integral equation rather than on the Schrödinger differential equation. This is intended as a preliminary to the paper by SAWYER on the Regge poles and high energy limits in field theory (Bethe-Salpeter amplitudes), where the integral formulation is definitely more advantageous than the differential formulation.

  4. Holography explained in the language of potential scattering

    International Nuclear Information System (INIS)

    Csonka, P.L.

    1978-04-01

    Holography is explained in the language of potential scattering kinematics (whereas usually the formalism of wave optics is used). This approach is probably more natural for those who were trained as atomic, nuclear, etc., physicists, but are now attracted by the possibility of x-ray holography. Classical optical instruments are hardly mentioned, and the approximations usually connected with them are not used. Many of the results derived in this report are not new. 5 figures

  5. Retrieval of the projected potential by inversion from the scattering matrix in electron-crystal scattering

    International Nuclear Information System (INIS)

    Allen, L.J.; Spargo, A.E.C.; Leeb, H.

    1998-01-01

    The retrieval of a unique crystal potential from the scattering matrix S in high energy transmission electron diffraction is discussed. It is shown that, in general, data taken at a single orientation are not sufficient to determine all the elements of S. Additional measurements with tilted incident beam are required for the determination of the whole S-matrix. An algorithm for the extraction of the crystal potential from the S-matrix measured at a single energy and thickness is presented. The limiting case of thin crystals is discussed. Several examples with simulated data are considered

  6. Chapter 8. Elementary notions on the quantum theory of potential scattering

    International Nuclear Information System (INIS)

    Anon.

    1977-01-01

    Elementary notions in quantum theory of potential scattering are exposed: stationary states of scattering, calculus of cross section, scattering by central potential, phase shift method. In complement, these questions are studied: free particle (stationary states of well defined kinetic momentum); phenomenological description of collisions with absorption; elementary examples of application of the scattering theory [fr

  7. Some phenomenological consequences of the time-ordered perturbation theory of QED on non-commutative spacetime

    CERN Document Server

    Liao, Y

    2003-01-01

    A framework was recently proposed for doing perturbation theory on non-commutative (NC) spacetime. It preserves the unitarity of the S matrix and differs from the naive, popular approach already at the lowest order in perturbation when time does not commute with space. In this work, we investigate its phenomenological implications at linear colliders, especially the TESLA at DESY, through the processes of e sup + e sup --> mu sup +mu sup - ,H sup + H sup - ,H sup 0 H sup 0. We find that some NC effects computed previously are now modified and that there are new processes which now exhibit NC effects. Indeed, the first two processes get corrected at tree level as opposed to the null result in the naive approach, while the third one coincides with the naive result only in the low energy limit. The impact of the earth's rotation is incorporated. The NC signals are generally significant when the NC scale is comparable to the collider energy. If this is not the case, the non-trivial azimuthal angle distribution an...

  8. Bound and scattering states with non-local potentials.

    Energy Technology Data Exchange (ETDEWEB)

    Viviani, M; Girlanda, L; Kievsky, A; Marcucci, L E; Rosati, S; Schiavilla, R

    2007-06-01

    The application of the hyperspherical harmonics method to the case of non-local potentials is described. Given the properties of the hyperspherical harmonic functions, there are no difficulties in considering the approach in both coordinate and momentum space. The results for the 3H and 4He binding energies and n - 3H scattering lengths are found to be in good agreement with those obtained with other different techniques. A study of the 4He form factor is also reported, with a careful investigation of the contribution from isospin symmetry violation. Its effect on parity violating elastic scattering of polarized electrons from 4He is investigated. In particular, a simple analysis of the recently measured left-right asymmetry at low Q2 shows that the contribution of these isospin admixture are found of comparable magnitude to that associated with strangeness components in the nucleon electric form factor.

  9. Scattering and pair production by a potential barrier

    International Nuclear Information System (INIS)

    Nikishov, A.I.

    2004-01-01

    Scattering and electron-positron pair production by a one-dimensional electric barrier is considered in the framework of the S-matrix formalism. The solution of the Dirac equation are classified according to frequency sign. The Bogolyubov transformations relating the in- and out-states are given. It is shown that the norm of a solution of the wave equation is determined by the largest amplitude of its asymptotic form when x 3 → ±∞. For the Sauter-type potential we give the explicit expressions for the complete in- and out-sets of orthonormalized wave functions. It is noted that in principle virtual vacuum processes in external field influence the phase of the wave function of the scattered particle [ru

  10. Invariant potential for elastic pion--nucleus scattering

    International Nuclear Information System (INIS)

    Cammarata, J.B.; Banerjee, M.K.

    1976-01-01

    From the Wick-Dyson expansion of the exact propagator of a pion in the presence of a nucleus, an invariant potential for crossing symmetric elastic pion-nucleus scattering is obtained in terms of a series of pion-nucleon diagrams. The Chew-Low theory is used to develop a model in which the most important class of diagrams is effectively summed. Included in this model is the exclusion principle restriction on the pion-bound nucleon interaction, the effects of the binding of nucleons, a kinematic transformation of energy from the lab to the πN center of mass frame, and the Fermi motion and recoil of the target nucleons. From a numerical study of the effects of these processes on the π- 12 C total cross section, the relative importance of each is determined. Other processes contributing to the elastic scattering of pions not included in the present model are also discussed

  11. Parametrization of the scattering wave functions of the Paris potential

    International Nuclear Information System (INIS)

    Loiseau, B.; Mathelitsch, L.

    1996-10-01

    The neutron-proton scattering wave functions of the Paris nucleon-nucleon potential are parametrized for partial waves of total angular momenta less than 5. The inner parts of the wave functions are approximated by polynomials with a continuous transition to the outer parts, which are given by the asymptotic regime and determined by the respective phase shifts. The scattering wave functions can then be calculated at any given energy below 400 MeV. Special attention is devoted to the zero-energy limit of the low partial waves. An easy-to-use FORTRAN program, which allows the user to calculate these parametrized wave functions, is available via electronic mail. (author)

  12. Three-nucleon scattering by using chiral perturbation theory potential

    International Nuclear Information System (INIS)

    Kamata, Hiroyuki

    2003-01-01

    Three-nucleon scattering problems are studied by using two-nucleon and three-nucleon potentials derived from chiral perturbation theory. The three-nucleon term is shown to appear in the effective potential of the rank of next-to-next-to-leading order (NNLO). New three-nucleon forces are taken into consideration in addition to the conventional Fujita-Miyazawa (FM) type three-nucleon potential. Two-nucleon potential of the chiral perturbation theory is as precise as the conventional ones in low energy region. The FM type three-nucleon force which explains Sagara discrepancy in high energy region is introduced automatically. Concerning the Ay puzzle, the results seems to behave as if the puzzle has been solved at the level of NLO, but at the NNLO (without three-nucleon force) level the result is similar to the cases of conventional potential indicating the need of three-nucleon force. In contrast to the FM type three-nucleon force, five free parameters exist in the new D and E type three-nucleon forces introduced by the NNLO, but they are reduced to two independent parameters by antisymmetrization, which are found to be sensitive to the coupling energy of tritons and to the nd scattering length (spin doublet state). Parameters determined from them cannot give satisfactory answer to the A y puzzle. It seems, however, too hasty to conclude that A y puzzle cannot be solved by the chiral perturbation theory. (S. Funahashi)

  13. Non-commutative gauge Gravity: Second- order Correction and Scalar Particles Creation

    International Nuclear Information System (INIS)

    Zaim, S.

    2009-01-01

    A noncommutative gauge theory for a charged scalar field is constructed. The invariance of this model under local Poincare and general coordinate transformations is verified. Using the general modified field equation, a general Klein-Gordon equation up to the second order of the noncommu- tativity parameter is derived. As an application, we choose the Bianchi I universe. Using the Seiberg-Witten maps, the deformed noncommutative metric is obtained and a particle production process is studied. It is shown that the noncommutativity plays the same role as an electric field, gravity and chemical potential.

  14. Local and non-local potentials for deuteron elastic scattering

    International Nuclear Information System (INIS)

    Ramirez, J.A.

    1976-01-01

    The nucleon--nucleus local potential (central and spin--orbit) and the deuteron--nucleus nonlocal potential (central, spin--orbit, spin--radial tensor) are calculated by the folding-model (FM). Simple analytic expressions are obtained for the nucleon--nucleus potential by the use of Gaussians to represent the nucleon--nucleus potential and the charge and mass densities of the target. The analytic expressions give qualitative descriptions of phenomenological nucleon--nucleus interactions. A systematic target--mass dependence of realistic local FM deueron potentials is also included. Local-equivalent, energy-dependent, deuteron potentials are obtained from the nonlocal FM deuteron potentials and the energy dependence of the local potential parameters are presented. The local FM deuteron potential is tested for 60 Ni(d,d) 60 Ni at E/sub α/ = 15 MeV by comparing the predictions of the FM potentials with data in which all five polarization moments were measured. A qualitative fit to the data is obtained, but it overestimates the volume integral of the central potential by 7%. Energy-dependence effects are estimated by evaluating the local-equivalent potentials at E/sub α/ = 30 MeV and comparing the predictions to the E/sub α/ = 15 MeV potentials. The energy dependence of the central potential dominates the angular dependence of all five observables while the energy dependence of the spin--orbit and tensor potentials produces only scale changes (approx. 3%) in the vector and tensor analyzing powers. The scattering formalism for a spin-1 on a spin-0 target nucleus, and a description of the coupled--channels computer code DDUNC1 which treats the spin--radial tensor potential exactly, are included

  15. Scattering matrix for magnetic potentials with Coulomb decay at infinity

    CERN Document Server

    Yafaev, D

    2003-01-01

    We consider the Schr\\"odinger operator $H$ in the space $L_2({\\R}^d)$ with a magnetic potential $A(x)$ decaying as $|x|^{-1}$ at infinity and satisfying the transversal gauge condition $ =0$. Such potentials correspond, for example, to magnetic fields $B(x)$ with compact support and hence are quite general. Our goal is to study properties of the scattering matrix $S(\\lambda)$ associated to the operator $H$. In particular, we find the essential spectrum $\\sigma_{ess}$ of $S(\\lambda)$ in terms of the behaviour of $A(x)$ at infinity. It turns out that $\\sigma_{ess}(S(\\lambda))$ is normally a rich subset of the unit circle ${\\Bbb T}$ or even coincides with ${\\Bbb T}$. We find also the diagonal singularity of the scattering amplitude (of the kernel of $S(\\lambda)$ regarded as an integral operator). In general, $S(\\lambda)$ is a sum of a multiplication operator and of a singular integral operator. However, if the magnetic field decreases faster than $ |x|^{-2}$ for $d\\geq 3$ (and the total magnetic flux is an integ...

  16. Inelastic multiple scattering of interacting bosons in weak random potentials

    International Nuclear Information System (INIS)

    Geiger, Tobias

    2013-01-01

    Within the present thesis we develop a diagrammatic scattering theory for interacting bosons in a three-dimensional, weakly disordered potential. Based on a microscopic N-body scattering theory, we identify the relevant diagrams including elastic and inelastic collision processes that are sufficient to describe quantum transport in the regime of weak disorder. By taking advantage of the statistical properties of the weak disorder potential, we demonstrate how the N-body dynamics can be reduced to a nonlinear integral equation of Boltzmann type for the single-particle diffusive flux. A presently available alternative description - based on the Gross-Pitaevskii equation - only includes elastic collisions. In contrast, we show that far from equilibrium the presence of inelastic collisions - even for weak interaction strength - must be accounted for and can induce the full thermalization of the single-particle current. In addition, we also determine the coherent corrections to the incoherent transport, leading to the effect of coherent backscattering. For the first time, we are able to analyze the influence of inelastic collisions on the coherent backscattering signal, which lead to an enhancement of the backscattered cone in a narrow spectral window, even for increasing non-linearity. With a short recollection of the presently available experimental techniques we furthermore show how an immediate implementation of our suggested setup with confined Bose-Einstein condensates can be accomplished. Thereby, the emergence of collective and/or thermodynamic behavior from fundamental, microscopic constituents can also be assessed experimentally. In a second part of this thesis, we present first results for light scattering off strongly interacting Rydberg atoms trapped in a one-dimensional, chain-like configuration. In order to monitor the time-dependence of this interacting many-body system, we devise a weak measurement scenario for which we derive a master equation for the

  17. Scattering of sine-Gordon kinks on potential wells

    International Nuclear Information System (INIS)

    Piette, Bernard; Zakrzewski, W J

    2007-01-01

    We study the scattering properties of sine-Gordon kinks on obstructions in the form of finite size potential 'wells'. We model this by making the coefficient of the cos(ψ) - 1 term in the Lagrangian position dependent. We show that when the kinks find themselves in the well they radiate and then interact with this radiation. As a result of this energy loss, the kinks become trapped for small velocities while at higher velocities they are transmitted with a loss of energy. However, the interaction with the radiation can produce 'unexpected' reflections by the well. We present two simple models which capture the gross features of this behaviour. Both involve standing waves either at the edges of the well or in the well itself

  18. CRAPONE, Optical Model Potential Fit of Neutron Scattering Data

    International Nuclear Information System (INIS)

    Fabbri, F.; Fratamico, G.; Reffo, G.

    2004-01-01

    1 - Description of problem or function: Automatic search for local and non-local optical potential parameters for neutrons. Total, elastic, differential elastic cross sections, l=0 and l=1 strength functions and scattering length can be considered. 2 - Method of solution: A fitting procedure is applied to different sets of experimental data depending on the local or non-local approximation chosen. In the non-local approximation the fitting procedure can be simultaneously performed over the whole energy range. The best fit is obtained when a set of parameters is found where CHI 2 is at its minimum. The solution of the system equations is obtained by diagonalization of the matrix according to the Jacobi method

  19. Nonlinear theory of scattering by localized potentials in metals

    Energy Technology Data Exchange (ETDEWEB)

    Howard, I A [Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp (Belgium); March, N H [Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp (Belgium); Oxford University, Oxford (United Kingdom); Echenique, P M [Donostia International Physics Center (DIPC), 20018 San Sebastian, Basque Country (Spain); Departamento de Fisica de Materiales and Centro Mixto CSIC-UPV/EHU, Facultad de Quimicas, UPV/EHU, Apartado 1072, 20080, San Sebastian (Spain)

    2003-11-14

    In early work, March and Murray gave a perturbation theory of the Dirac density matrix {gamma}(r, r') generated by a localized potential V(r) embedded in an initially uniform Fermi gas to all orders in V(r). For potentials sufficiently slowly varying in space, they summed the resulting series for r' = r to regain the Thomas-Fermi density {rho}(r) {proportional_to} [{mu} - V(r)]{sup 3/2}, with {mu} the chemical potential of the Fermi gas. For an admittedly simplistic repulsive central potential V(r) = vertical bar A vertical bar exp(-cr), it is first shown here that what amounts to the sum of the March-Murray series for the s-wave (only) contribution to the density, namely {rho}{sub s}(r, {mu}), can be obtained in closed form. Furthermore, for specific numerical values of A and c in this exponential potential, the long-range behaviour of {rho}{sub s}(r, {mu}) is related to the zero-potential form of March and Murray, which merely suffers a {mu}-dependent phase shift. This result is interpreted in relation to the recent high density screening theorem of Zaremba, Nagy and Echenique. A brief discussion of excess electrical resistivity caused by nonlinear scattering in a Fermi gas is added; this now involves an off-diagonal local density of states. Finally, for periodic lattices, contact is made with the quantum-mechanical defect centre models of Koster and Slater (1954 Phys. Rev. 96 1208) and of Beeby (1967 Proc. R. Soc. A 302 113), and also with the semiclassical approximation of Friedel (1954 Adv. Phys. 3 446). In appendices, solvable low-dimensional models are briefly summarized.

  20. Problems in the links between scattering data and interaction potentials

    International Nuclear Information System (INIS)

    Amos, K.

    1995-01-01

    The scattering function is of paramount importance in any approaches by which quantitative information on the interaction between colliding quantal systems of nuclear, atomic or molecular type, may be sought from measured, elastic scattering data. Therein there are two possible spectral parameters, the energy and the angular momentum. Most experimental results suggest use of fixed energy and variable angular momentum schemes. Such fixed energy data and their analyses are the subject of this report, with particular emphasis placed upon the problems of the link between data and the scattering function. 18 figs

  1. Problems in the links between scattering data and interaction potentials

    Energy Technology Data Exchange (ETDEWEB)

    Amos, K.

    1995-10-01

    The scattering function is of paramount importance in any approaches by which quantitative information on the interaction between colliding quantal systems of nuclear, atomic or molecular type, may be sought from measured, elastic scattering data. Therein there are two possible spectral parameters, the energy and the angular momentum. Most experimental results suggest use of fixed energy and variable angular momentum schemes. Such fixed energy data and their analyses are the subject of this report, with particular emphasis placed upon the problems of the link between data and the scattering function. 18 figs.

  2. Calculations on nucleon-deuteron scattering with realistic potentials

    International Nuclear Information System (INIS)

    Stolk, C.

    1978-01-01

    The purpose of this study is to find out how the three-nucleon observables are affected by details of the two-nucleon force. The theory of the perturbational treatment of the Faddeev equations for the three-particle transition matrix, for both elastic and breakup scattering is dealt with. Some details of the numerical treatment are discussed, results for the elastic and breakup scattering presented and conclusions drawn. (C.F.)

  3. Interatomic potentials from rainbow scattering of keV noble gas atoms under axial surface channeling

    International Nuclear Information System (INIS)

    Schueller, A.; Wethekam, S.; Mertens, A.; Maass, K.; Winter, H.; Gaertner, K.

    2005-01-01

    For grazing scattering of keV Ne and Ar atoms from a Ag(1 1 1) and a Cu(1 1 1) surface under axial surface channeling conditions we observe well defined peaks in the angular distributions for scattered projectiles. These peaks can be attributed to 'rainbow-scattering' and are closely related to the geometry of potential energy surfaces which can be approximated by the superposition of continuum potentials along strings of atoms in the surface plane. The dependence of rainbow angles on the scattering geometry provides stringent tests on the scattering potentials. From classical trajectory calculations based on universal (ZBL), adjusted Moliere (O'Connor and Biersack), and individual interatomic potentials we obtain corresponding rainbow angles for comparison with the experimental data. We find good overall agreement with the experiments for a description of trajectories based on adjusted Moliere and individual potentials, whereas the agreement is poorer for potentials with ZBL screening

  4. Effective potential in the problem of scattering of three charged particles

    International Nuclear Information System (INIS)

    Kvitsinskii, A.A.; Merkur'ev, S.P.

    1988-01-01

    We study the effective interaction potential in the scattering of a charged particle by a bound state of two other charged particles. Scattering by both the ground and excited states of the target is considered. Explicit representations describing the asymptotic structure of effective potentials are proved

  5. Distorted-wave Born approximation in the case of an optical scattering potential

    International Nuclear Information System (INIS)

    Mytnichenko, Sergey V.

    2005-01-01

    Application of the distorted-wave Born approximation in the conventional form developed for the case of a real scattering potential is shown to cause significant errors in calculating X-ray diffuse scattering from non-ideal crystals, superlattices, multilayers and other objects if energy dissipation (photoabsorption, inelastic scattering, and so on) is not negligible, or in other words, in the case of an optical (complex) scattering potential. We show how a correct expression for the X-ray diffuse-scattering cross-section can be obtained in this case. Generally, the diffuse-scattering cross-section from an optical potential is not T-invariant, i.e. the reciprocity principle is violated. Violations of T-invariance are more evident when the dynamical nature of the diffraction is more critical

  6. The scattering potential of partial derivative wavefields in 3-D elastic orthorhombic media: an inversion prospective

    KAUST Repository

    Oh, Juwon; Alkhalifah, Tariq Ali

    2016-01-01

    that includes large offsets, full azimuth, and multicomponent sensors, the potential for trade-off between the elastic orthorhombic parameters are large. The first step to understanding such trade-off is analysing the scattering potential of each parameter

  7. Scattering state solutions of the Duffin-Kemmer-Petiau equation with the Varshni potential model

    Energy Technology Data Exchange (ETDEWEB)

    Oluwadare, O.J. [Federal University Oye-Ekiti, Department of Physics, Oye-Ekiti, Ekiti State (Nigeria); Oyewumi, K.J. [Federal University of Technology, Department of Physics, Minna, Niger State (Nigeria)

    2017-02-15

    The scattering state of the Duffin-Kemmer-Petiau equation with the Varshni potential was studied. The asymptotic wave function, the scattering phase shift and normalization constant were obtained for any J states by dealing with the centrifugal term using a suitable approximation. The analytical properties of the scattering amplitude and the bound state energy were obtained and discussed. Our numerical and graphical results indicate that the scattering phase shift depends largely on total angular momentum J, screening parameter β and potential strengths a and b. (orig.)

  8. Multiple scattering theory for non-local and multichannel potentials

    Czech Academy of Sciences Publication Activity Database

    Natoli, C.R.; Krüger, P.; Hatada, K.; Hayakawa, K.; Sébilleau, D.; Šipr, Ondřej

    2012-01-01

    Roč. 24, č. 36 (2012), s. 1-20 ISSN 0953-8984 Institutional research plan: CEZ:AV0Z10100521 Keywords : multichannel scattering * correlation s * density matrix Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 2.355, year: 2012

  9. Low momentum scattering of the Dirac particle with an asymmetric cusp potential

    International Nuclear Information System (INIS)

    Jiang, Yu.; Dong, Shi-Hai; Lozada-Cassou, M.; Antillon, A.

    2006-01-01

    We study the exact solutions of the bound and scattering states of the one-dimensional Dirac equation with an asymmetric cusp potential and derive the condition of the supercriticality for this quantum system. We find that the scattering properties are invariant under reflection of the potential's shape, and the supercritical value for the potential amplitude V 0 varies with the degree of the potential asymmetry. (orig.)

  10. Inelastic plasmon and inter-band electron-scattering potentials for Si from dielectric matrix calculations

    International Nuclear Information System (INIS)

    Josefsson, T.W.; Smith, A.E.

    1994-01-01

    Inelastic scattering of electrons in a crystalline environment may be represented by a complex non-hermitian potential. Completed generalised expressions for this inelastic electron scattering potential matrix, including virtual inelastic scattering, are derived for outer-shell electron and plasmon excitations. The relationship between these expressions and the general anisotropic dielectric response matrix of the solid is discussed. These generalised expressions necessarily include the off-diagonal terms representing effects due to departure from translational invariance in the interaction. Results are presented for the diagonal back structure dependent inelastic and virtual inelastic scattering potentials for Si, from a calculation of the inverse dielectric matrix in the random phase approximation. Good agreement is found with experiment as a function of incident energies from 10 eV to 100 keV. Anisotropy effects and hence the interaction de localisation represented by the off-diagonal scattering potential terms, are found to be significant below 1 keV. 38 refs., 2 figs

  11. An evaluation of diverse methods of obtaining effective Schroedinger interaction potentials for elastic scattering

    International Nuclear Information System (INIS)

    Amos, K.; Allen, L.J.; Steward, C.; Hodgson, P.E.; Sofianos, S.A.

    1995-01-01

    Direct solution of the Schroedinger equation and inversion methods of analysis of elastic scattering data are considered to evaluate the information that they can provide about the physical interaction between colliding nuclear particles. It was found that both optical model and inversion methods based upon inverse scattering theories are subject to ambiguities. Therefore, it is essential that elastic scattering data analyses are consistent with microscopic calculations of the potential. 25 refs

  12. An evaluation of diverse methods of obtaining effective Schroedinger interaction potentials for elastic scattering

    Energy Technology Data Exchange (ETDEWEB)

    Amos, K.; Allen, L.J.; Steward, C. [Melbourne Univ., Parkville, VIC (Australia). School of Physics; Hodgson, P.E. [Oxford Univ. (United Kingdom). Dept. of Physics; Sofianos, S.A. [University of South Africa (UNISA), Pretoria (South Africa). Dept. of Physics

    1995-10-01

    Direct solution of the Schroedinger equation and inversion methods of analysis of elastic scattering data are considered to evaluate the information that they can provide about the physical interaction between colliding nuclear particles. It was found that both optical model and inversion methods based upon inverse scattering theories are subject to ambiguities. Therefore, it is essential that elastic scattering data analyses are consistent with microscopic calculations of the potential. 25 refs.

  13. Canonical transformations method in the potential scattering problem

    International Nuclear Information System (INIS)

    Pavlenko, Yu.G.

    1984-01-01

    Canonical formalism of the first order is used in the present paper to solve the problem of scattering and other problems of quantum mechanics. The theory of canonical transformations (CT) being the basis of hamiltonian approach permits to develop several methods of integration being beyond the scope of the standard theory of perturbations. In this case it is essential for numerical counting that the theory permits to obtain algorithm for plotting highest approximations

  14. SCATTER

    International Nuclear Information System (INIS)

    Broome, J.

    1965-11-01

    The programme SCATTER is a KDF9 programme in the Egtran dialect of Fortran to generate normalized angular distributions for elastically scattered neutrons from data input as the coefficients of a Legendre polynomial series, or from differential cross-section data. Also, differential cross-section data may be analysed to produce Legendre polynomial coefficients. Output on cards punched in the format of the U.K. A. E. A. Nuclear Data Library is optional. (author)

  15. Eikonal form of the dynamic polarization potential and its application to the scattering of exotic nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Canto, L F; Donangelo, R [Universidade Federal do Rio de Janeiro, RJ (Brazil). Inst. de Fisica; Hussein, M S [Sao Paulo Univ. (Brazil). Inst. de Fisica

    1991-07-01

    The eikonal theory of the dynamic polarization potential (DDP) is developed. Application to the scattering of loosely bound exotic nuclei is made. In particular, the effect of our DPP on the scattering of {sup 11}Li+{sup 12}C at 85 AxMeV is discussed. (orig.).

  16. Laser-Compton Scattering as a Potential Electron Beam Monitor

    International Nuclear Information System (INIS)

    Chouffani, K.; Wells, D.; Harmon, F.; Lancaster, G.; Jones, J.

    2002-01-01

    LCS experiments were carried out at the Idaho Accelerator Center (IAC); sharp monochromatic x-ray lines were observed. These are produced using the so-called inverse Compton effect, whereby optical laser photons are collided with a relativistic electron beam. The back-scattered photons are then kinematically boosted to keV x-ray energies. We have first demonstrated these beams using a 20 MeV electron beam collided with a 100 MW, 7 ns Nd; YAG laser. We observed narrow LCS x-ray spectral peaks resulting from the interaction of the electron beam with the Nd; YAG laser second harmonic (532 nm). The LCS x-ray energy lines and energy deviations were measured as a function of the electron beam energy and energy-spread respectively. The results showed good agreement with the predicted valves. LCS could provide an excellent probe of electron beam energy, energy spread, transverse and longitudinal distribution and direction

  17. Scattering and bound states for the Hulthen potential in a cosmic string background

    Energy Technology Data Exchange (ETDEWEB)

    Hosseinpour, Mansoureh; Hassanabadi, Hassan [Shahrood University of Technology, Physics Department, P. O. Box: 3619995161-316, Shahrood (Iran, Islamic Republic of); Andrade, Fabiano M. [Universidade Estadual de Ponta Grossa, Departamento de Matematica e Estatistica, Ponta Grossa, PR (Brazil); Silva, Edilberto O. [Universidade Federal do Maranhao, Departamento de Fisica, Sao Luis, MA (Brazil)

    2017-05-15

    In this work we study the Dirac equation with vector and scalar potentials in the spacetime generated by a cosmic string. Using an approximation for the centrifugal term, a solution for the radial differential equation is obtained. We consider the scattering states under the Hulthen potential and obtain the phase shifts. From the poles of the scattering S-matrix the states energies are determined as well. (orig.)

  18. Continuum and bound electronic wavefunctions for anisotropic multiple-scattering potentials

    International Nuclear Information System (INIS)

    Siegel, J.; Dill, D.; Dehmer, J.L.

    1975-01-01

    Standard multiple-scattering treatments of bound and continuum one-electron states are restricted to a monopole potential in each of the various spherical regions. We have extended the treatment within these regions to a general potential. The corresponding multiple-scattering equations should facilitate accurate treatment of effects of the build-up of charge due to bonding, of the dipole character of polar molecules, and of external fields

  19. An improved optical potential for low-energy pion-nucleus scattering

    International Nuclear Information System (INIS)

    Khankhasaev, M.Kh.; Topil'skaya, N.S.

    1988-01-01

    A new procedure for calculating the imaginary part the of Stricker, McManus and Carr (SMC) optical potential is proposed. It is based on an approximate expression for the pion-nucleon scattering amplitude including nuclear structure effects. It is shown that the resulting potential with the absorption parameters fitted to the pionic atom data provides a good description of the scattering up to 50 MeV

  20. Inverse scattering with mixed spectrum from δ-potentials

    International Nuclear Information System (INIS)

    Lin Jiancheng.

    1987-03-01

    The inverse problem is studied in a system with mixed spectrum, i.e. the continuous part of the spectrum coincides with that of a repulsive δ-potential and the discrete part coincides with that of an attractive δ-potential. (author). 2 refs, 5 figs

  1. Chemical binding effects in resonance - potential interference scattering for harmonic crystals

    International Nuclear Information System (INIS)

    Kuwaifi, A.; Summerfield, G.C.

    1991-01-01

    The neutron scattering cross section which is the quantity directly measured in experiments is given by the absolute square of the scattering amplitude. For energies near a resonance, this yields three terms: potential, resonant and interference. In this paper we deal with the interference neutron scattering cross section which is written in terms of a three-point correlation function. This function is calculated for the ideal gas and harmonic crystal models. For short collision times, the interference result for harmonic crystals is the same as the ideal gas but it has an effective temperature. This is the same effective temperature as was previously found for absorption and pure resonant processes. Therefore, the interference scattering cross section can be treated in the same way as resonant scattering and absorption are treated using an ideal gas result with the usual effective temperature. (author)

  2. Sensitivity of the elastic scattering matrix elements to the range of the inelastic potentials

    International Nuclear Information System (INIS)

    Rawitscher, G.H.; Rasoanaivo, R.Y.

    1983-01-01

    The solution to a system of coupled equations is examined with regard to the effect of the long range part of the inelastic potentials upon the elastic phase shifts. It is found that those parts of the inelastic potentials which occur beyond the range of the elastic to inelastic transition potentials affect the elastic phase shifts in only a minor way. The proof is given theoretically by means of a Green's function formulation which includes the long range part of the inelastic potentials perturbatively. When applied to the calculation of the effect of breakup on the deuteron-nucleus elastic scattering, the argument confirms the finding that errors in the long range part of the potentials in the breakup channels do not sensitively affect the elastic deuteron scattering cross section. This result explains why the elastic scattering is not very sensitive to the choice of the discretization procedure of the breakup space

  3. Resonances and analyticity of scattering wave function for square-well-type potentials

    International Nuclear Information System (INIS)

    Weber, T.A.; Hammer, C.L.; Zidell, V.S.

    1982-01-01

    In this paper we extend our previous analysis of the scattering of wave packets in one dimension to the case of the square-well potential. The analytic properties of the general scattering solution are emphasized thereby making the analysis useful as introductory material for a more sophisticated S-matrix treatment. The square-well model is particularly interesting because of its application to the deuteron problem. Resonance scattering, barrier penetration, time delay, and line shape are discussed at the level of the first-year graduate student

  4. Exact Time-Dependent Exchange-Correlation Potential in Electron Scattering Processes

    Science.gov (United States)

    Suzuki, Yasumitsu; Lacombe, Lionel; Watanabe, Kazuyuki; Maitra, Neepa T.

    2017-12-01

    We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are completely missed by adiabatic approximations that, consequently, significantly underestimate the scattering probability. A recently proposed nonadiabatic approximation is shown to correctly capture the approach of the electron to the target when the initial Kohn-Sham state is chosen judiciously, and it is more accurate than standard adiabatic functionals but ultimately fails to accurately capture reflection. These results may explain the underestimation of scattering probabilities in some recent studies on molecules and surfaces.

  5. Elastic scattering of a Bose-Einstein condensate at a potential landscape

    International Nuclear Information System (INIS)

    Březinová, Iva; Burgdörfer, Joachim; Lode, Axel U J; Streltsov, Alexej I; Cederbaum, Lorenz S; Alon, Ofir E; Collins, Lee A; Schneider, Barry I

    2014-01-01

    We investigate the elastic scattering of Bose-Einstein condensates at shallow periodic and disorder potentials. We show that the collective scattering of the macroscopic quantum object couples to internal degrees of freedom of the Bose-Einstein condensate such that the Bose-Einstein condensate gets depleted. As a precursor for the excitation of the Bose-Einstein condensate we observe wave chaos within a mean-field theory

  6. Scattering of the Dirac particle by a Coulomb plus scalar potential in two dimensions

    International Nuclear Information System (INIS)

    Dong Shihai; Lozada-Cassou, M.

    2004-01-01

    The scattering of the two-dimensional Dirac particle by the Coulomb potential Vc=-A1/r plus the scalar one Vs=-A2/r is studied. The phase shifts are obtained exactly. The special case A1=A2 is also discussed. We find that a very interesting feature of the cross section σ(θ) for the special case A1=A2 is symmetrical with respect to the scattering angle θ=π

  7. Model-unrestricted scattering potentials for light ions and their interpretation in the folding model

    International Nuclear Information System (INIS)

    Ermer, M.; Clement, H.; Frank, G.; Grabmayr, P.; Heberle, N.; Wagner, G.J.

    1989-01-01

    High-quality data for elastic proton, deuteron and α-particle scattering on 40 Ca and 208 Pb at 26-30 MeV/N have been analyzed in terms of the model-unrestricted Fourier-Bessel concept. While extracted scattering potentials show substantial deviations from Woods-Saxon shapes, their real central parts are well described by folding calculations using a common effective nucleon-nucleon interaction with a weak density dependence. (orig.)

  8. A new path-integral representation of the T-matrix in potential scattering

    International Nuclear Information System (INIS)

    Carron, J.; Rosenfelder, R.

    2011-01-01

    We employ the method used by Barbashov and collaborators in Quantum Field Theory to derive a path-integral representation of the T-matrix in nonrelativistic potential scattering which is free of functional integration over fictitious variables as was necessary before. The resulting expression serves as a starting point for a variational approximation applied to high-energy scattering from a Gaussian potential. Good agreement with exact partial-wave calculations is found even at large scattering angles. A novel path-integral representation of the scattering length is obtained in the low-energy limit. -- Highlights: → We derive a new path-integral representation for the T-matrix in quantum scattering from a potential. → The method is based on a technique used by Barbashov and collaborators in Quantum Field Theory. → Unlike previous approaches no unphysical degrees of freedom in the path integral are needed. → The new representation is used for a variational approximation of the T-matrix at high energies. → A new expression for the scattering length at low energy is derived.

  9. Nucleus-Nucleus Scattering in the High-Energy Approximation and the Optical Folding Potential

    CERN Document Server

    Lukyanov, V K; Lukyanov, K V

    2004-01-01

    For the nucleus-nucleus scattering, the complex potential is obtained which corresponds to the eikonal phase of an optical limit of the Glauber-Sitenko high-energy approximation. The potential does not include free parameters, its real and imaginary parts depend on energy and are determined by the reported data on the nuclear density distributions and nucleon-nucleon scattering amplitude. Alternatively, for the real part, the folding potential can be utilized which includes the effective NN-forces and the exchange term, as well. As a result, the microscopic optical potential is constructed where contributions of the calculated real and imaginary parts are formed by fitting the two respective factors. An efficient of the approach is confirmed by agreements of calculations with the experimental data on elastic scattering cross-sections.

  10. Intermediate-energy proton- 4He elastic scattering with a microscopic optical potential

    International Nuclear Information System (INIS)

    Alexander, Y.; Landau, R.H.

    1979-01-01

    A microscopic, momentum space, optical potential calculation of elastic p- 4 He scattering is compared with 100-200 MeV data over the full angular range. The least sophisticated potential explains the occurrence and energy dependence of the back angle peak. (Auth.)

  11. Geometrical-optics phenomena in the elastic scattering of fictitious heavy neutral nuclei by absorbing potentials

    International Nuclear Information System (INIS)

    Anni, R.; Taffara, L.

    1976-01-01

    A fictitious scattering phenomenon between neutral heavy particles is analysed by using both the square-well and trapezoidal complex potentials. After a preliminary phenomenological discussion based on the behaviour of the exact scattering matrix and the trajectories of Regge poles and zeros as continuous functions of the imaginary part of the potential, the contributions to the scattering amplitude from the external and multiple internal reflections and from the ''surface waves'' are separated by using the Debye expansion of the S(lambda)-matrix. The most important first two terms of this expansion are then compared with the exact behaviour of both the partial-wave scattering amplitude and cross-section, and the results are discussed. In particular, for potentials with large imaginary parts, the first term of the Debye expansion, which is associated with the rays directly reflected by the surface, well approximates the exact scattering matrix for all angular momenta. In these cases, by applying to this first term the Watson transformation, one is able to separate the contributions from the reflected rays (saddle-point contribution in the background integral)from that of the surface waves(surface pole contribution) which are responsible for the diffraction phenomenon. Studies are in progress in order to extend this approach to the Saxon-Wood potential with Coulomb interaction

  12. Total scattering cross sections and interatomic potentials for neutral hydrogen and helium on some noble gases

    International Nuclear Information System (INIS)

    Ruzic, D.N.; Cohen, S.A.

    1985-04-01

    Measurements of energy-dependent scattering cross sections for 30 to 1800 eV D incident on He, Ne, Ar, and Kr, and for 40 to 850 eV He incident on He, Ar, and Kr are presented. They are determined by using the charge-exchange efflux from the Princeton Large Torus tokamak as a source of D or He. These neutrals are passed through a gas-filled scattering cell and detected by a time-of-flight spectrometer. The cross section for scattering greater than the effective angle of the apparatus (approx. =20 mrad) is found by measuring the energy-dependent attenuation of D or He as a function of pressure in the scattering cell. The interatomic potential is extracted from the data

  13. Effects of periodic scattering potential on Landau quantization and ballistic transport of electrons in graphene

    Energy Technology Data Exchange (ETDEWEB)

    Gumbs, Godfrey [Department of Physics and Astronomy, Hunter College, CUNY, 695 Park Avenue, New York, NY 10065, USA and Donostia International Physics Center (DIPC), P de Manuel Lardizabal, 4, 20018 San Sebastian, Basque Country (Spain); Iurov, Andrii [Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, NY 10065 (United States); Huang, Danhong [Air Force Research Laboratory, Space Vehicles Directorate, Kirtland Air Force Base, NM 87117 (United States); Fekete, Paula [West Point Military Academy, West Point, NY (United States); Zhemchuzhna, Liubov [Department of Physics, North Carolina Central University, Durham, North Carolina 27707 (United States)

    2014-03-31

    A two-dimensional periodic array of scatterers has been introduced to a single layer of graphene in the presence of an external magnetic field perpendicular to the graphene layer. The eigenvalue equation for such a system has been solved numerically to display the structure of split Landau subbands as functions of both wave number and magnetic flux. The effects of pseudo-spin coupling and Landau subbands mixing by a strong scattering potential have been demonstrated. Additionally, we investigated the square barrier tunneling problem when magnetic field is present, as well as demonstrate the crucial difference in the modulated band structure between graphene and the two-dimensional electron gas. The low-magnetic field regime is particularly interesting for Dirac fermions and has been discussed. Tunneling of Dirac electrons through a magnetic potential barrier has been investigated to complement the reported results on electrostatic potential scattering in the presence of an ambient magnetic field.

  14. Elastic scattering of 90 - 120 MeV 3He particles and unique optical potential

    International Nuclear Information System (INIS)

    Hyakutake, M.; Matoba, M.; Kumabe, I.; Fukada, M.; Komatuzaki, T.

    1978-01-01

    The elastic scattering of 109.2 MeV 3 He particles by 40 Ca, 58 Ni, 90 Zr and 116 Sn has been investigated over a wide angular range. The elastic scattering cross sections have been analyzed in terms of the optical model. The data for each nucleus studied were sufficient to eliminate the discrete ambiguity in the strength of the optical potential; the unique potential which fits the data has real well depth of about 100 MeV and a corresponding volume integral per nucleon pair of about 310 MeV fm 3 . The elastic scattering of 3 He particles by 58 Ni has been further measured at bombarding energies of 89.3 and 118.5 MeV, and the incident-energy dependence of the optical potential of 3 He particles for 58 Ni was obtained. (author)

  15. Effects of periodic scattering potential on Landau quantization and ballistic transport of electrons in graphene

    International Nuclear Information System (INIS)

    Gumbs, Godfrey; Iurov, Andrii; Huang, Danhong; Fekete, Paula; Zhemchuzhna, Liubov

    2014-01-01

    A two-dimensional periodic array of scatterers has been introduced to a single layer of graphene in the presence of an external magnetic field perpendicular to the graphene layer. The eigenvalue equation for such a system has been solved numerically to display the structure of split Landau subbands as functions of both wave number and magnetic flux. The effects of pseudo-spin coupling and Landau subbands mixing by a strong scattering potential have been demonstrated. Additionally, we investigated the square barrier tunneling problem when magnetic field is present, as well as demonstrate the crucial difference in the modulated band structure between graphene and the two-dimensional electron gas. The low-magnetic field regime is particularly interesting for Dirac fermions and has been discussed. Tunneling of Dirac electrons through a magnetic potential barrier has been investigated to complement the reported results on electrostatic potential scattering in the presence of an ambient magnetic field

  16. Low energy 16O+208Pb elastic scattering: an attempt to analyze the microscopic effective potential

    International Nuclear Information System (INIS)

    Mau, N.V.; Ferrero, J.L.; Pacheco, J.C.; Bilwes, B.

    1991-03-01

    Elastic scattering of 16 O on 208 Pb is studied at 96, 104, 129.5, 192, 216.6 and 312.6 MeV. The 16 O+ 208 Pb potential is calculated first in the closure approximation model and compared to semi-phenomenological potentials. Then detailed contributions to the polarization real potential and to the imaginary potential due to the coupling of the elastic channels to the inelastic channels are calculated. The results are compared to the authors' model potential and used to test the main assumptions of the model. From that comparison a qualitative interpretation of the success of the model is proposed. At last the elastic scattering cross sections are calculated and compared to the data. (author) 41 refs., 6 figs., 5 tabs

  17. Analyzing power in pp scattering at low energies: the Paris potential predictions

    International Nuclear Information System (INIS)

    Cote, J.; Pires, P.; Tourreil, R. de; Lacombe, M.; Loiseau, B.; Vinh Mau, R.

    1979-12-01

    Predictions of the Paris potential for the analyzing power in pp scattering at low energies are compared with recent high precision measurements at 6.14MeV and earlier measurements at 10 and 16MeV. Phase shift values are also presented and discussed in view of previous analyses

  18. Proton optical potential and scattering matrix for tin nuclei at sub-coulomb energies

    International Nuclear Information System (INIS)

    Guzhovskij, B.Ya.; Dzyuba, B.M.

    1981-01-01

    A unified set of parameters of the proton optical potential (OP) for the n nuclei is searched for in the below-Coulomb-barrier energy range. The set must describe well the experimental data on the pn-reaction total cross sections and on the angular distributions of elastically scattered protons at E [ru

  19. On the completeness of the natural modes for quantum mechanical potential scattering

    NARCIS (Netherlands)

    Hoenders, B.J.

    1979-01-01

    The set of natural modes, associated with quantum mechanical scattering from a central potential of finite-range is shown to be complete. The natural modes satisfy a non-Hermitian homogeneous integral equation, or alternatively, are solutions of the time independent Schrödinger equation subject to a

  20. Investigation of second-order optical potential for elastic π4He scattering

    International Nuclear Information System (INIS)

    Mach, R.; Sapozhnikov, M.G.

    1982-01-01

    The calculations of elastic π - 4 He scattering within the framework of the optical model with a second-order potential were performed. The effects of recoil correlations, charge exchange and double spin (isospin) flip in the inter-- mediate states are studied. The correction of the impulse approximation is investigated. Comparison between Kerman-McManus-Thaler and Watson formalisms is made

  1. Role of potential scattering in the Shiba-Rusinov theory of the magnetic impurities in superconductors

    International Nuclear Information System (INIS)

    Okabe, Y.; Nagi, A.D.S.

    1983-01-01

    The Shiba-Rusinov theory of magnetic impurities in a superconductor is investigated, with special attention paid to the role of the potential scattering term in the electron-impurity interaction. The meaning of Anderson's theorem in the Shiba-Rusinov theory is discussed

  2. Optical potential study of positron scattering by hydrogenic-type atoms

    International Nuclear Information System (INIS)

    Kuru Ratnavelu; Nithyanandan Natchimuthu; Kalai Kumar Rajgopal

    1999-01-01

    An optical potential method based on the close-coupling formalism has been implemented to study positron scattering by hydrogenic-type atoms. The present work will be reviewed in the context of other theories. Preliminary results will be presented and compared with experimental results. (author)

  3. Non-commutative Hardy inequalities

    DEFF Research Database (Denmark)

    Hansen, Frank

    2009-01-01

    We extend Hardy's inequality from sequences of non-negative numbers to sequences of positive semi-definite operators if the parameter p satisfies 1 1. Applications to trace functions are given. We introduce the tracial geometric mean...

  4. Localized second-order optical potential for electron scattering in terms of imaginary-frequency susceptibilities

    International Nuclear Information System (INIS)

    Valone, S.M.; Truhlar, D.G.; Thirumialai, D.

    1982-01-01

    A local approximation to the second-order optical potential for elastic scattering of low-energy electrons from ground-state atoms is expressed in terms of the imaginary-frequency susceptibilities of the atom due to a point charge and to modified perturbing potentials. This provides a basis for the physically appealing concept of regarding the perturbation due to the projectile as having a position-dependent effective frequency associated with it. The result is extended to higher energies with the use of the concept of a local kinetic energy. With a semiclassical approximation the result reduces to a simple general form that should be useful for model potential studies of electron-atom and electron-molecule scattering. Alternatively, variational functionals for the susceptibilities can be used to calculate the approximate optical potential most rigorously without making effective-frequency, average-kinetic-energy, or semiclassical approximations. Intermediate levels of rigor are also possible

  5. Hydrogen potential in β-V2H studied by deep inelastic neutron scattering

    International Nuclear Information System (INIS)

    Hempelmann, R.; Price, D.L.; Reiter, G.; Richter, D.

    1989-02-01

    Two complementary techniques of deep inelastic neutron scattering were used to study hydrogen in β-V 2 H: (i) by means of neutron vibrational spectroscopy we measured hydrogen vibrations up to the fourteenth order; from these data we derived the effective single-particle potential, the shape of which is a parabola with a flattened bottom, and the hydrogen wave functions. (ii) By means of neutron Compton scattering we determined the kinetic of energy of the hydrogen; the value agrees with that calculated from the vibrational ground-state wave function. 6 refs., 5 figs

  6. Scattering at low energies by potentials containing power-law corrections to the Coulomb interaction

    International Nuclear Information System (INIS)

    Kuitsinskii, A.A.

    1986-01-01

    The low-energy asymptotic behavior is found for the phase shifts and scattering amplitudes in the case of central potentials which decrease at infinity as n/r+ar /sup -a/,a 1. In problems of atomic and nuclear physics one is generally interested in collisions of clusters consisting of several charged particles. The effective interaction potential of such clusters contains long-range power law corrections to the Coulomb interaction that is presented

  7. Local vs. Non-local core potentials in electron scattering from sodium atoms

    International Nuclear Information System (INIS)

    Bartschat, K.; Bray, I.

    1996-02-01

    We have tested the use of a local potential instead of the non-local Hartree-Fock potential to represent exchange effects between the valence or the projectile electron and the core in electron scattering from sodium atoms For some of the most detailed observables in this collision system/ the results of the two approaches are nearly identical, even though the effect of the exchange part is shown to be particularly large. (authors). 16 refs., 4 figs

  8. Local versus non-local core potentials in electron scattering from sodium atoms

    International Nuclear Information System (INIS)

    Bartschat, K.; Bray, I.

    1996-01-01

    We have tested the use of a local potential instead of the non-local Hartree-Fock potential to represent exchange effects between the valence or the projectile electron and the core in electron scattering from sodium atoms. For some of the most detailed observables in this collision system, the results of the two approaches are nearly identical, even though the effect of the exchange part is shown to be particularly large. (Author)

  9. Scattering in a spherical potential: Motion of complex-plane poles and zeros

    International Nuclear Information System (INIS)

    Arndt, R.A.; Roper, L.D.

    1989-01-01

    Scattering of spinless nucleons in a spherical potential is examined with the use of a computer graphics simulation VSCAT. The potential is defined stepwise and the Schroedinger equation is solved to obtain wavefunctions, scattering phases, partial-wave total cross sections, and differential cross sections, which are then displayed graphically. For the particular case of a square well, partial-wave amplitudes are displayed over the complex momentum plane in a three-dimensional plot. The well depth is then varied to follow the motion of poles in the complex momentum plane as they become resonances and then are bound states. Also displayed are the partial-wave zeros, which are required to satisfy Levinson's theorem for multiple states. The requirement on well depth is developed to produce a specified number of bound states and enumerate the energies which, at a given well depth, create equal scattering phases in adjoining partial waves δ/sub l//sub -1/ = δ/sub l/ = δ/sub l//sub +1/. This symmetry of scattering phases exists for both repulsive and attractive square potentials. A square repulsive core is also studied, which has the same triple-point symmetry as the square well

  10. Bound and scattering wave functions for a velocity-dependent Kisslinger potential for l>0

    International Nuclear Information System (INIS)

    Jaghoub, M.I.

    2002-01-01

    Using formal scattering theory, the scattering wave functions are extrapolated to negative energies corresponding to bound-state poles. It is shown that the ratio of the normalized scattering and the corresponding bound-state wave functions, at a bound-state pole, is uniquely determined by the bound-state binding energy. This simple relation is proved analytically for an arbitrary angular momentum quantum number l>0, in the presence of a velocity-dependent Kisslinger potential. The extrapolation relation is tested analytically by solving the Schroedinger equation in the p-wave case exactly for the scattering and the corresponding bound-state wave functions when the Kisslinger potential has the form of a square well. A numerical resolution of the Schroedinger equation in the p-wave case and of a square-well Kisslinger potential is carried out to investigate the range of validity of the extrapolated connection. It is found that the derived relation is satisfied best at low energies and short distances. (orig.)

  11. Intermolecular potential for Ar + D2O from differential scattering cross sections, and its implications for the water pair potential

    International Nuclear Information System (INIS)

    Brooks, R.; Porter, R.A.R.; Kalos, F.; Grosser, A.E.

    1975-01-01

    A velocity selected molecular beam of D 2 O was crossed with a nozzle beam of Ar and the angular distribution of the scattered D 2 O was measured mass spectrometrically. By varying the velocity of the D 2 O beam, the differential cross section was measured at two collision energies. The experimental results were compared with synthetic differential cross sections calculated from Lennard-Jones and Kihara-Stockmayer trial potentials to determine potential parameters. Implications for the H 2 O pair potential are discussed

  12. Multichannel scattering amplitudes of microparticles in a quantum well with two-dimensional -potential

    International Nuclear Information System (INIS)

    Sedrakian, D.M.; Badalyan, D.H.; Sedrakian, L.R.

    2015-01-01

    Quasi-one-dimensional quantum particle scattering on two-dimensional δ-potential is considered. Analytical expressions for the amplitudes of the multi-channel transmission and reflection are given. The problem for the case when the number of channels is finite and equal N, and the particle falls on the potential moving through the channel l is solved. The case of a three channel scattering is studied in details. It is shown that under conditions k 2 → 0 and k 3 → 0 'overpopulation' of particles on the second and third channels occurs. The points of δ-potential location which provide a full 'overpopulation' of particles is also found

  13. Geometric approach to inverse scattering for the Schroedinger equation with magnetic and electric potentials

    International Nuclear Information System (INIS)

    Arians, S.

    1997-01-01

    We consider the Hamiltonian H=(p-A(x)) 2 /(2m)+V(x) of a quantum particle in a magnetic field B=rotA and a potential V in space dimensions ν≥2. If V is of short range, then the high-velocity limit of the scattering operator uniquely determines the magnetic field B and the potential V. If, in addition, long-range potentials V l are present, some knowledge of (the far out tail of) V l is needed to define a modified Dollard wave operator and a scattering operator S D . Again its high- velocity limit uniquely determines B and V=V s +V l . Moreover, we give explicit error bounds which are inverse proportional to the velocity. copyright 1997 American Institute of Physics

  14. Small angle x-ray scattering as a potential tool for cancer diagnosis

    International Nuclear Information System (INIS)

    Kitchen, M.; Siu, K.K.W.; Lewis, R.A.

    2003-01-01

    Full text: The diagnostic potential of Small Angle X-ray Scattering (SAXS) patterns has recently been investigated for malignant breast tissues. The demonstrated systematic differences in the scattering signatures of malignant, benign and normal breast tissue specimens are believed to arise from the changes in the fibrous proteins making up the extracellular matrix (ECM) with the disease progression. The technique may also have the potential to aid in the diagnosis of gliomas, a highly aggressive type of brain tumour. Although complex and difficult to interpret, SAXS data from malignant tissues may prove to be a more effective classification tool than conventional histology techniques. Here we present the methodology of the technique, as applied to breast cancer and brain tumour specimens to date, and some directions for future investigations. We also present a novel analysis method, which employs wavelet decomposition and a naive Bayesian classifier, as a potential semi-automated classification tool

  15. Effective channel approach to nuclear scattering at high energies

    International Nuclear Information System (INIS)

    Rule, D.W.

    1975-01-01

    The description of high energy nuclear reactions is considered within the framework of the effective channel approach. A variational procedure is used to obtain an expression for the Green's function in the effective channel, which includes the average fluctuation potential, average energy, and an additional term arising from the non-commutability of the kinetic energy operator and the effective target wave function. The resulting expression for the effective channel, containing one variational parameter, is used to obtain the coupling potential. The resulting formulation is applied to the elastic scattering of 1 GeV protons by 4 He nuclei. A simple Gaussian form is used for the spin--isospin averaged proton--nucleon interaction. The variational parameter in the effective channel wave function is fixed a posteriori via the total p-- 4 He cross section. The effect of the coupling to the effective channel is demonstrated, as well as the effect of each term in the coupled equation for this channel. The calculated elastic cross sections were compared to both the recent data from Saclay and the earlier Brookhaven data for the 1-GeV p-- 4 He elastic scattering cross section. Using proton--nucleus elastic scattering experiments to study the proton--nucleon elastic scattering amplitude is discussed. The main purpose of our study is to investigate the effects on the cross section of varying, within its estimated range of uncertainty, each parameter which enters into the coupled equations. The magnitude of these effects was found to be large enough to conclude that any effects due to dynamical correlations would be obscured by the uncertainties in the input parameters

  16. Sum rules for the ed - NN scattering reactions and microscopic potential field-theoretical approach

    International Nuclear Information System (INIS)

    Machivariani, A.I.

    1996-01-01

    The connections between the equal-time commutators of nucleon and photon field-operators and relativistic potential approach of ed - NN scattering equations is established. Namely, it is demonstrated that: 1) equal-time commutator between nucleon field operators generated completeness condition for NN interaction functions, 2) the off-mass shell contributions in γd - NN exchange currents or in microscopic NN potential are determined by equal time commutator between nucleon field operator and photon or nucleon source operators, and 3) equal-time commutators between source operators produce sum rules for same vertex functions and effective potentials [ru

  17. Phenomenological and microscopic optical potentials for 88 MeV 7Li scattering

    International Nuclear Information System (INIS)

    Steeden, M.F.; Coopersmith, J.; Cartwright, S.J.; Cohler, M.D.; Clarke, N.M.; Griffiths, R.J.

    1980-01-01

    The elastic scattering cross sections for 88 MeV 7 Li ions have been measured for targets of 24 26 Mg and 40 48 Ca. Analyses using both phenomenological and microscopic optical potentials provide information on the energy dependence of optical parameters, and the extent to which the potentials are determined for these light ions. The use of a double-folding microscopic model demonstrates the need for normalisation of the real potential by a factor of 0.5 in contrast to measurements at lower energies. The contribution of exchange effects, density dependence and break-up are discussed. (author)

  18. Energy-dependent microscopic optical potential for scattering of nucleons on light nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Farag, M.Y.H.; Esmael, E.H. [Cairo University, Physics Department, Faculty of Science, Giza (Egypt); Maridi, H.M. [Cairo University, Physics Department, Faculty of Science, Giza (Egypt); Taiz University, Physics Department, Faculty of Applied Science, Taiz (Yemen)

    2014-06-15

    We present an energy-dependent microscopic optical model potential for elastic scattering of nucleons on light nuclei. The single-folding model is used for the real part of the optical potential (OP), while the imaginary part is derived within the high-energy approximation theory. The energy dependence of the OP is determined from the parameterization of the volume integrals those calculated from the best-fit OP that fit the experimental data of the cross sections and analyzing powers. This energy-dependent OP is successfully applied to analyze the proton elastic scattering of {sup 4,6,i8}He, {sup 6,7}Li, and {sup 9,10}Be nuclei at low and intermediate incident energies up to 200MeV/nucleon. (orig.)

  19. Reconciling semiclassical and Bohmian mechanics. III. Scattering states for continuous potentials

    International Nuclear Information System (INIS)

    Trahan, Corey; Poirier, Bill

    2006-01-01

    In a previous paper [B. Poirier, J. Chem. Phys. 121, 4501 (2004)] a unique bipolar decomposition Ψ=Ψ 1 +Ψ 2 was presented for stationary bound states Ψ of the one-dimensional Schroedinger equation, such that the components Ψ 1 and Ψ 2 approach their semiclassical WKB analogs in the large-action limit. The corresponding bipolar quantum trajectories, as defined in the usual Bohmian mechanical formulation, are classical-like and well behaved, even when Ψ has many nodes or is wildly oscillatory. A modification for discontinuous potential stationary scattering states was presented in a second, companion paper [C. Trahan and B. Poirier, J. Chem. Phys.124, 034115 (2006), previous paper], whose generalization for continuous potentials is given here. The result is an exact quantum scattering methodology using classical trajectories. For additional convenience in handling the tunneling case, a constant-velocity-trajectory version is also developed

  20. Full-potential multiple scattering theory with space-filling cells for bound and continuum states.

    Science.gov (United States)

    Hatada, Keisuke; Hayakawa, Kuniko; Benfatto, Maurizio; Natoli, Calogero R

    2010-05-12

    We present a rigorous derivation of a real-space full-potential multiple scattering theory (FP-MST) that is free from the drawbacks that up to now have impaired its development (in particular the need to expand cell shape functions in spherical harmonics and rectangular matrices), valid both for continuum and bound states, under conditions for space partitioning that are not excessively restrictive and easily implemented. In this connection we give a new scheme to generate local basis functions for the truncated potential cells that is simple, fast, efficient, valid for any shape of the cell and reduces to the minimum the number of spherical harmonics in the expansion of the scattering wavefunction. The method also avoids the need for saturating 'internal sums' due to the re-expansion of the spherical Hankel functions around another point in space (usually another cell center). Thus this approach provides a straightforward extension of MST in the muffin-tin (MT) approximation, with only one truncation parameter given by the classical relation l(max) = kR(b), where k is the electron wavevector (either in the excited or ground state of the system under consideration) and R(b) is the radius of the bounding sphere of the scattering cell. Moreover, the scattering path operator of the theory can be found in terms of an absolutely convergent procedure in the l(max) --> ∞ limit. Consequently, this feature provides a firm ground for the use of FP-MST as a viable method for electronic structure calculations and makes possible the computation of x-ray spectroscopies, notably photo-electron diffraction, absorption and anomalous scattering among others, with the ease and versatility of the corresponding MT theory. Some numerical applications of the theory are presented, both for continuum and bound states.

  1. Laplace transforms of the Hulthén Green's function and their application to potential scattering

    Science.gov (United States)

    Laha, U.; Ray, S.; Panda, S.; Bhoi, J.

    2017-10-01

    We derive closed-form representations for the single and double Laplace transforms of the Hulthén Green's function of the outgoing wave multiplied by the Yamaguchi potential and write them in the maximally reduced form. We use the expression for the double transform to compute the low-energy phase shifts for the elastic scattering in the systems α-nucleon, α-He3, and α-H3. The calculation results agree well with the experimental data.

  2. Regge-pole description of potential scattering by means of the phase-integral method

    International Nuclear Information System (INIS)

    Amaha, A.

    1992-01-01

    The application of Regge-pole theory to different atomic and molecular scattering has shown to have promising interpretational power in the differential cross sections. Differential cross sections can be analysed in terms of interference between the 'background' amplitude and a few Regge-pole positions of the scattering matrix (S matrix) representing surface waves around the interaction region. By the analytic continuation of the radial Schroedinger differential equation into the complex plane of angular momentum one can determine the analytic properties of the S matrix which contains the physical information in the scattering processes. For interaction potentials fulfilling certain properties, the study of the S matrix leads to the study of the F matrix introduced by Froeman and Froeman for the treatment of connection problems for phase-integral solutions of the differential equation. In this thesis the quantum mechanical scattering problem is analysed in the framework of Regge-pole theory with the use of the complex-angular-momentum formalism. To determine the S matrix, the relevant F matrix elements which give the stokes constants are derived and their properties are studied. The poles of the S matrix for particular complex values of the angular momentum quantum number are the Regge-poles. Using the Regge-pole positions and residues together with the background integral, the differential cross sections are calculated and compared with corresponding partial-wave representations

  3. Use of two-potential theory in electron-molecule scattering: Application to wide-angle e-H2 scattering at 40 eV

    International Nuclear Information System (INIS)

    Ritchie, B.

    1984-01-01

    A Green's-function approach is used to solve the Schroedinger equation in an effective potential (V 0 ), which is the sum of independent-atom static potentials. The equation for the Green's function is conveniently solved in momentum space (MS), where the MS ''potentials'' (Fourier transforms of the atom-centered potentials) have translational symmetry. The Green's function is then used to construct the solution to the Schroedinger equation for scattering in the potential V-V 0 (where V is the e-molecule static potential plus a local exchange potential) relative to scattering in V 0 . This solution is found in coordinate space using single-center expansions about the internuclear midpoint. These are more rapidly convergent for V-V 0 than for V or V 0 alone. The sum of the amplitudes for scattering in V 0 and in V-V 0 relative to V 0 then represents the amplitude for scattering from the molecule. This method is intended to combine the dynamical methods best suited for each type of potential (multicenter for V 0 and single center for V-V 0 ). It also exposes the shortcomings of the use of V 0 alone

  4. Systematic analysis of α elastic scattering with the São Paulo potential

    Energy Technology Data Exchange (ETDEWEB)

    Charry-Pastrana, F. E., E-mail: feecharrypa@unal.edu.co; Pinilla, E. C. [Universidad Nacional de Colombia, Sede Bogotá, Facultad de Ciencias, Departamento de Física, Grupo de Física Nuclear, Carrera 45 No. 26-85, Edificio Uriel Gutiérrez, Bogotá D.C., Código Postal 111321 (Colombia)

    2016-07-07

    We describe systematically by collision energy and target mass, alpha elastic scattering angular distributions by using the São Paulo potential as the real part of the optical potential. The imaginary part is proportional to the real one by a factor N{sub i}. We find this parameter by fitting the theoretical angular distributions to the experimental cross sections through a χ{sup 2} minimization. The N{sub i} and their respective uncertainties, σ{sub Ni}, fall in the range 0.4 ≤ N{sub i} ± σ{sub N{sub i}} ≤ 0.8 for all the systems studied.

  5. Potentials and scattering cross sections for collisions of He atoms with adsorbed CO

    International Nuclear Information System (INIS)

    Liu, W.K.; Gumhalter, B.

    1986-05-01

    Ab initio calculations of the total scattering cross section for the collision system He → CO/Pt(111) within the renormalized distorted wave Born approximation are reported. The interaction potential for this atom-adsorbate system consists of the usual two-body gas phase-like potential as well as two additional substrate mediated van de Waals contributions, all with similar long range behaviour. Comparison of the calculated cross sections for various incident velocities and angles with available experimental data is made without using any adjustable parameters to fit the data, and the importance of including the substrate-mediated forces is emphasized. (author)

  6. Neutron scattering from elemental indium, the optical model, and the bound-state potential

    Energy Technology Data Exchange (ETDEWEB)

    Chiba, S. (Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan)); Guenther, P.T.; Lawson, R.D.; Smith, A.B. (Argonne National Lab., IL (USA))

    1990-06-01

    Neutron differential elastic-scattering cross sections of elemental indium are measured from 4.5 to 10 MeV at incident-energy intervals of {approx}500 keV. Seventy or more differential values are obtained at each incident energy, distributed between {approx}18{degree} and 160{degree}. These experimental results are combined with lower-energy values previously obtained at this laboratory, and with 11 and 14 MeV results in the literature, to form a comprehensive elastic-scattering database extending from {approx}1.5 to 14 MeV. These data are interpreted in terms of a conventional spherical optical model. The resulting potential is extrapolated to the bound-state regime. It is shown that in the middle of the 50--82 neutron shell, the potential derived from the scattering results adequately describes the binding energies of article states, but does not do well for hole states. The latter shortcoming is attributed to the holes states having occupational probabilities sufficiently different from unity, so that the exclusion principle become a factor, and to the rearrangement of the neutron core. 68 refs.

  7. Neutron scattering from elemental indium, the optical model, and the bound-state potential

    International Nuclear Information System (INIS)

    Chiba, S.; Guenther, P.T.; Lawson, R.D.; Smith, A.B.

    1990-01-01

    Neutron differential elastic-scattering cross sections of elemental indium are measured from 4.5 to 10 MeV at incident-energy intervals of ∼500 keV. Seventy or more differential values are obtained at each incident energy, distributed between ∼18 degree and 160 degree. These experimental results are combined with lower-energy values previously obtained at this laboratory, and with 11 and 14 MeV results in the literature, to form a comprehensive elastic-scattering database extending from ∼1.5 to 14 MeV. These data are interpreted in terms of a conventional spherical optical model. The resulting potential is extrapolated to the bound-state regime. It is shown that in the middle of the 50--82 neutron shell, the potential derived from the scattering results adequately describes the binding energies of article states, but does not do well for hole states. The latter shortcoming is attributed to the holes states having occupational probabilities sufficiently different from unity, so that the exclusion principle become a factor, and to the rearrangement of the neutron core. 68 refs

  8. Analyses of the energy-dependent single separable potential models for the NN scattering

    International Nuclear Information System (INIS)

    Ahmad, S.S.; Beghi, L.

    1981-08-01

    Starting from a systematic study of the salient features regarding the quantum-mechanical two-particle scattering off an energy-dependent (ED) single separable potential and its connection with the rank-2 energy-independent (EI) separable potential in the T-(K-) amplitude formulation, the present status of the ED single separable potential models due to Tabakin (M1), Garcilazo (M2) and Ahmad (M3) has been discussed. It turned out that the incorporation of a self-consistent optimization procedure improves considerably the results of the 1 S 0 and 3 S 1 scattering phase shifts for the models (M2) and (M3) up to the CM wave number q=2.5 fm -1 , although the extrapolation of the results up to q=10 fm -1 reveals that the two models follow the typical behaviour of the well-known super-soft core potentials. It has been found that a variant of (M3) - i.e. (M4) involving one more parameter - gives the phase shifts results which are generally in excellent agreement with the data up to q=2.5 fm -1 and the extrapolation of the results for the 1 S 0 case in the higher wave number range not only follows the corresponding data qualitatively but also reflects a behaviour similar to the Reid soft core and Hamada-Johnston potentials together with a good agreement with the recent [4/3] Pade fits. A brief discussion regarding the features resulting from the variations in the ED parts of all the four models under consideration and their correlations with the inverse scattering theory methodology concludes the paper. (author)

  9. P11 πN scattering in a potential model and in the cloudy bag model

    International Nuclear Information System (INIS)

    Rinat, A.S.

    1982-01-01

    We discuss P 11 πN scattering in a model where the π is coupled to quark bags for baryons N, R, Δ. From the underlying qqπ couplings we derive B'Bπ vertices which are used in a solution of a πN, πΔ two-channel scattering problem. Using one bag radius from a fit to P 33 πN data, we are unable to reproduce delta 11 . A fit requires a Roper radius Rsub(R) > Rsub(N). We discuss the sensitivity of the fit to small variations in other bag parameters. The theory is compared with a simple potential model and with field theories employing baryons instead of quark fields. (orig.)

  10. Invariant potential for elastic pion--nucleus scattering. Technical report No. 75-075

    International Nuclear Information System (INIS)

    Cammarata, J.B.; Banerjee, M.K.

    1975-04-01

    From the Wick-Dyson expansion of the exact propagator of a pion in the presence of a nucleus an invariant potential for crossing symmetric, elastic pion-nucleus scattering is obtained in terms of a series of pion-nucleon diagrams. The Chew-Low theory is used to develop a model in which the most important class of diagrams is effectively summed. Included in this model is the Exclusion Principle restriction on the pion-bound nucleon interaction, the effects of the binding of nucleons, a kinematic transformation of energy from the lab to the πN center of mass frames, and the Fermi motion and recoil of the target nucleons. From a numerical study of the effects of these processes on the π- 12 C total cross section, the relative importance of each is determined. Other processes contributing to the elastic scattering of pions not included in the present model are also discussed. (9 figures) (U.S.)

  11. Energy-Dependent microscopic optical potential for p+{sup 9}Be elastic scattering

    Energy Technology Data Exchange (ETDEWEB)

    Maridi, H. M., E-mail: h.maridi@gmail.com [Physics Department, Faculty of Science, Cairo University, Giza 12613 (Egypt); Physics Department, Faculty of Applied Science, Taiz University, Taiz (Yemen); Farag, M. Y. H., E-mail: yehiafarag@cu.edu.eg; Esmael, E. H. [Physics Department, Faculty of Applied Science, Taiz University, Taiz (Yemen)

    2016-06-10

    The p+{sup 9}Be elastic scattering at an energy range up to 200 MeV/nucleon is analyzed using the single-folding model. The density- and isospin-dependent M3Y-Paris nucleon-nucleon (NN) interaction is used for the real part and the NN-scattering amplitude of the high-energy approximation for the imaginary one. The analysis reveals that the cross-section data are reproduced well at energies up to 100 MeV/nucleon by use of the partial-wave expansion. For higher energies, the eikonal approximation give results better than the partial-wave expansion calculations. The volume integrals of the optical-potential parts have systematic energy dependencies, and they are parameterized in empirical formulas.

  12. Multilevel fast multipole method based on a potential formulation for 3D electromagnetic scattering problems.

    Science.gov (United States)

    Fall, Mandiaye; Boutami, Salim; Glière, Alain; Stout, Brian; Hazart, Jerome

    2013-06-01

    A combination of the multilevel fast multipole method (MLFMM) and boundary element method (BEM) can solve large scale photonics problems of arbitrary geometry. Here, MLFMM-BEM algorithm based on a scalar and vector potential formulation, instead of the more conventional electric and magnetic field formulations, is described. The method can deal with multiple lossy or lossless dielectric objects of arbitrary geometry, be they nested, in contact, or dispersed. Several examples are used to demonstrate that this method is able to efficiently handle 3D photonic scatterers involving large numbers of unknowns. Absorption, scattering, and extinction efficiencies of gold nanoparticle spheres, calculated by the MLFMM, are compared with Mie's theory. MLFMM calculations of the bistatic radar cross section (RCS) of a gold sphere near the plasmon resonance and of a silica coated gold sphere are also compared with Mie theory predictions. Finally, the bistatic RCS of a nanoparticle gold-silver heterodimer calculated with MLFMM is compared with unmodified BEM calculations.

  13. Near-threshold quantization and scattering for deep potentials with attractive tails

    International Nuclear Information System (INIS)

    Eltschka, Christopher; Moritz, Michael J.; Friedrich, Harald

    2000-01-01

    Near-threshold properties of bound and continuum states in a deep potential with an attractive tail depend essentially on a few 'tail parameters', which are determined by the properties of the potential tail beyond the region of r-values where WKB wavefunctions are accurate solutions of the Schroedinger equation. One of these tail parameters is a length parameter which defines the singular contribution to the level density just below threshold and the reflectivity of the tail of the potential just above threshold; another is a phase difference which, together with the length parameter, determines the mean scattering length. The near-threshold quantization rule and the actual scattering length are determined by the tail parameters together with a dimensionless constant depending on the zero-energy value of the WKB action integral. We study potentials with tails consisting of two inverse-power terms, V(r)∼-C α /r α -C α 1 /r α 1 ,α 1 >α>2and we derive exact analytical expressions for the tail parameters in the special case α 1 =2(α-1). This enables us to demonstrate the effect of a significant non-homogeneity of the potential tail on the results derived previously for homogeneous tails. (author)

  14. Scattering states of the Klein-Gordon equation with Coulomb-like scalar plus vector potentials in arbitrary dimension

    International Nuclear Information System (INIS)

    Chen Changyuan; Sun Dongsheng; Lu Falin

    2004-01-01

    Properties of scattering states of the Klein-Gordon equation with Coulomb-like scalar plus vector potentials are investigated in an arbitrary dimension. Exact results of normalized wave functions of scattering states in the 'k/2π scale' and formula of phase shifts are presented

  15. Which potentials have to be surface peaked to reproduce large angle proton scattering at high energy?

    International Nuclear Information System (INIS)

    Raynal, J.

    1990-01-01

    Corrections to the usual form factors of the optical potential are studied with a view to getting a better fit for proton elastic scattering at large angles on 40 Ca at 497 and 800 MeV. When a real surface form factor is added to the central potential in the Schrodinger formalism, the experimental data are as well reproduced as in the standard Dirac formalism. Coupling to the strong 3 - collective state gives a better fit. The use of surface corrections to the imaginary Dirac potential also gives improved results. A slightly better fit is obtained by coupling to the 3 - state with, at the same time, a weakening of these corrections. Further corrections to the potential do not give significant improvements

  16. Microscopic local optical potentials and the nucleon–nucleus scattering at 65 MeV

    International Nuclear Information System (INIS)

    Haider, W.; Sharma, Manjari

    2010-01-01

    Microscopic local optical potentials from two sources were calculated by folding the numerical g-matrices over point proton and neutron RMF densities of target nuclei. The hard-core Hamada–Johnston and the soft-core Urbana v-14 local inter-nucleon potentials have been used to generate numerical g-matrices by solving Bethe–Goldstone integral equation. The calculated potentials have been used to analyze successfully both the proton and neutron differential elastic scattering and polarization data at 65 MeV over a wide mass region of targets: 12 C– 208 Pb. Comparison of the present results with a phenomenological optical model analyzes is also presented. Mass number dependence of the mean square radii of the two microscopic potentials are in close agreement with each other as well as with empirical results. (author)

  17. The scattering potential of partial derivative wavefields in 3-D elastic orthorhombic media: an inversion prospective

    KAUST Repository

    Oh, Ju-Won

    2016-07-04

    Multiparameter full waveform inversion (FWI) applied to an elastic orthorhombic model description of the subsurface requires in theory a nine-parameter representation of each pixel of the model. Even with optimal acquisition on the Earth surface that includes large offsets, full azimuth, and multicomponent sensors, the potential for trade-off between the elastic orthorhombic parameters are large. The first step to understanding such trade-off is analysing the scattering potential of each parameter, and specifically, its scattering radiation patterns. We investigate such radiation patterns for diffraction and for scattering from a horizontal reflector considering a background isotropic model. The radiation patterns show considerable potential for trade-off between the parameters and the potentially limited resolution in their recovery. The radiation patterns of C11, C22, and C33 are well separated so that we expect to recover these parameters with limited trade-offs. However, the resolution of their recovery represented by recovered range of model wavenumbers varies between these parameters. We can only invert for the short wavelength components (reflection) of C33 while we can mainly invert for the long wavelength components (transmission) of the elastic coefficients C11 and C22 if we have large enough offsets. The elastic coefficients C13, C23, and C12 suffer from strong trade-offs with C55, C44, and C66, respectively. The trade-offs between C13 and C55, as well as C23 and C44, can be partially mitigated if we acquire P–SV and SV–SV waves. However, to reduce the trade-offs between C12 and C66, we require credible SH–SH waves. The analytical radiation patterns of the elastic constants are supported by numerical gradients of these parameters.

  18. Reconciling semiclassical and Bohmian mechanics. II. Scattering states for discontinuous potentials

    International Nuclear Information System (INIS)

    Trahan, Corey; Poirier, Bill

    2006-01-01

    In a previous paper [B. Poirier, J. Chem. Phys. 121, 4501 (2004)] a unique bipolar decomposition, Ψ=Ψ 1 +Ψ 2 , was presented for stationary bound states Ψ of the one-dimensional Schroedinger equation, such that the components Ψ 1 and Ψ 2 approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to Ψ itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well behaved, even when Ψ has many nodes or is wildly oscillatory. In this paper, the previous decomposition scheme is modified in order to achieve the same desirable properties for stationary scattering states. Discontinuous potential systems are considered (hard wall, step potential, and square barrier/well), for which the bipolar quantum potential is found to be zero everywhere, except at the discontinuities. This approach leads to an exact numerical method for computing stationary scattering states of any desired boundary conditions, and reflection and transmission probabilities. The continuous potential case will be considered in a companion paper [C. Trahan and B. Poirier, J. Chem. Phys. 124, 034116 (2006), following paper

  19. Two-body relativistic scattering with an O(1,1)-symmetric square-well potential

    International Nuclear Information System (INIS)

    Arshansky, R.; Horwitz, L.P.

    1984-01-01

    Scattering theory in the framework of a relativistic manifestly covariant quantum mechanics is applied to the relativistic analog of the nonrelativistic one-dimensional square-well potential, a two-body O(1,1)-symmetric hyperbolic square well in one space and one time dimension. The unitary S matrix is explicitly obtained. For well sizes large compared to the de Broglie wavelength of the reduced motion system, simple formulas are obtained for the associated sequence of resonances. This sequence has equally spaced levels and constant widths for higher resonances, and linearly increasing widths for lower-lying levels

  20. The optical potential for 6Li-6Li elastic scattering at 156 MeV

    International Nuclear Information System (INIS)

    Micek, S.; Majka, Z.; Klewe-Nebenius, H.; Rebel, H.; Gils, H.J.

    1984-10-01

    Elastic scattering of 6 Li from 6 Li has been studied for the beam energy of 156 MeV. The experimental differential cross section has been analysed on the basis of the optical model using various phenomenological forms. The spin-orbit interaction proves to be less significant. A semi-microscopic double-folding cluster model which generates the real part of the optical potential by an antisymmetrized d-α cluster wave function of 6 Li and α-α, d-d and d-α interactions is well able to describe the experimental data. (orig.) [de

  1. Single-site Green function of the Dirac equation for full-potential electron scattering

    Energy Technology Data Exchange (ETDEWEB)

    Kordt, Pascal

    2012-05-30

    I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schroedinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity. (orig.)

  2. Single-site Green function of the Dirac equation for full-potential electron scattering

    International Nuclear Information System (INIS)

    Kordt, Pascal

    2012-01-01

    I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schroedinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity. (orig.)

  3. Dynamic. cap alpha. -transfer polarisation potentials and the large angle scattering of /sup 16/O + /sup 28/Si

    Energy Technology Data Exchange (ETDEWEB)

    Hussein, M S; Aleixo, A N; Canto, L F; Carrilho, P; Donangelo, R; Paula, L.S. de

    1987-07-01

    A closed expression is derived for the dynamic ..cap alpha..-transfer polarisation potential for heavy-ion elastic scattering. The back-angle angular distributions for the elastic scattering of /sup 16/O + /sup 28/Si obtained by adding this polarisation potential to the E-18 interaction are shown to be in good agreement with the data if an ..cap alpha..-transfer spectroscopic factor of 0.4 is used.

  4. Description of nucleon scattering on 208Pb by a fully Lane-consistent dispersive spherical optical model potential

    Science.gov (United States)

    Sun, W. L.; Wang, J.; Soukhovitskii, E. Sh.; Capote, R.; Quesada, J. M.

    2017-09-01

    A fully Lane-consistent dispersive spherical optical potential is proposed to describe nucleon scattering interaction with doubly magic nucleus 208Pb up to 200 MeV. The experimental neutron total cross sections, elastically scattered nucleon angular distributions and (p,n) data had been used to search the potential parameters. Good agreement between experiments and the calculations with this potential is observed. Meanwhile, the application of the determined optical potential with the same parameters to neighbouring near magic Pb-Bi isotopes is also examined to show the predictive power of this potential.

  5. An optical potential from inversion of the 350 MeV 16 O - 16 O scattering data

    International Nuclear Information System (INIS)

    Allen, L.J.; Berge, L.; Steward, C.; Lipperheide, R.; Froebrich, P.

    1992-01-01

    A quantal inversion of the 16 O- 16 O scattering data at 350 MeV yields an optical potential which gives an excellent fit (χ 2 /F = 1.65) to the measured cross-section. The real part of this potential is shallower than any potential used by others for distances between 2 and 6 fm. The imaginary potential is also relatively weak. This potential does not favour a rainbow interpretation of the structure in data observed at large scattering angles. 12 refs., 1 tab., 4 figs

  6. A new potential of π-nucleus scattering and its application to nuclear structure study using elastic scattering and charge exchange reactions

    International Nuclear Information System (INIS)

    Durand, Gerard.

    1974-01-01

    First the different theories used for studying pion-nucleus scattering and especially Glauber microscopic model and Kisslinger optical model are summarized. From the comparison of these two theories it was concluded that Kisslinger's was better for studying pion-nucleus scattering near the (3/2-3/2) resonance. The potential was developed, with a local corrective term, proposed by this author. This new term arises from taking into account correctly the Lorentz transformation from the pion-nucleon center of mass to the pion nucleus center of mass system. A coupled-channel formalism was developed allowing the study of pion-nucleus elastic scattering and also the study of single and double charge exchange reactions on nucleus with N>Z. The influence of the new term and the shape of nucleon densities on π- 12 C scattering was studied near 200MeV. It was found that at the nucleus surface the neutron density was larger than the proton density. On the other hand, a maximum of sensibility to the different nuclear parameters was found near 180MeV and for elastic scattering angles greater than 100 deg. The calculations of the total cross section for simple and double charge exchange for 13 C and 63 Cu yielded results simular to those of previous theories and showed the same discrepancy between theory and experiment in the resonance region [fr

  7. Spin-dependent scattering by a potential barrier on a nanotube

    International Nuclear Information System (INIS)

    Abranyos, Yonatan; Gumbs, Godfrey; Fekete, Paula

    2010-01-01

    The electron spin effects on the surface of a nanotube have been considered through the spin-orbit interaction (SOI), arising from the electron confinement on the surface of the nanotube. This is of the same nature as the Rashba-Bychkov SOI at a semiconductor heterojunction. We estimate the effect of disorder within a potential barrier on the transmission probability. Using a continuum model, we obtain analytic expressions for the spin-split energy bands for electrons on the surface of nanotubes in the presence of SOI. First we calculate analytically the amplitudes of scattering from a potential barrier located around the axis of the nanotube into spin-dependent states. The effect of disorder on the scattering process is included phenomenologically and induces a reduction in the transition probability. We analyze the relative role of SOI and disorder in the transmission probability which depends on the angular and linear momentum of the incoming particle, and its spin orientation. Finally we demonstrate that in the presence of disorder, perfect transmission may not be achieved for finite barrier heights.

  8. Comparison of local exchange potentials for electron--N2 scattering

    International Nuclear Information System (INIS)

    Rumble, J.R. Jr.; Truhlar, D.G.

    1980-01-01

    We consider vibrationally and electronically elastic electron scattering by N 2 at 2--30 eV impact energy. We consider static, static-exchange, and static--exchange-plus-polarization potentials, Cade--Sales--Wahl and INDO/1s wave functions, and semiclassical exchange and Hara free-electron--gas exchange potentials. We show that the semiclassical exchange approximation is too attractive at low energy for N 2 . We show quantitatively by consideration of partial and total integral cross sections how the effects of approximations to exchange become smaller as the incident energy is increased until these differences are about 8% for the total integral cross section at 30 eV

  9. The new nucleon-nucleon scattering data and the Paris potential predictions

    International Nuclear Information System (INIS)

    Lacombe, M.; Loiseau, B.; Vinh Mau, R.; Cote, J.; Pires, P.

    1980-11-01

    New data (cross section, polarization, Wolfenstein parameters and spin-correlations) on proton-proton and neutron-proton scattering have been recently published by different groups. These include high precision and/or original measurements covering the energy range 6 MeV < Tsub(lab)< 800 MeV. A direct comparison of these data with the values produced by the Paris NN potential for energies Tsub(lab) < 350 MeV is reported here. The agreement between theory and experiment is very satisfactory both for low and medium energies. The total chi-squared for the world NN data set for Tsub(lab) < 350 MeV is also reported and compared with those given by the Arndt et al. phase shift-analysis and by the phenomenological Reid soft-core potential

  10. P-odd two-pion potentials and asymmetry of pp scattering at low energies

    International Nuclear Information System (INIS)

    Musakhanov, M.M.; Podgornov, Y.Y.

    1986-01-01

    The asymmetry of pp scattering A/sub p//sub p/ is calculated using the potential approach for incident proton energies of 15 and 45 MeV taking into account the isovector P-odd two-pion interaction. The corresponding 2π potentials are obtained in the static approximation of the noncovariant technique taking into account Δ-isobar configurations. The pion-baryon cutoff form factors are taken from chiral bag models. Owing to the lack of reliable information on the nucleon bag radius R, the contribution of 2π exchange to A/sub p//sub p/ is given for the fairly wide range R = 0.4--1.0 F. The strong interaction is taken into account by the introduction of the phenomenological Reid soft-core and Paris potentials. It is shown that most of the 2π-exchange contribution comes from the region where the internucleon separations are larger than they are where the contribution of rho 0 - and ω-meson exchange dominates and that the former contribution must be included in A/sub p//sub p/. The resulting contribution of the 2π potential to A/sub p//sub p/ is of the same order as the contribution of the rho 0 and ω potentials

  11. Semiclassical expansion of quantum characteristics for many-body potential scattering problem

    International Nuclear Information System (INIS)

    Krivoruchenko, M.I.; Fuchs, C.; Faessler, A.

    2007-01-01

    In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star-product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical coordinates and momenta, can be used to solve the evolution equations for symbols of other operators acting in the Hilbert space. To any fixed order in the Planck's constant, many-body potential scattering problem simplifies to a statistical-mechanical problem of computing an ensemble of quantum characteristics and their derivatives with respect to the initial canonical coordinates and momenta. The reduction to a system of ordinary differential equations pertains rigorously at any fixed order in ℎ. We present semiclassical expansion of quantum characteristics for many-body scattering problem and provide tools for calculation of average values of time-dependent physical observables and cross sections. The method of quantum characteristics admits the consistent incorporation of specific quantum effects, such as non-locality and coherence in propagation of particles, into the semiclassical transport models. We formulate the principle of stationary action for quantum Hamilton's equations and give quantum-mechanical extensions of the Liouville theorem on conservation of the phase-space volume and the Poincare theorem on conservation of 2p-forms. The lowest order quantum corrections to the Kepler periodic orbits are constructed. These corrections show the resonance behavior. (Abstract Copyright [2007], Wiley Periodicals, Inc.)

  12. The threshold behaviour of scattering phase shifts in singular potentials; Das Schwellenverhalten von Streuphasen in singulaeren Potentialen

    Energy Technology Data Exchange (ETDEWEB)

    Arnecke, Florian

    2009-01-19

    In this thesis we have studied the threshold behaviour od scattering phases in attactive, singular potentials proportional to -1/r{sup {alpha}}, {alpha}>2, in two and three dimensions. Total absorption on the surface was described by incoming boundary condition in form of WKB waves, so that the scattering phase {delta}(k) is because of the particle loss a complex quantity and the S matrix no longer unitary. As application example we use the scattering behaviour of ultracold atoms on an absorbing sphere. The parameters were so chosen that they correspond to those of metastable helium (2{sup 3}S) atoms respectively sodium atoms in the ground state and a radius of the sphere of 200 respectively 2000 a. u. The final chapter presents a survey about the scattering on a circularly symmetric potential in two dimensions.

  13. Regularization and the potential of effective field theory in nucleon-nucleon scattering

    International Nuclear Information System (INIS)

    Phillips, D.R.

    1998-04-01

    This paper examines the role that regularization plays in the definition of the potential used in effective field theory (EFT) treatments of the nucleon-nucleon interaction. The author considers N N scattering in S-wave channels at momenta well below the pion mass. In these channels (quasi-)bound states are present at energies well below the scale m π 2 /M expected from naturalness arguments. He asks whether, in the presence of such a shallow bound state, there is a regularization scheme which leads to an EFT potential that is both useful and systematic. In general, if a low-lying bound state is present then cutoff regularization leads to an EFT potential which is useful but not systematic, and dimensional regularization with minimal subtraction leads to one which is systematic but not useful. The recently-proposed technique of dimensional regularization with power-law divergence subtraction allows the definition of an EFT potential which is both useful and systematic

  14. Light scattering changes follow evoked potentials from hippocampal Schaeffer collateral stimulation

    DEFF Research Database (Denmark)

    Rector, D M; Poe, G R; Kristensen, Morten Pilgaard

    1997-01-01

    , concurrently with larger population postsynaptic potentials. Optical signals occurred over a time course similar to that for electrical signals and increased with larger stimulation amplitude to a maximum, then decreased with further increases in stimulation current. Camera images revealed a topographic......We assessed relationships of evoked electrical and light scattering changes from cat dorsal hippocampus following Schaeffer collateral stimulation. Under anesthesia, eight stimulating electrodes were placed in the left hippocampal CA field and an optic probe, coupled to a photodiode or a charge....... Electrode recordings and photodiode output were simultaneously acquired at 2.4 kHz during single biphasic pulse stimuli 0.5 ms in duration with 0.1-Hz intervals. Camera images were digitized at 100 Hz. An average of 150 responses was calculated for each of six stimulating current levels. Stimuli elicited...

  15. Further application of angular momentum dependent potentials to proton elastic scattering

    International Nuclear Information System (INIS)

    Kobos, A.M.; Mackintosh, R.S.

    1981-01-01

    We extend our application of the iota-dependent model to a wider range of cases. We include more non-closed shell nuclei and some heavy nuclei as targets, getting better fits than previously found, with no substantial exceptions to the systematic properties of the iota-dependent potential. For one mass sequence we find shell effects, but note that the results would be more certain if more analysing powers data were available. A simple pattern of iota-dependence is a universal feature of proton scattering between 20 and 60 MeV. Since the effect on (p,p') is large the effect of iota-dependence on direct reactions should not be ignored. (author)

  16. Tetraquark resonances computed with static lattice QCD potentials and scattering theory

    Directory of Open Access Journals (Sweden)

    Bicudo Pedro

    2018-01-01

    Full Text Available We study tetraquark resonances with lattice QCD potentials computed for two static quarks and two dynamical quarks, the Born-Oppenheimer approximation and the emergent wave method of scattering theory. As a proof of concept we focus on systems with isospin I = 0, but consider different relative angular momenta l of the heavy b quarks. We compute the phase shifts and search for S and T matrix poles in the second Riemann sheet. We predict a new tetraquark resonance for l = 1, decaying into two B mesons, with quantum numbers I(JP = 0(1−, mass m=10576−4+4 MeV and decay width Γ=112−103+90 MeV.

  17. Resonating rays in ion-ion scattering from an optical potential

    International Nuclear Information System (INIS)

    Farhan, A.R.; Stoyanov, B.J.; Nagl, A.; Uberall, H.; de Llano, M.

    1986-01-01

    The amplitude of ion-ion scattering, described, e.g., by an optical potential, separates into a ''surface-wave'' part (which, as shown before, may give rise to resonances) and a ''geometrical-ray'' part. The amplitude as alternately expressed here by the Wentzel-Kramers-Brillouin approximation resolves into an externally reflected ''barrier wave'' and into ''internal'' or ''penetrating rays'' that undergo an internal reflection together with possible additional multiple reflections. Our numerical calculations show that resonances also occur in the penetrating rays, which take place when a characteristic equation is satisfied. The geometrical meaning of the latter is determined by the optical path length of penetration being an integer multiple of π, plus a 1/2π caustic phase jump, and an extra phase shift due to barrier penetration

  18. Investigation of the shape of the imaginary part of the optical-model potential for electron scattering by rare gases

    International Nuclear Information System (INIS)

    Staszewska, G.; Schwenke, D.W.; Truhlar, D.G.

    1984-01-01

    We present a comparative study of several empirical and nonempirical models for the absorption potential, which is the imaginary part of an optical-model potential, for electron scattering by rare gases. We show that the elastic differential cross section is most sensitive to the absorption potential for high-impact energy and large scattering angles. We compare differential cross sections calculated by several models for the absorption potential and by several arbitrary modifications of these model potentials. We are able to associate the effect of the absorption potential on the elastic differential cross section with its form at small electron-atom distances r, and we are able to deduce various qualitative features that the absorption potential must possess at small and large r in order to predict both accurate differential cross sections and accurate absorption cross sections. Based on these observations, the Pauli blocking conditions of the quasifree scattering model for the absorption potential are modified empirically, thus producing a more accurate model that may be applied to other systems; e.g., electron-molecule scattering, with no adjustable parameters

  19. Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

    Science.gov (United States)

    Liu, Xianglin; Wang, Yang; Eisenbach, Markus; Stocks, G. Malcolm

    2018-03-01

    The Green function plays an essential role in the Korringa-Kohn-Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn-Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). The pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. By using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.

  20. Estimate of repulsive interatomic pair potentials by low-energy alkali-metal-ion scattering and computer simulation

    International Nuclear Information System (INIS)

    Ghrayeb, R.; Purushotham, M.; Hou, M.; Bauer, E.

    1987-01-01

    Low-energy ion scattering is used in combination with computer simulation to study the interaction potential between 600-eV potassium ions and atoms in metallic surfaces. A special algorithm is described which is used with the computer simulation code marlowes. This algorithm builds up impact areas on the simulated solid surface from which scattering cross sections can be estimated with an accuracy better than 1%. This can be done by calculating no more than a couple of thousand trajectories. The screening length in the Moliere approximation to the Thomas-Fermi potential is fitted in such a way that the ratio between the calculated cross sections for double and single scattering matches the scattering intensity ratio measured experimentally and associated with the same mechanisms. The consistency of the method is checked by repeating the procedure for different incidence conditions and also by predicting the intensities associated with other surface scattering mechanisms. The screening length estimates are found to be insensitive to thermal vibrations. The calculated ratios between scattering cross sections by different processes are suggested to be sensitive enough to the relative atomic positions in order to be useful in surface-structure characterization

  1. Various scattering properties of a new PT-symmetric non-Hermitian potential

    Energy Technology Data Exchange (ETDEWEB)

    Ghatak, Ananya, E-mail: gananya04@gmail.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India); Mandal, Raka Dona Ray, E-mail: rakad.ray@gmail.com [Department of Physics, Rajghat Besant School, Varanasi-221001 (India); Mandal, Bhabani Prasad, E-mail: bhabani.mandal@gmail.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India)

    2013-09-15

    We complexify a 1-d potential V(x)=V{sub 0}cosh{sup 2}μ(tanh[(x−μd)/d]+tanh(μ)){sup 2} which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters (μ,d) becomes imaginary. For the case of μ→iμ, we have an entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from the left (or right) at certain discrete energies. The penetrating states in the other case (d→id) are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. The presence of MSS and reflectionlessness is also discussed for the free states in the later case. -- Highlights: •Existence of multiple spectral singularities (MSS) in PT-symmetric non-Hermitian system is shown. •Reciprocity is restored at discrete positive energies even for parity non-invariant complex system. •Co-existence of MSS with deep energy minima of transitivity is obtained. •Possibilities of both unidirectional and bidirectional invisibility are explored for a non-Hermitian system. •Penetrating states are shown to be reciprocal for all energies for PT-symmetric system.

  2. Various scattering properties of a new PT-symmetric non-Hermitian potential

    International Nuclear Information System (INIS)

    Ghatak, Ananya; Mandal, Raka Dona Ray; Mandal, Bhabani Prasad

    2013-01-01

    We complexify a 1-d potential V(x)=V 0 cosh 2 μ(tanh[(x−μd)/d]+tanh(μ)) 2 which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters (μ,d) becomes imaginary. For the case of μ→iμ, we have an entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from the left (or right) at certain discrete energies. The penetrating states in the other case (d→id) are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. The presence of MSS and reflectionlessness is also discussed for the free states in the later case. -- Highlights: •Existence of multiple spectral singularities (MSS) in PT-symmetric non-Hermitian system is shown. •Reciprocity is restored at discrete positive energies even for parity non-invariant complex system. •Co-existence of MSS with deep energy minima of transitivity is obtained. •Possibilities of both unidirectional and bidirectional invisibility are explored for a non-Hermitian system. •Penetrating states are shown to be reciprocal for all energies for PT-symmetric system

  3. A fortran program for elastic scattering of deuterons with an optical model containing tensorial potentials

    International Nuclear Information System (INIS)

    Raynal, J.

    1963-01-01

    The optical model has been applied with success to the elastic scattering of particles of spin 0 and 1/2 and to a lesser degree to that of deuterons. For particles of spin l/2, an LS coupling term is ordinarily used; this term is necessary to obtain a polarization; for deuterons, this coupling has been already introduced, but the possible forms of potentials are more numerous (in this case, scalar products of a second rank spin tensor with a tensor of the same rank in space or momentum can occur). These terms which may be necessary are primarily important for the tensor polarization. This problem is of particular interest at Saclay since a beam of polarized deuterons has become available. The FORTRAN program SPM 037 permits the study of the effect of tensorial potentials constructed from the distance of the deuteron from the target and its angular momentum with respect to it. This report should make possible the use and even the modification of the program. It consists of: a description of the problem and of the notation employed, a presentation of the methods adopted, an indication of the necessary data and how they should be introduced, and finally tables of symbols which are in equivalence or common statements: these tables must be considered when making any modification. (author) [fr

  4. Evolution of a wave packet scattered by a one-dimensional potential

    Energy Technology Data Exchange (ETDEWEB)

    Khachatrian, A Zh; Alexanyan, Al G; Khoetsyan, V A; Alexanyan, N A

    2013-06-30

    We consider the evolution of a wave packet that is made up of a group of the wave functions describing the stationary scattering process and tunnels through a one-dimensional potential of arbitrary form. As the main characteristics of the time difference of the tunnelling process, use is made of the propagation speed of the wave-packet maximum. We show that the known Hartman formula for the tunnelling time corresponds to the wave packet with a wavenumber-uniform spectral composition in the case, when the phase and transmission coefficient modulus dispersions are taken into account only in the linear approximation. The amplitude of the main peak of the transmitted wave intensity is proven to be independent of the tunnelling time and is determined by the transmission coefficient of the spectral component at the carrier frequency and the spectral width of the wave packet. In the limit of an infinitely wide potential barrier the amplitude of the wave-packet maximum is shown to tend to zero slower than the tunnelling time tends to its asymptotic value, i.e., indeed we deal with the paradox of an infinitely large propagation speed of a wave disturbance through the barrier. (propagation of wave fronts)

  5. Evolution of a wave packet scattered by a one-dimensional potential

    International Nuclear Information System (INIS)

    Khachatrian, A Zh; Alexanyan, Al G; Khoetsyan, V A; Alexanyan, N A

    2013-01-01

    We consider the evolution of a wave packet that is made up of a group of the wave functions describing the stationary scattering process and tunnels through a one-dimensional potential of arbitrary form. As the main characteristics of the time difference of the tunnelling process, use is made of the propagation speed of the wave-packet maximum. We show that the known Hartman formula for the tunnelling time corresponds to the wave packet with a wavenumber-uniform spectral composition in the case, when the phase and transmission coefficient modulus dispersions are taken into account only in the linear approximation. The amplitude of the main peak of the transmitted wave intensity is proven to be independent of the tunnelling time and is determined by the transmission coefficient of the spectral component at the carrier frequency and the spectral width of the wave packet. In the limit of an infinitely wide potential barrier the amplitude of the wave-packet maximum is shown to tend to zero slower than the tunnelling time tends to its asymptotic value, i.e., indeed we deal with the paradox of an infinitely large propagation speed of a wave disturbance through the barrier. (propagation of wave fronts)

  6. Quantization and scattering in the presence of singular attractive potential tails

    Energy Technology Data Exchange (ETDEWEB)

    Mueller, Tim-Oliver

    2013-01-17

    The interaction of atoms and molecules with each other and with ions is, at large distances, essentially determined by dispersion forces. The present thesis analyzes their influence on quantization and scattering phenomena. The formalism presented transparently reveals the interdependence of the scattering properties and the bound-state spectrum. The applicability of the theory is demontrated for different examples.

  7. Energy and Momentum Relaxation Times of 2D Electrons Due to Near Surface Deformation Potential Scattering

    Science.gov (United States)

    Pipa, Viktor; Vasko, Fedor; Mitin, Vladimir

    1997-03-01

    The low temperature energy and momentum relaxation rates of 2D electron gas placed near the free or clamped surface of a semi-infinit sample are calculated. To describe the electron-acoustic phonon interaction with allowance of the surface effect the method of elasticity theory Green functions was used. This method allows to take into account the reflection of acoustic waves from the surface and related mutual conversion of LA and TA waves. It is shown that the strength of the deformation potential scattering at low temperatures substantially depends on the mechanical conditions at the surface: relaxation rates are suppressed for the free surface while for the rigid one the rates are enhanced. The dependence of the conductivity on the distance between the 2D layer and the surface is discussed. The effect is most pronounced in the range of temperatures 2 sl pF < T < (2 hbar s_l)/d, where pF is the Fermi momentum, sl is the velocity of LA waves, d is the width of the quantum well.

  8. Determination of the potential scattering parameter and parameterization of neutron cross-sections in the low-energy region

    International Nuclear Information System (INIS)

    Novoselov, G.M.; Litvinskij, L.L

    2001-01-01

    Different cross-section parameterization methods in the low-energy region are considered. It is shown that the potential scattering parameter value derived from analysis of experimental cross-section data is dependent essentially on the method used to take account of the nearest resonances. A formula describing this dependence is obtained. The results are verified by numerical model calculations. (author)

  9. Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

    Science.gov (United States)

    Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.

    2018-04-01

    We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.

  10. How a change in the interaction potential affects the p-wave scattering volume

    International Nuclear Information System (INIS)

    Jamieson, M J; Dalgarno, A

    2012-01-01

    We derive a simple expression for the change in the s-wave scattering length in terms of zero-energy wavefunctions, we generalize it to obtain an expression for the change in the p-wave scattering volume and we use both expressions to derive the first order differential equations of variable phase theory that are satisfied by the closely related accumulated scattering length and volume. We provide numerical demonstrations for the example of a pair of hydrogen atoms interacting via the X 1 Σ + g molecular state. (fast track communication)

  11. The anisotropic potential of molecular hydrogen determined from the scattering of oriented H2 on inert gases

    International Nuclear Information System (INIS)

    Zandee, A.P.L.M.

    1977-01-01

    This thesis deals with an experiment aimed at determining the angle dependence of an intermolecular potential between H 2 molecule and a rare gas atom. The small relative difference in total collision cross section for beams of differently oriented H 2 molecules colliding with inert gas atoms in a scattering box is measured (anisotropy A). Through variation of the orientation and by studying its influence on the total collision cross sections, the angle dependence of the intermolecular potential can be arrived at

  12. On the use of a Hamiltonian with projected potential for the calculation of scattering wave functions : Methods and general properties

    International Nuclear Information System (INIS)

    Colle, R.; Simonucci, S.

    1996-01-01

    The theoretical framework of a method that utilizes a projected potential operator to construct scattering wave functions is presented. Theorems and spectral properties of a Hamiltonian with the potential energy operator represented in terms of L'2(R'3)-functions are derived. The computational advantages offered by the method for calculating spectroscopic quantities, like resonance energies, decay probabilities and photoionization cross-sections, are discussed

  13. Potentials of the inverse scattering problem in the three-nucleon problem

    International Nuclear Information System (INIS)

    Pushkash, A.M.; Simenog, I.V.; Shapoval, D.V.

    1993-01-01

    Possibilities of using the method of the inverse scattering problem for describing simultaneously the two-nucleon and the low-energy three-nucleon data in the S-interaction approximation are examined. 20 refs., 3 figs., 1 tab

  14. Scattering Study of a Modified Cusp Potential in Conformable Fractional Formalism

    Energy Technology Data Exchange (ETDEWEB)

    Chung, Won Sang [Gyeongsang National University, Jinju (Korea, Republic of); Zarrinkamar, Saber [Islamic Azad University, Garmsar (Iran, Islamic Republic of); Zare, Soroush [Islamic Azad University North Tehran Branch, Tehran (Iran, Islamic Republic of); Hassanabadi, Hassan [Shahrood University of Technology, Shahrood (Iran, Islamic Republic of)

    2017-02-15

    The fractional Schr¨odinger equation is considered with a cusp interaction. Exact analytical solutions are obtained and thereby the scattering states as well as transmission and reflection coefficients are determined.

  15. Effective theories of scattering with an attractive inverse-square potential and the three-body problem

    International Nuclear Information System (INIS)

    Barford, Thomas; Birse, Michael C

    2005-01-01

    A distorted-wave version of the renormalization group is applied to scattering by an inverse-square potential and to three-body systems. In attractive three-body systems, the short-distance wavefunction satisfies a Schroedinger equation with an attractive inverse-square potential, as shown by Efimov. The resulting oscillatory behaviour controls the renormalization of the three-body interactions, with the renormalization-group flow tending to a limit cycle as the cut-off is lowered. The approach used here leads to single-valued potentials with discontinuities as the bound states are cut off. The perturbations around the cycle start with a marginal term whose effect is simply to change the phase of the short-distance oscillations, or the self-adjoint extension of the singular Hamiltonian. The full power counting in terms of the energy and two-body scattering length is constructed for short-range three-body forces

  16. The potential influence of multiple scattering on longwave flux and heating rate simulations with clouds

    Science.gov (United States)

    Kuo, C. P.; Yang, P.; Huang, X.; Feldman, D.; Flanner, M.; Kuo, C.; Mlawer, E. J.

    2017-12-01

    Clouds, which cover approximately 67% of the globe, serve as one of the major modulators in adjusting radiative energy on the Earth. Since rigorous radiative transfer computations including multiple scattering are costly, only absorption is considered in the longwave spectral bands in the radiation sub-models of the general circulation models (GCMs). Quantification of the effect of ignoring longwave scattering for flux and heating rate simulations is performed by using the GCM version of the Longwave Rapid Radiative Transfer Model (RRTMG_LW) with an implementation with the 16-stream Discrete Ordinates Radiative Transfer (DISORT) Program for a Multi-Layered Plane-Parallel Medium in conjunction with the 2010 CCCM products that merge satellite observations from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO), the CloudSat, the Clouds and the Earth's Radiant Energy System (CERES) and the Moderate Resolution Imaging Spectrometer (MODIS). One-year global simulations show that neglecting longwave scattering overestimates upward flux at the top of the atmosphere (TOA) and underestimates downward flux at the surface by approximately 2.63 and 1.15 W/m2, respectively. Furthermore, when longwave scattering is included in the simulations, the tropopause is cooled by approximately 0.018 K/day and the surface is heated by approximately 0.028 K/day. As a result, the radiative effects of ignoring longwave scattering and doubling CO2 are comparable in magnitude.

  17. Differential elastic scattering of He* (21S) by Ar, Kr and Xe: Repulsive rainbows and optical potentials

    International Nuclear Information System (INIS)

    Martin, D.W.; Gregor, R.W.; Jordan, R.M.; Siska, P.E.

    1978-01-01

    Elastic scattering angular distributions of He* (2 1 S) with Ar, Kr, and Xe measured in crossed atomic beams at collision energies from 0.4--2.8 kcal/mole are analyzed using a physically motivated optical potential model. The resulting potentials show some features expected on the basis of the analogous Li--rare gas potentials: monotonically increasing van der Waals well depths epsilon in the sequence Ar, Kr, Xe, and nearly constant well position r/sub m/. However, structure occurs in the repulsive parts of the potentials in the form of a local slope maximum (force minimum) at low positive potential energy, as suggested by other studies. The potential energy at the slope maximum decreases monotonically in the Ar, Kr, Xe sequence, while its position increases monotonically. The slope maximum is manifested in the angular distributions through the appearance of rainbow scattering peaks for Ar and Kr at angles well removed from those at which attractive rainbows are expected, with both repulsive and attractive rainbows evident in the same distribution. The resonance widths are constrained to be simple exponentials. Table I contains all potential parameters derived. Reasonably good agreement is obtained between measured total ionization cross sections and quenching rate constants and those calculated from the optical potentials

  18. Central-field intermolecular potentials from the differential elastic scattering of H2(D2) by other molecules

    International Nuclear Information System (INIS)

    Kuppermann, Aron; Gordon, R.J.; Coggiola, M.J.

    1974-01-01

    Differential elastic scattering cross sections for the systems H 2 +O 2 , SF 6 , NH 3 , CO, and CH 4 and for D 2 +O 2 , SF 6 , and NH 3 have been obtained from crossed beam studies. In all cases, rapid quantum oscillations have been resolved which permit the determination of intermolecular potentiel parameters if a central-field assumption is adopted. These potentials were found to be independent of both the isotopic form of the hydrogen molecule, and the relative collision energy. As a result of this, and the ability of these spherical potentials to quantitatively describe the measured scattering, it is concluded that anisotropy effects do not seem important in these H 2 (D 2 ) systems

  19. Off-shell properties of the second-order Born approximation for laser-assisted potential scattering

    International Nuclear Information System (INIS)

    Trombetta, F.

    1991-01-01

    A formal method is presented to evaluate the second-order Born approximation of the laser-assisted potential scattering. It is an implicit closure technique that includes intermediate virtual-state transitions and enables one to find the exact explicit expression of the transition amplitude. This is of interest from two standpoints: first, one can deal with ranges of parameters in which the first-order Born approximation is a poor one; second, one can set limits of on-shell approximations that are also widely used to analyze recent laser-assisted experiments. The off-shell character yields new terms in the exact amplitude, and in particular, it is shown to play a crucial role in forward scattering from a long-range potential

  20. Influence of interfacial scattering and surface roughness on giant magnetoresistance in Fe/Cr trilayers using ab initio layer potentials

    International Nuclear Information System (INIS)

    Pereiro, M.; Botana, J.; Baldomir, D.; Warda, K.; Wojtczak, L.; Man'kovsky, S.V.; Iglesias, M.; Pardo, V.; Arias, J.E.

    2005-01-01

    Ab initio full-potential linearized augmented-plane-wave (FP-LAPW) method combined with the semiclassical Boltzmann formalism was employed to calculate the giant magnetoresistance ratio in the trilayers nFe/3Cr/nFe (1=< n=<8). The present results emphasize the very important role of the ferromagnetic layer as well as the interfacial scattering and surface roughness on the giant magnetoresistance effect

  1. Scattering of thermal He beams by crossed atomic and molecular beams. II. The He--Ar van der Waals potential

    International Nuclear Information System (INIS)

    Keilb, M.; Slankas, J.T.; Kuppermann, A.

    1979-01-01

    Differential cross sections for He--Ar scattering at room temperature have been measured. The experimental consistency of these measurements with others performed in different laboratories is demonstrated. Despite this consistency, the present van der Waals well depth of 1.78 meV, accurate to 10%, is smaller by 20% to 50% than the experimental values obtained previously. These discrepancies are caused by differences between the assumed mathematical forms or between the assumed dispersion coefficients of the potentials used in the present paper and those of previous studies. Independent investigations have shown that the previous assumptions are inappropriate for providing accurate potentials from fits to experimental differential cross section data for He--Ar. We use two forms free of this inadequacy in the present analysis: a modified version of the Simons--Parr--Finlan--Dunham (SPFD) potential, and a double Morse--van der Waals (M 2 SV) type of parameterization. The resulting He--Ar potentials are shown to be equal to with experimental error, throughout the range of interatomic distances to which the scattering data are sensitive. The SPFD or M 2 SV potentials are combined with a repulsive potential previously determined exclusively from fits to gas phase bulk properties. The resulting potentials, valid over the extended range of interatomic distances r> or approx. =2.4 A, are able to reproduce all these bulk properties quite well, without adversely affecting the quality of the fits to the DCS

  2. Monitoring human neutrophil granule secretion by flow cytometry: secretion and membrane potential changes assessed by light scatter and a fluorescent probe of membrane potential

    International Nuclear Information System (INIS)

    Fletcher, M.P.; Seligmann, B.E.

    1985-01-01

    Purified human peripheral blood polymorphonuclear neutrophils (PMN) were incubated at 37 degrees C with the fluorescent membrane potential sensitive cyanine dye di-O-C(5)(3) and exposed to a number of stimulatory agents (N-formylmethionylleucylphenylalanine (FMLP), cytochalasin B (cyto B) + FMLP, phorbol myristate acetate (PMA). Flow cytometry was utilized to measure changes in forward light scatter (FS), orthogonal light scatter (90 degrees-SC), and fluorescence intensity of individual cells over time. A saturating (10(-6) M) dose of FMLP lead to a significant increase in the cells' FS without a change in 90 degrees-SC as well as a heterogeneous loss of di-O-C(5)(3) fluorescence. PMA (100 ng/ml) also caused an increase in FS but a uniform loss of dye fluorescence by all cells (apparent depolarization). Cyto B + FMLP produced an increase in FS, a marked loss of 90 degrees-SC, and a uniform loss of fluorescence. Secretion experiments under identical incubation conditions indicated a significantly positive relationship between loss of enzyme markers or cell granularity and orthogonal light scatter (r . 0.959, 0.998, and 0.989 for loss of 90 degrees-SC vs lysozyme, beta-glucuronidase, and granularity index, respectively). Flow cytometric light scatter measurements may yield important information on the extent of prior cell degranulation or activation

  3. Study on the generalized WKB approximation for the inverse scattering problem at fixed energy for complex potentials

    International Nuclear Information System (INIS)

    Pozdnyakov, Yu.A.; Terenetskij, K.O.

    1981-01-01

    The approximate method for solution of the inverse scattering problem (ISP) at fixed energy for complex spherically symmetric potentials decreasing faster 1/r is considered. The method is based on using a generalized WKB approximation. For the designed potential V(r) a sufficiently ''close'' reference potential V(r) has been chosen. For both potentials S-matrix elements (ME) have been calculated and inversion procedure has been carried out. S-ME have been calculated for integral-valued and intermediate angular moment values. S-ME are presented in a graphical form for being restored reference, and restored potentials for proton scattering with Esub(p)=49.48 MeV energy on 12 C nuclei. The restoration is the better the ''closer'' the sought-for potential to the reference one. This allows to specify the potential by means of iterations: the restored potential can be used as a reference one, etc. The operation of a restored potential smoothing before the following iteration is introduced. Drawbacks and advantages of the ISP solution method under consideration are pointed out. The method application is strongly limited by the requirement that the energy should be higher than a certain ''critical'' one. The method is applicable in a wider region of particle energies (in the low-energies direction) than the ordinary WKB method. The method is more simple in realization conformably to complex potentials. The investigations carried out of the proposed ISP solution method at fixed energy for complex spherically-symmetric potentials allow to conclude that the method can be successFully applied to specify the central part of interaction of nucleons, α-particles and heavy ions of average and high energies with atomic nuclei [ru

  4. High-efficiency γ-ray flash generation via multiple-laser scattering in ponderomotive potential well.

    Science.gov (United States)

    Gong, Z; Hu, R H; Shou, Y R; Qiao, B; Chen, C E; He, X T; Bulanov, S S; Esirkepov, T Zh; Bulanov, S V; Yan, X Q

    2017-01-01

    γ-ray flash generation in near-critical-density target irradiated by four symmetrical colliding laser pulses is numerically investigated. With peak intensities about 10^{23} W/cm^{2}, the laser pulses boost electron energy through direct laser acceleration, while pushing them inward with the ponderomotive force. After backscattering with counterpropagating laser, the accelerated electron is trapped in the electromagnetic standing waves or the ponderomotive potential well created by the coherent overlapping of the laser pulses, and emits γ-ray photons in a multiple-laser-scattering regime, where electrons act as a medium transferring energy from the laser to γ rays in the ponderomotive potential valley.

  5. s-wave scattering for deep potentials with attractive tails falling off faster than -1/r2

    International Nuclear Information System (INIS)

    Mueller, Tim-Oliver; Kaiser, Alexander; Friedrich, Harald

    2011-01-01

    For potentials with attractive tails, as occur in typical atomic interactions, we present a simple formula for the s-wave phase shift δ 0 . It exposes a universal dependence of δ 0 (E) on the potential tail and the influence of effects specific to a given potential, which enter via the scattering length a, or equivalently, the noninteger part Δ th of the threshold quantum number n th . The formula accurately reproduces δ 0 (E) from threshold up to the semiclassical regime, far beyond the validity of the effective-range expansion. We derive the tail functions occurring in the formula for δ 0 (E) and demonstrate the validity of the formula for attractive potential tails proportional to 1/r 6 or to 1/r 4 , and also for a mixed potential tail consisting of a 1/r 4 term together with a non-negligible 1/r 6 contribution.

  6. Simple and easy method to evaluate uptake potential of nanoparticles in mammalian cells using a flow cytometric light scatter analysis.

    Science.gov (United States)

    Suzuki, Hiroshi; Toyooka, Tatsushi; Ibuki, Yuko

    2007-04-15

    Many classes of nanoparticles have been synthesized and widely applied, however, there is a serious lack of information concerning their effects on human health and the environment. Considering that their use will increase, accurate and cost-effective measurement techniques for characterizing "nanotoxicity" are required. One major toxicological concern is that nanoparticles are easily taken up in the human body. In this study, we developed a method of evaluating the uptake potential of nanosized particles using flow cytometric light scatter. Suspended titanium dioxide (TiO2) particles (5, 23, or 5000 nm) were added to Chinese hamster ovary cells. Observation by confocal laser scanning microscopy showed that the TiO2 particles easily moved to the cytoplasm of the cultured mammalian cells, not to the nucleus. The intensity of the side-scattered light revealed that the particles were taken up in the cells dose-, time-, and size-dependently. In addition, surface-coating of TiO2 particles changed the uptake into the cells, which was accurately reflected in the intensity of the side-scattered light. The uptake of other nanoparticles such as silver (Ag) and iron oxide (Fe3O4) also could be detected. This method could be used for the initial screening of the uptake potential of nanoparticles as an index of "nanotoxicity".

  7. An effective potential for electron-nucleus scattering in neutrino-pair bremsstrahlung in neutron star crust

    International Nuclear Information System (INIS)

    Ofengeim, D D; Kaminker, A D; Yakovlev, D G

    2015-01-01

    We derive an analytic approximation for the emissivity of neutrino-pair bremsstrahlung (NPB) due to scattering of electrons by atomic nuclei in a neutron star (NS) crust of any realistic composition. The emissivity is expressed through generalized Coulomb logarithm by introducing an effective potential of electron-nucleus scattering. In addition, we study the conditions at which NPB in the crust is affected by strong magnetic fields and outline the main effects of the fields on neutrino emission in NSs. The results can be used for modelling of many phenomena in NSs, such as cooling of young isolated NSs, thermal relaxation of accreting NSs with overheated crust in soft X-ray transients and evolution of magnetars. (paper)

  8. Effects of tube potential and scatter rejection on image quality and effective dose in digital chest X-ray examination: An anthropomorphic phantom study

    Energy Technology Data Exchange (ETDEWEB)

    Shaw, D.J., E-mail: daniel.shaw@christie.nhs.uk [Diagnostic Radiology, Department of Medical Physics and Engineering, Leeds Teaching Hospitals, Leeds General Infirmary, Great George Street, Leeds LS1 3EX (United Kingdom); Crawshaw, I. [Diagnostic X-ray Department, York Teaching Hospital NHS Foundation Trust, The York Hospital, Wigginton Road, York YO31 8HE (United Kingdom); Rimmer, S. D. [Diagnostic Radiology, Department of Medical Physics and Engineering, Leeds Teaching Hospitals, Leeds General Infirmary, Great George Street, Leeds LS1 3EX (United Kingdom)

    2013-11-15

    Objectives: The purpose of this study was to investigate the effects of tube potential and scatter rejection techniques on image quality of digital posteroanterior (PA) chest radiographs. Methods: An anthropomorphic phantom was imaged using a range of tube potentials (81–125 kV{sub p}) without scatter rejection, with an anti-scatter grid, and using a 10 cm air gap. Images were anonymised and randomised before being evaluated using a visual graded analysis (VGA) method. Results: The effects of tube potential on image quality were found to be negligible (p > 0.63) for the flat panel detector (FPD). Decreased image quality (p = 0.031) was noted for 125 kV{sub p} relative to 109 kV{sub p}, though no difference was noted for any of the other potentials (p > 0.398) for computed radiography (CR). Both scatter rejection techniques improved image quality (p < 0.01). For FPD imaging the anti-scatter grid offered slightly improved image quality relative to the air gap (p = 0.038) but this was not seen for CR (p = 0.404). Conclusions: For FPD chest imaging of the anthropomorphic phantom there was no dependence of image quality on tube potential. Scatter rejection improved image quality, with the anti-scatter grid giving greater improvements than an air-gap, but at the expense of increased effective dose. CR imaging of the chest phantom demonstrated negligible dependence on tube potential except at 125 kV{sub p}. Scatter rejection improved image quality, but with no difference found between techniques. The air-gap resulted in a smaller increase in effective dose than the anti-scatter grid and would be the preferred scatter rejection technique.

  9. Simultaneous measurement of non-commuting observables

    NARCIS (Netherlands)

    Allahverdyan, A.E.; Balian, R.; Nieuwenhuizen, T.M.

    2010-01-01

    A dynamical model of a quantum measurement process is introduced, where the tested system S, a spin 1/2, is simultaneously coupled with two apparatuses A and A'. Alone, A would measure the component (s) over cap (z) whereas A' alone would measure (s) over cap (x). The apparatus A simulates an Ising

  10. Multiplication modules over non-commutative rings

    International Nuclear Information System (INIS)

    Tuganbaev, A A

    2003-01-01

    It is proved that each submodule of a multiplication module over a regular ring is a multiplicative module. If A is a ring with commutative multiplication of right ideals, then each projective right ideal is a multiplicative module, and a finitely generated A-module M is a multiplicative module if and only if all its localizations with respect to maximal right ideals of A are cyclic modules over the corresponding localizations of A. In addition, several known results on multiplication modules over commutative rings are extended to modules over not necessarily commutative rings

  11. Anosov actions on non-commutative algebras

    International Nuclear Information System (INIS)

    Emch, G.G.; Narnhofer, H.; Thirring, W.; Sewell, G.L.

    1994-01-01

    We construct an axiomatic framework for a quantum mechanical extension to the theory of Anosov systems, and show that this retains some of the characteristic features of its classical counterpart, e.g. positive Lyapunov exponents, a vectorial K-property, and exponential clustering. We then investigate the effects of quantisation on two prototype examples of Anosov systems, namely the iterations of an automorphism of the torus (the 'Arnold Cat' model) and the free dynamics of a particle on a surface of negative curvature. It emerges that the Anosov property survives quantisation in the case of the former model, but not of the latter one. Finally, we show that the modular dynamics of a relativistic quantum field on the Rindler wedge of Minkowski space is that of an Anosov system. (authors)

  12. Non-Commutative Orders. A Preliminary Study

    International Nuclear Information System (INIS)

    Brzezinski, T.

    2011-01-01

    The first steps towards linearization of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that makes the linearization (almost) automatic. The linearization is then achieved by replacing sets by coalgebras and the Cartesian product by the tensor product of vector spaces. As a result, definitions of orders and equivalence relations on coalgebras are proposed. These are illustrated by explicit examples that include relations on coalgebras spanned by grouplike elements (or linearized sets), the diagonal relation, and an order on a three-dimensional non-cocommutative coalgebra. Although relations on coalgebras are defined for vector spaces, all the definitions are formulated in a way that is immediately applicable to other braided monoidal categories. (author)

  13. The quasi-classical limit of scattering amplitude - L2-approach for short range potentials

    International Nuclear Information System (INIS)

    Yajima, K.; Vienna Univ.

    1984-01-01

    We are concerned with the asymptotic behaviour as Planck's constant h → 0 of the scattering operator Ssup(h) associated with the pair of Schroedinger equations i h/2π delta u/delta t = - ((h/2π) 2 /2m)Δu + V(x) u equivalent to Hsup(h)u and i h/2π delta u/delta t = - ((h/2π) 2 /2m)Δu equivalent to Hsup(h) 0 u. We shall show under certain conditions that the scattering matrix S-circumflexsup(h)(p,q), the distribution kernel of Ssup(h) in momentum representation, may be expressed in terms of a Fourier integral operator. Then applying the stationary phase method to it, we shall prove that S-circumflexsup(h) has an asymptotic expansion in powers of h/2π up to any order in L 2 -space and that the limit as h → 0 of the total cross section is twice the one of classical mechanics, in generic. (Author)

  14. Nucleus-nucleus potential with repulsive core and elastic scattering. Part 1. Nucleus-nucleus interaction potential

    International Nuclear Information System (INIS)

    Davidovs'ka, O.Yi.; Denisov, V.Yu.; Nesterov, V.O.

    2010-01-01

    Various approaches for nucleus-nucleus interaction potential evaluation are discussed in details. It is shown that the antisymmetrization of nucleons belonging to different nuclei and the Pauli principle give the essential contribution into the nucleus-nucleus potential at distances, when nuclei are strongly overlapping, and lead to appearance of the repulsive core of nucleus nucleus interaction at small distances between nuclei.

  15. Is the concept of the non-Hermitian effective Hamiltonian relevant in the case of potential scattering?

    International Nuclear Information System (INIS)

    Savin, Dmitry V.; Sokolov, Valentin V.; Sommers, Hans-Juergen

    2003-01-01

    We examine the notion and properties of the non-Hermitian effective Hamiltonian of an unstable system using as an example potential resonance scattering with a fixed angular momentum. We present a consistent self-adjoint formulation of the problem of scattering on a finite-range potential, which is based on the separation of the configuration space into two segments, internal and external. The scattering amplitude is expressed in terms of the resolvent of a non-Hermitian operator H. The explicit form of this operator depends on both the radius of separation and the boundary conditions at this place, which can be chosen in many different ways. We discuss this freedom and show explicitly that the physical scattering amplitude is, nevertheless, unique, although not all choices are equally adequate from the physical point of view. The energy-dependent operator H should not be confused with the non-Hermitian effective Hamiltonian H eff which is usually exploited to describe interference of overlapping resonances. We note that the simple Breit-Wigner approximation is as a rule valid for any individual resonance in the case of few-channel scattering on a flat billiardlike cavity, leaving no room for nontrivial H eff to appear. The physics is appreciably richer in the case of an open chain of L connected similar cavities whose spectrum has a band structure. For a fixed band of L overlapping resonances, the smooth energy dependence of H can be ignored so that the constant LxL submatrix H eff approximately describes the time evolution of the chain in the energy domain of the band and the complex eigenvalues of H eff define the energies and widths of the resonances. We apply the developed formalism to the problem of a chain of L δ barriers, whose solution is also found independently in a closed form. We construct H eff for the two commonly considered types of boundary conditions (Neumann and Dirichlet) for the internal motion. Although the final results are in perfect

  16. Potential scattering in the presence of a static magnetic field and a radiation field of arbitrary polarization

    Science.gov (United States)

    Ferrante, G.; Zarcone, M.; Nuzzo, S.; McDowell, M. R. C.

    1982-05-01

    Expressions are obtained for the total cross sections for scattering of a charged particle by a potential in the presence of a static uniform magnetic field and a radiation field of arbitrary polarization. For a Coulomb field this is closely related to the time reverse of photoionization of a neutral atom in a magnetic field, including multiphoton effects off-resonance. The model is not applicable when the radiation energy approaches one of the quasi-Landau state separations. The effects of radiation field polarization are examined in detail.

  17. Use of analytical Born amplitude representation in studies of dispersion potentials and electron-atom scattering

    International Nuclear Information System (INIS)

    Carvalho, I.L. de.

    1985-01-01

    Two distinct problems have been studied using simplifield Born's Amplitude Analitical Expressions. The first problem deals with the dispersion energy between the constituent members of the systems He - Ne, - He and H 2 - H 2 . In the second problem second order Born Aproximation has been used for the Electron - Atom Inelastic Scattering for the transitions 1 1 S → 2 1 S and 1 1 S → 2 1 P of helium atom and 1 S → 1 s 2 ([3s' {1/2} sup(o) 1; M sub(j)>) of neon atom (in the case of neon we have used the coupling scheme proposed by Cowan and Andrew). The results obtained by us have been compared with the theoretical and experimental results available in the literature. (author) [pt

  18. Effects of tube potential and scatter rejection on image quality and effective dose in digital chest X-ray examination: An anthropomorphic phantom study

    International Nuclear Information System (INIS)

    Shaw, D.J.; Crawshaw, I.; Rimmer, S.D.

    2013-01-01

    Objectives: The purpose of this study was to investigate the effects of tube potential and scatter rejection techniques on image quality of digital posteroanterior (PA) chest radiographs. Methods: An anthropomorphic phantom was imaged using a range of tube potentials (81–125 kV p ) without scatter rejection, with an anti-scatter grid, and using a 10 cm air gap. Images were anonymised and randomised before being evaluated using a visual graded analysis (VGA) method. Results: The effects of tube potential on image quality were found to be negligible (p > 0.63) for the flat panel detector (FPD). Decreased image quality (p = 0.031) was noted for 125 kV p relative to 109 kV p , though no difference was noted for any of the other potentials (p > 0.398) for computed radiography (CR). Both scatter rejection techniques improved image quality (p p . Scatter rejection improved image quality, but with no difference found between techniques. The air-gap resulted in a smaller increase in effective dose than the anti-scatter grid and would be the preferred scatter rejection technique

  19. Investigation of {sup 16}O+{sup 12}C refractive elastic scattering using the α-cluster model potential

    Energy Technology Data Exchange (ETDEWEB)

    Hassanain, Mahmoud A. [King Khalid University, Department of Physics, Abha (Saudi Arabia); Assiut University, Department of Physics, New-Valley Faculty of Science, Assiut (Egypt)

    2016-01-15

    Differential cross-section of the {sup 16}O+{sup 12}C elastic scattering at E{sub lab} = 132, 181, 200, 260, 300, 608 and 1503MeV has been reanalyzed in the framework of double-folding cluster (DFC1) potential over a wide angular range which cover both diffractive and refractive regions. Based upon the α-cluster structure of both colliding nuclei, the real DFC1 optical potential has been generated by using α-α effective interaction and new cluster modified Gaussian (CMGD) of target and projectile has also been extracted. Successful descriptions of the data were obtained over the full measured angular range at all considered energies. The results have been compared with the findings obtained by using the phenomenological approach as well as experimental data. Furthermore, the consistency between the real and imaginary volume integrals is checked by the dispersion relation and the total reaction cross-section has also been investigated. (orig.)

  20. Fiber optic probe enabled by surface-enhanced Raman scattering for early diagnosis of potential acute rejection of kidney transplant

    Science.gov (United States)

    Chi, Jingmao; Chen, Hui; Tolias, Peter; Du, Henry

    2014-06-01

    We have explored the use of a fiber-optic probe with surface-enhanced Raman scattering (SERS) sensing modality for early, noninvasive and, rapid diagnosis of potential renal acute rejection (AR) and other renal graft dysfunction of kidney transplant patients. Multimode silica optical fiber immobilized with colloidal Ag nanoparticles at the distal end was used for SERS measurements of as-collected urine samples at 632.8 nm excitation wavelength. All patients with abnormal renal graft function (3 AR episodes and 2 graft failure episodes) who were clinically diagnosed independently show common unique SERS spectral features in the urines collected just one day after transplant. SERS-based fiber-optic probe has excellent potential to be a bedside tool for early diagnosis of kidney transplant patients for timely medical intervention of patients at high risk of transplant dysfunction.

  1. Convergence of an L2-approach in the coupled-channels optical potential method for e-H scattering

    International Nuclear Information System (INIS)

    Bray, I.; Konovalov, D.A.; McCarthy, I.E.

    1990-08-01

    An L 2 approach to the coupled-channels optical method is studied. The investigation is done for electron-hydrogen elastic scattering at projectile energies of 30, 50, 100 and 200 eV. Weak coupling, free-particle Green's function and no exchange in Q-space are appoximations used to calculate the polarization potential. This model problem is solved exactly using actual hydrogen discrete and continuum functions. The convergence of an L 2 approach with the Laguerre basis to the exact result is investigated. It is found that a basis of 10 Laguerre functions is sufficient for convergence of approximately 5% in the polarization potential matrix elements and 2% in the differential cross sections for non-large angles. The convergence is faster for smaller energies. In general, the convergence to the exact result is slow. 12 refs., 2 tabs., 2 figs

  2. Contribution of the two-pion exchange potentials to the P-odd pp-scattering asymmetry at low energies

    International Nuclear Information System (INIS)

    Musakhanov, M.M.; Podgornov, Yu.Yu.

    1985-01-01

    The P-odd asymmetry Asub(pp) of the pp-scattering is calculated within the potential approach for 15 and 45 MeV taking account of the isovector 2π-exchange in additionto the rho 0 ω-exchanges. The corresponding 2 π-potentials areobtained with the account of Δ-isobar configurations. The main contribution of the 2π-exchange to the Asub(pp) is shown to lie in the range of larger internucleon distances than that of the rho 0 , ω-exchange the former must be taken into account while calculating the Asub(pp). The obtained 2π-exchange contribution to the Asub(pp) is comparable with that of the rho 0 , ω-exchange

  3. Semiclassical derivation of a local optical potential for heavy-ion plastic scattering

    International Nuclear Information System (INIS)

    Donangelo, R.; Qanto, L.F.; Hussein, M.S.

    A semiclassical method to determine the contribution to the optical potential in the elastic channel due to the coupling to other processes taking place in heavy-ion collisions is developed. An application is made to the case of coulomb excitation. The lowest order term of our potential is shown to be identical to the quantum mechanical expression of Baltz et al

  4. Local and non-local equivalent potentials for p-12C scattering

    International Nuclear Information System (INIS)

    Lovell, A.; Amos, K.

    2000-01-01

    A Newton-Sabatier fixed energy inversion scheme has been used to equate inherently non-local p- 12 C potentials at a variety of energies to pion threshold, with exactly phase equivalent local ones. Those energy dependent local potentials then have been recast in the form of non-local Frahn-Lemmer interactions

  5. Corrugation in the nitrogen-graphite potential probed by inelastic neutron scattering

    DEFF Research Database (Denmark)

    Hansen, Flemming Yssing; Frank, V. L. P.; Taub, H.

    1990-01-01

    -center energy gap of ∼0.4 THz in the acoustic-phonon branches is a factor of 2 larger than calculated from central atom-atom potentials. We conclude that current models of the corrugation in the adatom substrate potential greatly underestimate the lateral restoring forces in this relatively simple molecular...

  6. Comparison of the Born series and rational approximants in potential scattering. [Pade approximants, Yikawa and exponential potential

    Energy Technology Data Exchange (ETDEWEB)

    Garibotti, C R; Grinstein, F F [Rosario Univ. Nacional (Argentina). Facultad de Ciencias Exactas e Ingenieria

    1976-05-08

    It is discussed the real utility of Born series for the calculation of atomic collision processes in the Born approximation. It is suggested to make use of Pade approximants and it is shown that this approach provides very fast convergent sequences over all the energy range studied. Yukawa and exponential potential are explicitly considered and the results are compared with high-order Born approximation.

  7. Scattering theory

    International Nuclear Information System (INIS)

    Sitenko, A.

    1991-01-01

    This book emerged out of graduate lectures given by the author at the University of Kiev and is intended as a graduate text. The fundamentals of non-relativistic quantum scattering theory are covered, including some topics, such as the phase-function formalism, separable potentials, and inverse scattering, which are not always coverded in textbooks on scattering theory. Criticisms of the text are minor, but the reviewer feels an inadequate index is provided and the citing of references in the Russian language is a hindrance in a graduate text

  8. Multi-property isotropic intermolecular potentials and predicted spectral lineshapes of collision-induced absorption (CIA), collision-induced light scattering (CILS) and collision-induced hyper-Rayleigh scattering (CIHR) for H2sbnd Ne, -Kr and -Xe

    Science.gov (United States)

    El-Kader, M. S. A.; Godet, J.-L.; Gustafsson, M.; Maroulis, G.

    2018-04-01

    Quantum mechanical lineshapes of collision-induced absorption (CIA), collision-induced light scattering (CILS) and collision-induced hyper-Rayleigh scattering (CIHR) at room temperature (295 K) are computed for gaseous mixtures of molecular hydrogen with neon, krypton and xenon. The induced spectra are detected using theoretical values for induced dipole moment, pair-polarizability trace and anisotropy, hyper-polarizability and updated intermolecular potentials. Good agreement is observed for all spectra when the literature and the present potentials which are constructed from the transport and thermo-physical properties are used.

  9. Argon intermolecular potential from a measurement of the total scattering cross-section

    International Nuclear Information System (INIS)

    Wong, Y.W.

    1975-01-01

    An inversion method to obtain accurate intermolecular potentials from experimental total cross section measurements is presented. This method is based on the high energy Massey--Smith approximation. The attractive portion of the potential is represented by a multi-parameter spline function and the repulsive part by a Morse function. The best fit potential is obtained by a least squares minimization based on comparison of experimental cross sections with those obtained by a Fourier transform of the reduced Massey--Smith phase shift curve. An experimental method was developed to obtain the total cross sections needed for the above inversion procedure. In this technique, integral cross sections are measured at various resolutions and the total cross section is obtained by extrapolating to infinite resolution. Experimental results obtained for the Ar--Ar system are in excellent agreement with total cross sections calculated using the Barker-Fisher-Watts potential. Inversion of the data to obtain a potential distinguishable from the BFW-potential requires an extension of the method based on the Massey--Smith approximation to permit use of JWKB phase shifts and was not attempted

  10. Potential-splitting approach applied to the Temkin-Poet model for electron scattering off the hydrogen atom and the helium ion

    Science.gov (United States)

    Yarevsky, E.; Yakovlev, S. L.; Larson, Å; Elander, N.

    2015-06-01

    The study of scattering processes in few body systems is a difficult problem especially if long range interactions are involved. In order to solve such problems, we develop here a potential-splitting approach for three-body systems. This approach is based on splitting the reaction potential into a finite range core part and a long range tail part. The solution to the Schrödinger equation for the long range tail Hamiltonian is found analytically, and used as an incoming wave in the three body scattering problem. This reformulation of the scattering problem makes it suitable for treatment by the exterior complex scaling technique in the sense that the problem after the complex dilation is reduced to a boundary value problem with zero boundary conditions. We illustrate the method with calculations on the electron scattering off the hydrogen atom and the positive helium ion in the frame of the Temkin-Poet model.

  11. Reflection at a complex potential barrier in the semiclassical theory of scattering

    International Nuclear Information System (INIS)

    Avishai, Y.; Knoll, J.

    1976-01-01

    The reflection of spherical waves at a complex potential barrier is discussed in the semiclassical approximation. We study the complex WKB method and the Uniform Approximation in the special case of weakly absorptive barriers, typical of surface transparent optical potentials used in heavy-ion reactions. It is found that the complex WKB results lead to a very accurate cross-section despite their inaccuracy in the most important phase shifts. Thereby, the amazing stamina of the WKB has been confirmed once more. (orig.) [de

  12. 6Li real potential volume integrals in elastic scattering and distorted-waveBorn approximation analyses

    International Nuclear Information System (INIS)

    Lezoch, P.; Trost, H.; Strohbusch, U.

    1981-01-01

    The magnitudes of volume integrals per interacting nucleon pair J/sub R/' calculated from a compilation of 6 Li potentials vary between 100 and 500 MeV fm 3 . They are grouped in discrete branches with J/sub R/(A) smoothly increasing with decreasing target mass. Comparison with the results for lighter projectiles restricts the ''physically meaningful'' branches to those characterized by J/sub R/ (A> or =48) 3 . ( 6 Li,d) reaction analyses yield the same fit qualities for 6 Li potentials of the different discrete families, but deduced spectroscopic factors jump (by factors of approx.3) when changing between successive families

  13. Bound states and scattering coefficients of the -aδ(x)+bδ'(x) potential

    International Nuclear Information System (INIS)

    Gadella, M.; Negro, J.; Nieto, L.M.

    2009-01-01

    We show that a one-dimensional Schroedinger equation in which the potential is a delta well plus a δ ' interaction at the same point has a bound state, and we obtain the energy of this bound state in terms of the parameters. In addition, the expression of the reflection and transmission coefficients is also fully determined

  14. Image potential effect on the specular reflection coefficient of alkali ions scattered from a nickel surface at low energy

    International Nuclear Information System (INIS)

    Zemih, R.; Boudjema, M.; Benazeth, C.; Boudouma, Y.; Chami, A.C.

    2002-01-01

    The resonant charge exchange in the incoming path of alkali ions scattered at low energy from a polycrystalline nickel surface is studied by using the image effect occurring at glancing incidence (2-10 deg. from the surface plane) and for specular reflection. The part of the experimental artefacts (geometrical factor, surface roughness ...) is extracted from the reflection coefficient of almost completely neutralised projectiles (He + or Ne + ) compared with the coefficient obtained from numerical simulations (TRIM and MARLOWE codes). The present model explains very well the lowering of the reflection coefficient measured at grazing incidence (below 4 deg.). Furthermore, the optimised values of the charge fraction in the incoming path and the image potential are in agreement with the theoretical calculations in the case of Na + /Ni at 4 keV

  15. On using of R-matrix approach for description of nucleon scattering by potential with diffuse edge

    International Nuclear Information System (INIS)

    Tertychnyj, G.Ya.; Yadrovskij, E.L.

    1982-01-01

    Problems of convergence of R-matrix method for calculation of scattering phases and bound states of neutrons in the Woods-Saxon potential are investigated. It is revealed that this convergence in respect to the number of R-matrix poles turns to be faster if the value of the parameter of boundary conditions bsub(ej)sup(0) is close to the value of logarithmic derivative of the function of continuous spectrum at given energy E and radius of joining a. Bound states are satisfactorily described in unipolar approximation in a wide range of energy and bsub(ej)sup(0) parameter variations. The conducted comparison of the R-matrix method with the method of numerical integration testifies to their equivalence irrespective of the choice of a and bsub(ej)sup(0) parameters, but under the condition that the R-matrix series comprises a large number of members

  16. Connection between one-parameter problems in the theory of charged particle potential scattering

    International Nuclear Information System (INIS)

    Popushoj, M.N.

    1989-01-01

    Schroedinger equation for superposition of centrifugal Coulomb and nuclear potentials was used to establish the similarity of direct and inverse problems: 1) at k=const, a=const, λ=Var and a=const, λ=1/2, k=var (k -wave number, λ=l+1/2, l - orbital momentum, a - Coulomb coupling constant); 2) at k=const, λ=const, a=var and λ=const, a=0, k=var

  17. Regge poles and Mandelstam representation in potential scattering; Poles de regge et representation de Mandelstam en theorie du potentiel

    Energy Technology Data Exchange (ETDEWEB)

    Bessis, D [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1965-03-01

    We deal with the scattering of two spinless particles interacting by a superposition of Yukawa potentials. We first obtain an upper bound for the scattering amplitude for simultaneous complex values of energy and angular momentum. We then show that the Regge poles remain confined in small domains of the complex angular momentum plane, we study the variation of these domains when the energy (complex) varies. These first results allow us to deduce an upper bound for the double spectral function, this upper bound is used to rigorously show that the Schroedinger equation implies the Mandelstam representation for the type of potentials we deal with. Finally, the problem of subtractions is entirely solved, showing that the Mellin transform of the double spectral function can be analytically continued into the different simple spectral functions. (author) [French] On traite de la diffusion de deux particules sans spin interagissant par l'intermediaire d'une superposition de potentiels de Yukawa. Nous obtenons tout d'abord une majorante pour l'amplitude de diffusion pour des valeurs simultanement complexes de l'energie et du moment cinetique. On montre alors que les Poles de Regge restent confines dans des domaines restreints du plan complexe du moment cinetique, domaines dont nous etudions la variation pour des valeurs complexes de l'energie. Ces premiers resultats nous permettent alors de deduire une majorante pour la fonction spectrale double, majorante qui est utilisee pour demontrer rigoureusement que l'equation de Schroedinger implique la representation de Mandelstam pour la classe des potentiels envisages. Enfin le probleme des soustractions est entierement resolu, en montrant que la transformee de Mellin de la fonction spectrale double se prolonge analytiquement dans les diverses fonctions spectrales simples. (auteur)

  18. Analysis of elastic scattering cross-section for 18O + 206Pb in the CRC formalism and dependence on the choice of double folding potential

    International Nuclear Information System (INIS)

    Sonika; Roy, B.J.; Parmar, A.; Jha, V.; Pal, U.K.; Pandit, S.K.; Parkar, V.V.; Ramachandran, K.; Mahata, K.; Pal, A.; Santra, S.; Mohanty, A.K.; Sinha, T.; Parihari, A.

    2014-01-01

    Measurement and detailed analysis of elastic scattering and inelastic excitations in 206 Pb( 18 O, 18 O) have been reported here. First, the elastic scattering cross-section was calculated with a bare double folded real potential. The DF potential consists of folding of a harmonic oscillator density distribution to simulate 18 O with the sum of two Fermi density distributions for the proton and neutron in 206 Pb with correct normalizations. Our measured higher energy data for the same system was first analyzed with this DF potential

  19. A variational approach to operator and matrix Pade approximation. Applications to potential scattering and field theory

    International Nuclear Information System (INIS)

    Mery, P.

    1977-01-01

    The operator and matrix Pade approximation are defined. The fact that these approximants can be derived from the Schwinger variational principle is emphasized. In potential theory, using this variational aspect it is shown that the matrix Pade approximation allow to reproduce the exact solution of the Lippman-Schwinger equation with any required accuracy taking only into account the knowledge of the first two coefficients in the Born expansion. The deep analytic structure of this variational matrix Pade approximation (hyper Pade approximation) is discussed

  20. A new potential energy surface for vibration-vibration coupling in HF-HF collisions. Formulation and quantal scattering calculations

    Science.gov (United States)

    Schwenke, David W.; Truhlar, Donald G.

    1988-04-01

    We present new ab initio calculations of the HF-HF interaction potential for the case where both molecules are simultaneously displaced from their equilibrium internuclear distance. These and previous ab initio calculations are then fit to a new analytic representation which is designed to be efficient to evaluate and to provide an especially faithful account of the forces along the vibrational coordinates. We use the new potential for two sets of quantal scattering calculations for collisions in three dimensions with total angular momentum zero. First we test that the angular harmonic representation of the anisotropy is adequate by comparing quantal rigid rotator calculations to those carried out for potentials involving higher angular harmonics and for which the expansion in angular harmonics is systematically increased to convergence. Then we carry out large-scale quantal calculations of vibration-vibration energy transfer including the coupling of both sets of vibrational and rotational coordinates. These calculations indicate that significant rotational energy transfer accompanies the vibration-to-vibration energy transfer process.

  1. Inclusion of the strong interaction in low-energy hydrogen-antihydrogen scattering using a complex potential

    International Nuclear Information System (INIS)

    Armour, E A G; Liu, Y; Vigier, A

    2005-01-01

    The aim of experimentalists currently working on the preparation of antihydrogen is to trap it at very low temperatures so that its properties can be studied. Any process that can lead to loss of antihydrogen is thus of great concern to them. In view of this, we have carried out a calculation of the antiproton annihilation cross section in very low-energy hydrogen-antihydrogen scattering using a complex potential to represent the strong interaction that brings about the annihilation. The potential takes into account the isotopic spin state of the proton and the antiproton and the possibility that they may be in either a singlet or a triplet spin state. The results for the annihilation cross section and the percentage change in the elastic cross section due to the inclusion of the strong interaction are similar to those obtained in a recent calculation (Jonsell et al 2004 J. Phys. B: At. Mol. Opt. Phys. 37 1195), using an effective range expansion. They are smaller by a factor of 2 and 3, respectively, than those obtained in an earlier calculation (Voronin and Carbonell 2001 Nucl. Phys. A 689 529c), using a coupled channel method and a complex strong interaction potential. (letter to the editor)

  2. A finite-element visualization of quantum reactive scattering. II. Nonadiabaticity on coupled potential energy surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Warehime, Mick [Chemical Physics Program, University of Maryland, College Park, Maryland 20742-2021 (United States); Kłos, Jacek; Alexander, Millard H., E-mail: mha@umd.edu [Department of Chemistry and Biochemistry and Institute of Physical Science and Technology, University of Maryland, College Park, Maryland 20742-2021 (United States)

    2015-01-21

    This is the second in a series of papers detailing a MATLAB based implementation of the finite element method applied to collinear triatomic reactions. Here, we extend our previous work to reactions on coupled potential energy surfaces. The divergence of the probability current density field associated with the two electronically adiabatic states allows us to visualize in a novel way where and how nonadiabaticity occurs. A two-dimensional investigation gives additional insight into nonadiabaticity beyond standard one-dimensional models. We study the F({sup 2}P) + HCl and F({sup 2}P) + H{sub 2} reactions as model applications. Our publicly available code (http://www2.chem.umd.edu/groups/alexander/FEM) is general and easy to use.

  3. Double Polarized Neutron-Proton Scattering and Meson-Exchange Nucleon-Nucleon Potential Models

    International Nuclear Information System (INIS)

    Raichle, B.W.; Gould, C.R.; Haase, D.G.; Seely, M.L.; Walston, J.R.; Tornow, W.; Wilburn, W.S.; Raichle, B.W.; Gould, C.R.; Haase, D.G.; Seely, M.L.; Walston, J.R.; Tornow, W.; Wilburn, W.S.; Penttilae, S.I.; Hoffmann, G.W.

    1999-01-01

    We report on polarized beam - polarized target measurements of the spin-dependent neutron-proton total cross-section differences in longitudinal and transverse geometries (Δσ L and Δσ T , respectively) between E n =5 and 20MeV. Single-parameter phase-shift analyses were performed to extract the phase-shift mixing parameter var-epsilon 1 , which characterizes the strength of the nucleon-nucleon tensor interaction at low energies. Consistent with the trend of previous determinations at E n =25 and 50MeV, our values for var-epsilon 1 imply a stronger tensor force than predicted by meson-exchange nucleon-nucleon potential models and nucleon-nucleon phase-shift analyses. copyright 1999 The American Physical Society

  4. Exact potential and scattering amplitudes from the tachyon non-linear β -function

    International Nuclear Information System (INIS)

    Coletti, E.; Forini, V.; Nardelli, G.; Orselli, M.; Grignani, G.

    2004-01-01

    We compute, on the disk, the non-linear tachyon β-function, β T , of the open bosonic string theory. β T is determined both in an expansion to the third power of the field and to all orders in derivatives and in an expansion to any power of the tachyon field in the leading order in derivatives. We construct the Witten-Shatashvili (WS) space-time effective action S and prove that it has a very simple universal form in terms of the renormalized tachyon field and β T . The expression for S is well suited to studying both processes that are far off-shell, such as tachyon condensation, and close to the mass-shell, such as perturbative on-shell amplitudes. We evaluate S in a small derivative expansion, providing the exact tachyon potential. The normalization of S is fixed by requiring that the field redefinition that maps S into the tachyon effective action derived from the cubic string field theory is regular on-shell. The normalization factor is in precise agreement with the one required for verifying all the conjectures on tachyon condensation. The coordinates in the space of couplings in which the tachyon β-function is non linear are the most appropriate to study RG fixed points that can be interpreted as solitons of S, i.e. D-branes. (author)

  5. Complex Kohn variational principle for two-nucleon bound-state and scattering with the tensor potential

    International Nuclear Information System (INIS)

    Araujo Junior, C.F. de; Adhikari, S.K.; Tomio, L.

    1993-10-01

    Complex Kohn variational principle is applied to the numerical solution of the fully off-shell Lippmann-Schwinger equation for nucleon-nucleon scattering for various partial waves including the coupled 3 S 1 - 3 D 1 channel. Analytic expressions are obtained for all the integrals in the method for a suitable choice of expansion functions. Calculations with the partial waves 1 S 0 , 1 P 1 , 1 D 2 , and 3 S 1 - 3 D 1 of the Reid soft core potential show that the method converges faster than other solution schemes not only for the phase shift but also for the off-shell t matrix elements. It is also shown that its is trivial to modify this variational principle in order to make it suitable for bound-stage calculations. The bound-state approach is illustrated for the 3 S 1 - 3 D 1 channel of the Reid soft-core potential for calculating the deuteron binding, wave function and the D state asymptotic parameters. (author)

  6. Determination of the potential and coherent scattering cross-sections of the elements Si, Ca, Cr, Mn, Co, Zn, Zr, Sb and Ta

    International Nuclear Information System (INIS)

    Adib, M.; Abdel-Kawy, A.; Hamouda, I.

    1976-01-01

    The potential scattering cross-sections for slow neutrons have been measured for Si, Ca, Cr, Mn, Co, Zn, Zr, Sb and Ta in order to determine the nuclear potential radius and to investigate the prediction of nuclear optical model. The coherent scattering cross-sections for these elements have been measured from the obtained values of the Bragg cut-offs observed in the behaviour of the total cross-sections at cold neutron energies. The measurements were based on the total neutron cross-sections resulting from transmission experiments performed with the neutron chopper at ET-RR-1 reactor

  7. Inelastic 12C(12C, 12C)12C scattering via the Glauber optical potential at E/A=30 MeV and 85 MeV

    International Nuclear Information System (INIS)

    Chauvin, J.; Lebrun, D.; Durand, F.; Buenerd, M.

    1984-07-01

    It is shown that some approximations implied in the optical limit of the Glauber theory are justified for low energies heavy-ions surface collisions. The Glauber optical potential -with no free parameters- leads to reasonable predictions for both elastic and inelastic scattering in the 12 C + 12 C system

  8. THE PHYSICAL ORIGIN AND THE DIAGNOSTIC POTENTIAL OF THE SCATTERING POLARIZATION IN THE Li I RESONANCE DOUBLET AT 6708 A

    International Nuclear Information System (INIS)

    Belluzzi, Luca; Landi Degl'Innocenti, Egidio; Trujillo Bueno, Javier

    2009-01-01

    High-sensitivity measurements of the linearly polarized solar limb spectrum produced by scattering processes in quiet regions of the solar atmosphere showed that the Q/I profile of the lithium doublet at 6708 A has an amplitude ∼10 -4 and a curious three-peak structure, qualitatively similar to that found and confirmed by many observers in the Na I D 2 line. Given that a precise measurement of the scattering polarization profile of the lithium doublet lies at the limit of the present observational possibilities, it is worthwhile to clarify the physical origin of the observed polarization, its diagnostic potential, and what kind of Q/I shapes can be expected from theory. To this end, we have applied the quantum theory of atomic level polarization taking into account the hyperfine structure of the two stable isotopes of lithium, as well as the Hanle effect of a microturbulent magnetic field of arbitrary strength. We find that quantum interferences between the sublevels pertaining to the upper levels of the D 2 and D 1 line transitions of lithium do not cause any observable effect on the emergent Q/I profile. Our theoretical calculations show that only two Q/I peaks can be expected, with the strongest one caused by the D 2 line of 7 Li I and the weakest one due to the D 2 line of 6 Li I. Interestingly, we find that these two peaks in the theoretical Q/I profile stand out clearly only when the kinetic temperature of the thin atmospheric region that produces the emergent spectral line radiation is lower than 4000 K. The fact that such a thin atmospheric region is located around a height of 200 km in standard semi-empirical models, where the kinetic temperature is about 5000 K, leads us to suggest that the most likely Q/I profile produced by the Sun in the lithium doublet should be slightly asymmetric and dominated by the 7 Li I peak.

  9. Scattered image artifacts from cone beam computed tomography and its clinical potential in bone mineral density estimation.

    Science.gov (United States)

    Ko, Hoon; Jeong, Kwanmoon; Lee, Chang-Hoon; Jun, Hong Young; Jeong, Changwon; Lee, Myeung Su; Nam, Yunyoung; Yoon, Kwon-Ha; Lee, Jinseok

    2016-01-01

    Image artifacts affect the quality of medical images and may obscure anatomic structure and pathology. Numerous methods for suppression and correction of scattered image artifacts have been suggested in the past three decades. In this paper, we assessed the feasibility of use of information on scattered artifacts for estimation of bone mineral density (BMD) without dual-energy X-ray absorptiometry (DXA) or quantitative computed tomographic imaging (QCT). To investigate the relationship between scattered image artifacts and BMD, we first used a forearm phantom and cone-beam computed tomography. In the phantom, we considered two regions of interest-bone-equivalent solid material containing 50 mg HA per cm(-3) and water-to represent low- and high-density trabecular bone, respectively. We compared the scattered image artifacts in the high-density material with those in the low-density material. The technique was then applied to osteoporosis patients and healthy subjects to assess its feasibility for BMD estimation. The high-density material produced a greater number of scattered image artifacts than the low-density material. Moreover, the radius and ulna of healthy subjects produced a greater number of scattered image artifacts than those from osteoporosis patients. Although other parameters, such as bone thickness and X-ray incidence, should be considered, our technique facilitated BMD estimation directly without DXA or QCT. We believe that BMD estimation based on assessment of scattered image artifacts may benefit the prevention, early treatment and management of osteoporosis.

  10. Neutron-proton scattering

    International Nuclear Information System (INIS)

    Doll, P.

    1990-02-01

    Neutron-proton scattering as fundamental interaction process below and above hundred MeV is discussed. Quark model inspired interactions and phenomenological potential models are described. The seminar also indicates the experimental improvements for achieving new precise scattering data. Concluding remarks indicate the relevance of nucleon-nucleon scattering results to finite nuclei. (orig.) [de

  11. Angular scattering of 1–50 keV ions through graphene and thin carbon foils: Potential applications for space plasma instrumentation

    International Nuclear Information System (INIS)

    Ebert, Robert W.; Allegrini, Frédéric; Fuselier, Stephen A.; Nicolaou, Georgios; Bedworth, Peter; Sinton, Steve; Trattner, Karlheinz J.

    2014-01-01

    We present experimental results for the angular scattering of ∼1–50 keV H, He, C, O, N, Ne, and Ar ions transiting through graphene foils and compare them with scattering through nominal ∼0.5 μg cm −2 carbon foils. Thin carbon foils play a critical role in time-of-flight ion mass spectrometers and energetic neutral atom sensors in space. These instruments take advantage of the charge exchange and secondary electron emission produced as ions or neutral atoms transit these foils. This interaction also produces angular scattering and energy straggling for the incident ion or neutral atom that acts to decrease the performance of a given instrument. Our results show that the angular scattering of ions through graphene is less pronounced than through the state-of-the-art 0.5 μg cm −2 carbon foils used in space-based particle detectors. At energies less than 50 keV, the scattering angle half width at half maximum, ψ 1/2 , for ∼3–5 atoms thick graphene is up to a factor of 3.5 smaller than for 0.5 μg cm −2 (∼20 atoms thick) carbon foils. Thus, graphene foils have the potential to improve the performance of space-based plasma instruments for energies below ∼50 keV

  12. Class of exactly solvable scattering potentials in two dimensions, entangled-state pair generation, and a grazing-angle resonance effect

    Science.gov (United States)

    Loran, Farhang; Mostafazadeh, Ali

    2017-12-01

    We provide an exact solution of the scattering problem for the potentials of the form v (x ,y ) =χa(x ) [v0(x ) +v1(x ) ei α y] , where χa(x ) :=1 for x ∈[0 ,a ] , χa(x ) :=0 for x ∉[0 ,a ] , vj(x ) are real or complex-valued functions, χa(x ) v0(x ) is an exactly solvable scattering potential in one dimension, and α is a positive real parameter. If α exceeds the wave number k of the incident wave, the scattered wave does not depend on the choice of v1(x ) . In particular, v (x ,y ) is invisible if v0(x ) =0 and k α and v1(x ) ≠0 , the scattered wave consists of a finite number of coherent plane-wave pairs ψn± with wave vector: kn=(±√{k2-[nα ] 2 },n α ) , where n =0 ,1 ,2 ,...generating quantum states with a quantized component of momentum and pairs of states with an entangled momentum. We examine a realization of these potentials in terms of certain optical slabs. If k =N α for some positive integer N , ψN± coalesce and their amplitude diverge. If k exceeds N α slightly, ψN± have a much larger amplitude than ψn± with n scattered waves whose wave vector makes a small angle with the faces of the slab.

  13. Neutron scattering from 208Pb at 30.4 and 40.0 MeV and isospin dependence of the nucleon optical potential

    Science.gov (United States)

    Devito, R. P.; Khoa, Dao T.; Austin, Sam M.; Berg, U. E. P.; Loc, Bui Minh

    2012-02-01

    Background: Analysis of data involving nuclei far from stability often requires the optical potential (OP) for neutron scattering. Because neutron data are seldom available, whereas proton scattering data are more abundant, it is useful to have estimates of the difference of the neutron and proton optical potentials. This information is contained in the isospin dependence of the nucleon OP. Here we attempt to provide it for the nucleon-208Pb system.Purpose: The goal of this paper is to obtain accurate n+208Pb scattering data and use it, together with existing p+208Pb and 208Pb(p,n)208BiIAS* data, to obtain an accurate estimate of the isospin dependence of the nucleon OP at energies in the 30-60-MeV range.Method: Cross sections for n+208Pb scattering were measured at 30.4 and 40.0 MeV, with a typical relative (normalization) accuracy of 2-4% (3%). An angular range of 15∘ to 130∘ was covered using the beam-swinger time-of-flight system at Michigan State University. These data were analyzed by a consistent optical-model study of the neutron data and of elastic p+208Pb scattering at 45 and 54 MeV. These results were combined with a coupled-channel analysis of the 208Pb(p,n) reaction at 45 MeV, exciting the 0+ isobaric analog state (IAS) in 208Bi.Results: The new data and analysis give an accurate estimate of the isospin impurity of the nucleon-208Pb OP at 30.4 MeV caused by the Coulomb correction to the proton OP. The corrections to the real proton OP given by the CH89 global systematics were found to be only a few percent, whereas for the imaginary potential it was greater than 20% at the nuclear surface. On the basis of the analysis of the measured elastic n+208Pb data at 40 MeV, a Coulomb correction of similar strength and shape was also predicted for the p+208Pb OP at energies around 54 MeV.Conclusions: Accurate neutron scattering data can be used in combination with proton scattering data and (p,n) charge exchange data leading to the IAS to obtain reliable

  14. The effect of a non-hermitian crystal potential on the scattering matrix in reflection electron diffraction

    International Nuclear Information System (INIS)

    Smith, A.E.; Josefsson, T.W.

    1994-01-01

    An extension to include general inelastic scattering effects is developed for the case of reflection electron diffraction scattering from surfaces. In this extension of work by Lynch and Moodie, it is shown how the resultant non-Hermitian matrix problem can be recast in a form that is suitable for computation. In particular, a computational method is outlined based on techniques developed by Eberlein for matrix diagonalisation using complex rotations and shears. The resultant methods are applied to the problem of Convergent Beam RHEED. 23 refs., 3 figs

  15. Evaluation of interatomic potentials for rainbow scattering under axial channeling at KCl(0 0 1) surface by three-dimensional computer simulations based on binary collision approximation

    Energy Technology Data Exchange (ETDEWEB)

    Takeuchi, Wataru, E-mail: take@sp.ous.ac.jp

    2017-05-01

    The rainbow angles corresponding to prominent peaks in the angular distributions of scattered projectiles with small angle, attributed to rainbow scattering (RS), under axial surface channeling conditions are strongly influenced by the interatomic potentials between projectiles and target atoms. The dependence of rainbow angles on normal energy of projectile energy to the target surface, being experimentally obtained by Specht et al. for RS of He, N, Ne and Ar atoms under 〈1 0 0〉 and 〈1 1 0〉 axial channeling conditions at a KCl(0 0 1) surface with projectile energies of 1–60 keV, was evaluated by the three-dimensional computer simulations using the ACOCT code based on the binary collision approximation with interatomic pair potentials. Good agreement between the ACOCT results using the ZBL pair potential and the individual pair potentials calculated from Hartree-Fock (HF) wave functions and the experimental ones was found for RS of He, N and Ne atoms from the atomic rows along 〈1 0 0〉 direction. For 〈1 1 0〉 direction, the ACOCT results employing the Moliere pair potential with adjustable screening length of O’Connor-Biersack (OB) formula, the ZBL pair potential and the individual HF pair potentials except for Ar → KCl using the OB pair potential are nearly in agreement with the experimental ones.

  16. Optical potentials and isoscalar transition rates from 104 MeV alpha-particle scattering by the N=28 isotopes 48Ca, 50Ti and 52Cr

    International Nuclear Information System (INIS)

    Friedman, E.; Pesl, R.; Gils, H.J.; Rebel, H.; Buschmann, J.; Klewe-Nebenius, H.; Zagromski, S.

    1983-02-01

    Precisely measured differential cross sections for elastic and inelastic scattering from 104 MeV alpha-particles by 48 Ca, 50 Ti and 52 Cr are reported. The analyses aim primarily at the determination of strength, radial shapes and deformation of the scattering potentials, looking for isotonic differences of N = 28 isotones. The mean square radii of the (real) potentials are discussed in terms of mean square radius differences of the matter distributions. The isoscalar transition rates derived by coupled channel analyses of the measured cross sections are compared with electromagnetic rates. In addition to the analyses on the basis of a slightly generalized extended optical model a semi-microscopic deformed folding model has been applied, using a density-dependent effective alpha-bound nucleon interaction. Though an excellent description of the data over the full angular range is obtained the resulting values of the deformation parameters appear to be not consistent with results from various different methods. (orig.) [de

  17. Inversion of real and complex phase shifts to potentials by the generalized Cox-Thompson inverse scattering method at fixed energy

    International Nuclear Information System (INIS)

    Melchert, O; Scheid, W; Apagyi, B

    2006-01-01

    The Cox-Thompson inverse scattering method at fixed energy has been generalized to treat complex phase shifts derived from experiments. New formulae for relating phase shifts to shifted angular momenta are derived. The method is applied to phase shifts of known potentials in order to test its quality and stability and, further, it is used to invert experimental n-α and n- 12 C phase shifts

  18. Scattering of thermal He beams by crossed atomic and molecular beams. I. Sensitivity of the elastic differential cross section to the interatomic potential

    International Nuclear Information System (INIS)

    Keil, M.; Kuppermann, A.

    1978-01-01

    The ability of diffraction oscillations in atomic beam scattering experiments to uniquely determine interatomic potentials for highly quantal systems is examined. Assumed but realistic potentials are used to generate, by scattering calculations and incorporation of random errors, differential cross sections which are then treated as if they were ''experimental'' data. From these, attempts are made to recover the initial potential by varying the parameters of assumed mathematical forms different from the original one, until a best fit to the ''experimental'' results is obtained. It is found that the region of the interaction potential around the van der Waals minimum is accurately determined by the ''measured'' differential cross sections over a range of interatomic separations significantly wider than would be expected classically. It is also found, for collision energies at which the weakly repulsive wall is appreciably sampled, that the SPF--Dunham and double Morse--van der Waals types of potentials lead to accurate determinations of the interatomic potential, whereas many other mathematical forms do not. Analytical parameterizations most appropriate for obtaining accurate interatomic potentials from thermal DCS experiments, for a given highly quantal system, may depend on the collision energy used

  19. Introducing single-crystal scattering and optical potentials into MCNPX: Predicting neutron emission from a convoluted moderator

    Energy Technology Data Exchange (ETDEWEB)

    Gallmeier, F.X., E-mail: gallmeierfz@ornl.gov [Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Iverson, E.B.; Lu, W. [Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Baxter, D.V. [Center for the Exploration of Energy and Matter, Indiana University, Bloomington, IN 47408 (United States); Muhrer, G.; Ansell, S. [European Spallation Source, ESS AB, Lund (Sweden)

    2016-04-01

    Neutron transport simulation codes are indispensable tools for the design and construction of modern neutron scattering facilities and instrumentation. Recently, it has become increasingly clear that some neutron instrumentation has started to exploit physics that is not well-modeled by the existing codes. In particular, the transport of neutrons through single crystals and across interfaces in MCNP(X), Geant4, and other codes ignores scattering from oriented crystals and refractive effects, and yet these are essential phenomena for the performance of monochromators and ultra-cold neutron transport respectively (to mention but two examples). In light of these developments, we have extended the MCNPX code to include a single-crystal neutron scattering model and neutron reflection/refraction physics. We have also generated silicon scattering kernels for single crystals of definable orientation. As a first test of these new tools, we have chosen to model the recently developed convoluted moderator concept, in which a moderating material is interleaved with layers of perfect crystals to provide an exit path for neutrons moderated to energies below the crystal's Bragg cut–off from locations deep within the moderator. Studies of simple cylindrical convoluted moderator systems of 100 mm diameter and composed of polyethylene and single crystal silicon were performed with the upgraded MCNPX code and reproduced the magnitude of effects seen in experiments compared to homogeneous moderator systems. Applying different material properties for refraction and reflection, and by replacing the silicon in the models with voids, we show that the emission enhancements seen in recent experiments are primarily caused by the transparency of the silicon and void layers. Finally we simulated the convoluted moderator experiments described by Iverson et al. and found satisfactory agreement between the measurements and the simulations performed with the tools we have developed.

  20. A Potential Cyclotron Resonant Scattering Feature in the Ultraluminous X-Ray Source Pulsar NGC 300 ULX1 Seen by NuSTAR and XMM-Newton

    Science.gov (United States)

    Walton, D. J.; Bachetti, M.; Fürst, F.; Barret, D.; Brightman, M.; Fabian, A. C.; Grefenstette, B. W.; Harrison, F. A.; Heida, M.; Kennea, J.; Kosec, P.; Lau, R. M.; Madsen, K. K.; Middleton, M. J.; Pinto, C.; Steiner, J. F.; Webb, N.

    2018-04-01

    Based on phase-resolved broadband spectroscopy using XMM-Newton and NuSTAR, we report on a potential cyclotron resonant scattering feature (CRSF) at E ∼ 13 keV in the pulsed spectrum of the recently discovered ultraluminous X-ray source (ULX) pulsar NGC 300 ULX1. If this interpretation is correct, the implied magnetic field of the central neutron star is B ∼ 1012 G (assuming scattering by electrons), similar to that estimated from the observed spin-up of the star, and also similar to known Galactic X-ray pulsars. We discuss the implications of this result for the connection between NGC 300 ULX1 and the other known ULX pulsars, particularly in light of the recent discovery of a likely proton cyclotron line in another ULX, M51 ULX-8.

  1. Evaluation of interatomic potentials for noble gas atoms from rainbow scattering under axial channeling at Ag(1 1 1) surface by computer simulations based on binary collision approximation

    Energy Technology Data Exchange (ETDEWEB)

    Takeuchi, Wataru, E-mail: take@sp.ous.ac.jp

    2016-01-01

    The rainbow angles corresponding to pronounced peaks in the angular distributions of scattered projectiles with small angle, attributed to rainbow scattering (RS), under axial surface channeling conditions are strongly dependent on the interatomic potentials between projectiles and target atoms. The dependence of rainbow angles on normal energy of projectile energy to the target surface that has been experimentally obtained by Schüller and Winter (SW) (2007) for RS of He, Ne and Ar atoms from a Ag(1 1 1) surface with projectile energies of 3–60 keV was evaluated by the three-dimensional computer simulations using the ACOCT code based on the binary collision approximation with interatomic pair potentials. Consequently, the ACOCT results employing the Moliere pair potential with screening length correction close to adjustable one of O’Connor and Biersack (OB) formula are almost in agreement with the experimental ones, being self-consistent with the SW’s ones analyzed by computer simulations of classical trajectory calculations as RS from corrugated equipotential planes based on continuum potentials including the Moliere pair potential with screening length correction of the OB formula.

  2. Boosting the Amount of Molecular Information Through Polarized Resolved Resonance Raman Scattering

    DEFF Research Database (Denmark)

    Hassing, Søren

    2017-01-01

    and near-infrared absorption spectroscopy, i.e. only the spectral distribution is analysed. The goal of the present chapter is to demonstrate that the amount of molecular information (also for solutions and powders) can be increased considerably by analysing also the polarization of the Raman and resonance...... Ramanscattered light. The goal is achieved through: (1) a discussion of the basic properties of Raman scattering with special focus on polarization and polarization dispersion. The discussion includes the rotational invariants of Raman tensors, the non-commuting generator approach to molecular symmetry as a tool...... for construction of state and Raman tensors for single molecules and dimers and higher aggregates and thereby predict the polarization; (2) a discussion of two illustrative case studies: Case study 1: Aggregation of haemoglobin in red blood cells (RBC); and Case study 2: In vitro polarization resolved RRS study...

  3. Stationary theory of scattering

    International Nuclear Information System (INIS)

    Kato, T.

    1977-01-01

    A variant of the stationary methods is described, and it is shown that it is useful in a wide range of problems, including scattering, by long-range potentials, two-space scattering, and multichannel scattering. The method is based on the notion of spectral forms. The paper is restricted to the simplest case of continuous spectral forms defined on a Banach space embedded in the basic Hilbert space. (P.D.)

  4. Physical evaluation of prototype high-performance anti-scatter grids: potential for improved digital radiographic image quality

    International Nuclear Information System (INIS)

    Fetterly, Kenneth A; Schueler, Beth A

    2009-01-01

    Grid evaluation for a screen-film x-ray system has typically included independent measurement of the opposing contrast improvement factor and Bucky factor. Neither of these metrics, however, is appropriate when assessing grid performance in a digital imaging environment. For digital radiographic systems, the benefit of an anti-scatter grid is well characterized by the quantum signal-to-noise ratio improvement factor (K SNR ) provided by the grid. The purpose of this work was to measure K SNR of prototype grids designed for use with digital radiographic systems. The prototype grids had 5 mm tall lead septa, fiber interspace material, line rate N = 25 and 36 cm -1 and ratio r = 15 and 21, respectively. The primary and scatter transmission properties of the grids were measured, and K SNR was evaluated over a phantom thickness range of 10-50 cm. To provide a comparison, the K SNR of similarly constructed N44r15 and N80r15 grids is also reported. K SNR of the prototype grids ranged from 1.4 for the 10 cm phantom to 2.4 for the 50 cm phantom. For the thickest phantom, the SNR improvement factor of the prototype grids was 18-83% higher than that of the N44r15 and N80r15 grids, respectively. (note)

  5. Extended two-particle Green close-quote s functions and optical potentials for two particle scattering by by many-body targets

    International Nuclear Information System (INIS)

    Brand, J.; Cederbaum, L.S.

    1996-01-01

    An extension of the fermionic particle-particle propagator is presented that possesses similar algebraic properties to the single-particle Green close-quote s function. In particular, this extended two-particle Green close-quote s function satisfies Dyson close-quote s equation and its self energy has the same analytic structure as the self energy of the single-particle Green close-quote s function. For the case of a system interacting with one-particle potentials only, the two-particle self energy takes on a particularly simple form, just like the common self energy does. The new two-particle self energy also serves as a well behaved optical potential for the elastic scattering of a two-particle projectile by a many-body target. Due to its analytic structure, the two-particle self energy avoids divergences that appear with effective potentials derived by other means. Copyright copyright 1996 Academic Press, Inc

  6. Sum rules and other properties involving resonance projection operators. [for optical potential description of electron scattering from atoms and ions

    Science.gov (United States)

    Berk, A.; Temkin, A.

    1985-01-01

    A sum rule is derived for the auxiliary eigenvalues of an equation whose eigenspectrum pertains to projection operators which describe electron scattering from multielectron atoms and ions. The sum rule's right-hand side depends on an integral involving the target system eigenfunctions. The sum rule is checked for several approximations of the two-electron target. It is shown that target functions which have a unit eigenvalue in their auxiliary eigenspectrum do not give rise to well-defined projection operators except through a limiting process. For Hylleraas target approximations, the auxiliary equations are shown to contain an infinite spectrum. However, using a Rayleigh-Ritz variational principle, it is shown that a comparatively simple aproximation can exhaust the sum rule to better than five significant figures. The auxiliary Hylleraas equation is greatly simplified by conversion to a square root equation containing the same eigenfunction spectrum and from which the required eigenvalues are trivially recovered by squaring.

  7. Semiclassical derivation of a local optical potential for heavy-ion elastic scattering. [Coupling to other processes

    Energy Technology Data Exchange (ETDEWEB)

    Donangelo, R; Canto, L F [Rio de Janeiro Univ. (Brazil). Inst. de Fisica; Hussein, M S [Sao Paulo Univ. (Brazil). Inst. de Fisica

    1979-05-21

    A semiclassical method to determine the contribution to the optical potential in the elastic channel due to the coupling to other processes taking place in heavy-ion collisions is developed. An application is made to the case of Coulomb excitation. The lowest-order term of the potential used is shown to be identical to the potential derived by Baltz et al.

  8. Determinable solutions for one-dimensional quantum potentials: scattering, quasi-bound and bound-state problems

    International Nuclear Information System (INIS)

    Lee, Hwasung; Lee, Y J

    2007-01-01

    We derive analytic expressions of the recursive solutions to Schroedinger's equation by means of a cutoff-potential technique for one-dimensional piecewise-constant potentials. These solutions provide a method for accurately determining the transmission probabilities as well as the wavefunction in both classically accessible regions and inaccessible regions for any barrier potentials. It is also shown that the energy eigenvalues and the wavefunctions of bound states can be obtained for potential-well structures by exploiting this method. Calculational results of illustrative examples are shown in order to verify this method for treating barrier and potential-well problems

  9. Simulations of the azimuthal distribution of low-energy H atoms scattered off Ag(1 1 0) at grazing incidence: DFT many-body versus model pair potentials

    CERN Document Server

    Cafarelli, P; Benazeth, C; Nieuwjaer, N; Lorente, N

    2003-01-01

    We compare the azimuthal distribution of H atoms after scattering off Ag(1 1 0) obtained by molecular dynamics with different H-Ag(1 1 0) potential energy surfaces (PES) and experimental results. We use grazing incident H atoms and low energies (up to 4 keV). Density functional theory (DFT) calculations are performed for the static case of an H atom in front of an Ag(1 1 0) surface. The surface is represented by an 8-atom slab, and the H atoms form 1x1 and 2x2 supercells. The generalized gradient approximation is used. Classical trajectories are evaluated on the obtained PES, and the azimuthal distribution of the scattered atoms is calculated. Good agreement with experiment is obtained which gives us some confidence in the correct description of the system at low energies by the static DFT calculations. These results are also compared with pair-potential calculations. The accuracy of trajectories may be important for the correct evaluation of charge transfer, energy loss and straggling during ion-surface coll...

  10. Scattering theory and chemical reactions

    International Nuclear Information System (INIS)

    Kuppermann, A.

    1988-01-01

    In this course, scattering theory and chemical reactions are presented including scattering of one particle by a potential, n-particle systems, colinear triatomic molecules and the study of reactive scattering for 3-dimensional triatomic systems. (A.C.A.S.) [pt

  11. Visualizing redox orbitals and their potentials in advanced lithium-ion battery materials using high-resolution x-ray Compton scattering.

    Science.gov (United States)

    Hafiz, Hasnain; Suzuki, Kosuke; Barbiellini, Bernardo; Orikasa, Yuki; Callewaert, Vincent; Kaprzyk, Staszek; Itou, Masayoshi; Yamamoto, Kentaro; Yamada, Ryota; Uchimoto, Yoshiharu; Sakurai, Yoshiharu; Sakurai, Hiroshi; Bansil, Arun

    2017-08-01

    Reduction-oxidation (redox) reactions are the key processes that underlie the batteries powering smartphones, laptops, and electric cars. A redox process involves transfer of electrons between two species. For example, in a lithium-ion battery, current is generated when conduction electrons from the lithium anode are transferred to the redox orbitals of the cathode material. The ability to visualize or image the redox orbitals and how these orbitals evolve under lithiation and delithiation processes is thus of great fundamental and practical interest for understanding the workings of battery materials. We show that inelastic scattering spectroscopy using high-energy x-ray photons (Compton scattering) can yield faithful momentum space images of the redox orbitals by considering lithium iron phosphate (LiFePO 4 or LFP) as an exemplar cathode battery material. Our analysis reveals a new link between voltage and the localization of transition metal 3d orbitals and provides insight into the puzzling mechanism of potential shift and how it is connected to the modification of the bond between the transition metal and oxygen atoms. Our study thus opens a novel spectroscopic pathway for improving the performance of battery materials.

  12. Hulthén potential models for α−α and α−He3 elastic scattering

    Indian Academy of Sciences (India)

    2017-02-09

    Feb 9, 2017 ... considered between each pair of particles, is a finite- depth central potential. As the α-particles are tightly bound, the low-lying states of such systems can be determined fairly well through the relative motion of α-particles. The general procedure to understand such a system is to make use of the partial wave ...

  13. Scattering of a two skyrmion configuration on potential holes or barriers in a model Landau-Lifshitz equation

    International Nuclear Information System (INIS)

    Collins, J C; Zakrzewski, W J

    2009-01-01

    The dynamics of a baby-skyrmion configuration, in a model Landau-Lifshitz equation, was studied in the presence of various potential obstructions. The baby-skyrmion configuration was constructed from two Q = 1 hedgehog solutions to the baby-skyrme model in (2+1) dimensions. The potential obstructions were created by introducing a new term into the Lagrangian which resulted in a localized inhomogeneity in the potential terms' coefficient. In the barrier system, the normal circular path was deformed as the skyrmions traversed the barrier. During the same period, it was seen that the skyrmions sped up as they went over the barrier. For critical values of the barrier height and width, the skyrmions were no longer bound and were free to separate. In the case of a potential hole, the baby skyrmions no longer formed a bound state and moved asymptotically along the axis of the hole. It is shown how to modify the definition of the angular momentum to include the effects of the obstructions, so that it is conserved

  14. Dynamics of a bright soliton in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential

    International Nuclear Information System (INIS)

    Liang, Z.X.; Zhang, Z.D.; Liu, W.M.

    2005-01-01

    We present a family of exact solutions of the one-dimensional nonlinear Schroedinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background

  15. pd Scattering Using a Rigorous Coulomb Treatment: Reliability of the Renormalization Method for Screened-Coulomb Potentials

    International Nuclear Information System (INIS)

    Hiratsuka, Y.; Oryu, S.; Gojuki, S.

    2011-01-01

    Reliability of the screened Coulomb renormalization method, which was proposed in an elegant way by Alt-Sandhas-Zankel-Ziegelmann (ASZZ), is discussed on the basis of 'two-potential theory' for the three-body AGS equations with the Coulomb potential. In order to obtain ASZZ's formula, we define the on-shell Moller function, and calculate it by using the Haeringen criterion, i. e. 'the half-shell Coulomb amplitude is zero'. By these two steps, we can finally obtain the ASZZ formula for a small Coulomb phase shift. Furthermore, the reliability of the Haeringen criterion is thoroughly checked by a numerically rigorous calculation for the Coulomb LS-type equation. We find that the Haeringen criterion can be satisfied only in the higher energy region. We conclude that the ASZZ method can be verified in the case that the on-shell approximation to the Moller function is reasonable, and the Haeringen criterion is reliable. (author)

  16. Low temperature rate coefficients of the H + CH(+) → C(+) + H2 reaction: New potential energy surface and time-independent quantum scattering.

    Science.gov (United States)

    Werfelli, Ghofran; Halvick, Philippe; Honvault, Pascal; Kerkeni, Boutheïna; Stoecklin, Thierry

    2015-09-21

    The observed abundances of the methylidyne cation, CH(+), in diffuse molecular clouds can be two orders of magnitude higher than the prediction of the standard gas-phase models which, in turn, predict rather well the abundances of neutral CH. It is therefore necessary to investigate all the possible formation and destruction processes of CH(+) in the interstellar medium with the most abundant species H, H2, and e(-). In this work, we address the destruction process of CH(+) by hydrogen abstraction. We report a new calculation of the low temperature rate coefficients for the abstraction reaction, using accurate time-independent quantum scattering and a new high-level ab initio global potential energy surface including a realistic model of the long-range interaction between the reactants H and CH(+). The calculated thermal rate coefficient is in good agreement with the experimental data in the range 50 K-800 K. However, at lower temperatures, the experimental rate coefficient takes exceedingly small values which are not reproduced by the calculated rate coefficient. Instead, the latter rate coefficient is close to the one given by the Langevin capture model, as expected for a reaction involving an ion and a neutral species. Several recent theoretical works have reported a seemingly good agreement with the experiment below 50 K, but an analysis of these works show that they are based on potential energy surfaces with incorrect long-range behavior. The experimental results were explained by a loss of reactivity of the lowest rotational states of the reactant; however, the quantum scattering calculations show the opposite, namely, a reactivity enhancement with rotational excitation.

  17. The interpretation of resonance formation in coupled-channel models of positron scattering by atomic hydrogen using localized optical potentials

    International Nuclear Information System (INIS)

    Bransden, B.H.; Hewitt, R.N.

    1997-01-01

    Above-threshold resonances can occur in coupled-channel models of the e + + H system when Ps formation is taken into account (although it should be pointed out that, in this specific system, resonances do not occur in an exact theory). In general, to understand the mechanism of resonance formation it is useful to obtain the exact optical potential in a given channel in a localized form. The methods of achieving this localization are discussed with reference to a specific application to the resonance found in the two-state approximation for the l = 0 partial wave. (author)

  18. Applications of inverse and algebraic scattering theories

    Energy Technology Data Exchange (ETDEWEB)

    Amos, K. [Qinghua Univ., Beijing, BJ (China). Dept. of Physics

    1997-06-01

    Inverse scattering theories, algebraic scattering theory and exactly solvable scattering potentials are diverse ways by which scattering potentials can be defined from S-functions specified by fits to fixed energy, quantal scattering data. Applications have been made in nuclear (heavy ion and nucleon-nucleus scattering), atomic and molecular (electron scattering from simple molecules) systems. Three inverse scattering approaches are considered in detail; the semiclassical WKB and fully quantal Lipperheide-Fiedeldey method, than algebraic scattering theory is applied to heavy ion scattering and finally the exactly solvable Ginocchio potentials. Some nuclear results are ambiguous but the atomic and molecular inversion potentials are in good agreement with postulated forms. 21 refs., 12 figs.

  19. Quasiresonant scattering

    International Nuclear Information System (INIS)

    Hategan, Cornel; Comisel, Horia; Ionescu, Remus A.

    2004-01-01

    The quasiresonant scattering consists from a single channel resonance coupled by direct interaction transitions to some competing reaction channels. A description of quasiresonant Scattering, in terms of generalized reduced K-, R- and S- Matrix, is developed in this work. The quasiresonance's decay width is, due to channels coupling, smaller than the width of the ancestral single channel resonance (resonance's direct compression). (author)

  20. Thomson Scattering

    NARCIS (Netherlands)

    Donne, A. J. H.

    1994-01-01

    Thomson scattering is a very powerful diagnostic which is applied at nearly every magnetic confinement device. Depending on the experimental conditions different plasma parameters can be diagnosed. When the wave vector is much larger than the plasma Debye length, the total scattered power is

  1. Equivalence of two non-commutative geometry approaches

    International Nuclear Information System (INIS)

    Guo Hanying; Wu Ke; Li Jianming.

    1994-10-01

    We show that differential calculus on discrete group Z 2 is equivalent to A. Connes' approach in the case of two discrete points. They are the same theory in terms of different basis and the discrete group Z 2 is the permutation group of two discrete point. (author). 11 refs

  2. Einstein–Podolski–Rosen paradox, non-commuting operator ...

    Indian Academy of Sciences (India)

    Rosen (EPR) moved on to show that the quantum theory is incomplete .... discuss the notion of entanglement due to Bohm [4] because it is the only surviving issue ..... If this internal time-scales are extremely rapid, then it is meaningless to ...

  3. Muon 2 measurements and non-commutative geometry of quantum ...

    Indian Academy of Sciences (India)

    Abstract. We discuss a completely quantum mechanical treatment of the measurement of the anomalous magnetic moment of the muon. A beam of muons move in a strong uniform magnetic field and a weak focusing electrostatic field. Errors in the classical beam analysis are exposed. In the Dirac quantum beam analysis, ...

  4. The Urbanik generalized convolutions in the non-commutative ...

    Indian Academy of Sciences (India)

    −sν(dx) < ∞. Now we apply this construction to the Kendall convolution case, starting with the weakly stable measure δ1. Example 1. Let △ be the Kendall convolution, i.e. the generalized convolution with the probability kernel: δ1△δa = (1 − a)δ1 + aπ2 for a ∈ [0, 1] and π2 be the Pareto distribution with the density π2(dx) =.

  5. Quasi-normal modes from non-commutative matrix dynamics

    Science.gov (United States)

    Aprile, Francesco; Sanfilippo, Francesco

    2017-09-01

    We explore similarities between the process of relaxation in the BMN matrix model and the physics of black holes in AdS/CFT. Focusing on Dyson-fluid solutions of the matrix model, we perform numerical simulations of the real time dynamics of the system. By quenching the equilibrium distribution we study quasi-normal oscillations of scalar single trace observables, we isolate the lowest quasi-normal mode, and we determine its frequencies as function of the energy. Considering the BMN matrix model as a truncation of N=4 SYM, we also compute the frequencies of the quasi-normal modes of the dual scalar fields in the AdS5-Schwarzschild background. We compare the results, and we finda surprising similarity.

  6. Non commutative geometry methods for group C*-algebras

    International Nuclear Information System (INIS)

    Do Ngoc Diep.

    1996-09-01

    This book is intended to provide a quick introduction to the subject. The exposition is scheduled in the sequence, as possible for more understanding for beginners. The author exposed a K-theoretic approach to study group C * -algebras: started in the elementary part, with one example of description of the structure of C * -algebra of the group of affine transformations of the real straight line, continued then for some special classes of solvable and nilpotent Lie groups. In the second advanced part, he introduced the main tools of the theory. In particular, the conception of multidimensional geometric quantization and the index of group C * -algebras were created and developed. (author). Refs

  7. Non commutative geometry methods for group C{sup *}-algebras

    Energy Technology Data Exchange (ETDEWEB)

    Diep, Do Ngoc

    1996-09-01

    This book is intended to provide a quick introduction to the subject. The exposition is scheduled in the sequence, as possible for more understanding for beginners. The author exposed a K-theoretic approach to study group C{sup *}-algebras: started in the elementary part, with one example of description of the structure of C{sup *}-algebra of the group of affine transformations of the real straight line, continued then for some special classes of solvable and nilpotent Lie groups. In the second advanced part, he introduced the main tools of the theory. In particular, the conception of multidimensional geometric quantization and the index of group C{sup *}-algebras were created and developed. (author). Refs.

  8. Non-commutative Chern numbers for generic aperiodic discrete systems

    Science.gov (United States)

    Bourne, Chris; Prodan, Emil

    2018-06-01

    The search for strong topological phases in generic aperiodic materials and meta-materials is now vigorously pursued by the condensed matter physics community. In this work, we first introduce the concept of patterned resonators as a unifying theoretical framework for topological electronic, photonic, phononic etc (aperiodic) systems. We then discuss, in physical terms, the philosophy behind an operator theoretic analysis used to systematize such systems. A model calculation of the Hall conductance of a 2-dimensional amorphous lattice is given, where we present numerical evidence of its quantization in the mobility gap regime. Motivated by such facts, we then present the main result of our work, which is the extension of the Chern number formulas to Hamiltonians associated to lattices without a canonical labeling of the sites, together with index theorems that assure the quantization and stability of these Chern numbers in the mobility gap regime. Our results cover a broad range of applications, in particular, those involving quasi-crystalline, amorphous as well as synthetic (i.e. algorithmically generated) lattices.

  9. A high resolution helium atom scattering and far infrared study of the dynamics and the lateral potential energy surface of CO molecules chemisorbed on Cu(001)

    International Nuclear Information System (INIS)

    Graham, A.P.; Hofmann, F.; Toennies, J.P.; Williams, G.P.; Hirschmugl, C.J.; Ellis, J.

    1998-01-01

    Inelastic helium scattering (HAS) and infrared reflection adsorption spectroscopy (IRAS) have been used to measure the isotope shifts of the frequencies of both the parallel and perpendicular frustrated translation modes, as well as the frustrated rotation mode of CO molecules at on top sites on Cu(001). The measured isotope shifts for four different isotopomers indicates a significant rotational contribution to the parallel frustrated translation (T-mode), where the vibrational amplitude of the oxygen atom is significantly larger than for the carbon atom. Conversely, for the frustrated rotation the vibrational amplitude of the carbon atom was observed to be larger than for the oxygen atom. At surface temperatures above T s =100 K a careful analysis of the peak shape of the HAS quasielastic peak shows a small broadening, which is attributed to a rapid diffusion of the CO molecules. The measured dynamic diffusion barrier of 31±10 meV is compatible with the shape of the potential at the on-top site and makes it possible to extend the potential energy surface to the region between the on-top sites. copyright 1998 American Institute of Physics

  10. Electron-atom scattering

    International Nuclear Information System (INIS)

    McCarthy, I.E.

    1991-07-01

    The coupled-channels-optical method has been implemented using two different approximations to the optical potential. The half-on-shell optical potential involves drastic approximations for numerical feasibility but still gives a good semiquantitative description of the effect of uncoupled channels on electron scattering from hydrogen, helium and sodium. The distorted-wave optical potential makes no approximations other than the weak coupling approximation for uncoupled channels. In applications to hydrogen and sodium it shows promise of describing scattering phenomena excellently at all energies. 27 refs., 5 figs

  11. Introduction to Schroedinger inverse scattering

    International Nuclear Information System (INIS)

    Roberts, T.M.

    1991-01-01

    Schroedinger inverse scattering uses scattering coefficients and bound state data to compute underlying potentials. Inverse scattering has been studied extensively for isolated potentials q(x), which tend to zero as vertical strokexvertical stroke→∞. Inverse scattering for isolated impurities in backgrounds p(x) that are periodic, are Heaviside steps, are constant for x>0 and periodic for x<0, or that tend to zero as x→∞ and tend to ∞ as x→-∞, have also been studied. This paper identifies literature for the five inverse problems just mentioned, and for four other inverse problems. Heaviside-step backgrounds are discussed at length. (orig.)

  12. Boson-triboson Scattering with Yamaguchi potential. 2. Inclusion of additional p-wave component for the 3+1-subamplitude

    International Nuclear Information System (INIS)

    Matsui, Yoshiko

    1999-01-01

    In order to investigate the p-wave contribution from the 3+1-subamplitude in the S-wave phase shift for boson-triboson elastic scattering when the Yamaguchi potential for the two-body interaction is assumed, the Faddeev-Osborn equation for a system of four identical bosons in solved numerically by extending the previous calculation to include the p-wave component for the 3+1-subamplitude. The results obtained closely resemble the previous results. The calculated phase shift generally has the standard behavior of the two-body phase shift for a loosely bound state and has further characteristic behavior represented by a valley witha peak as fine structure. The phase shift obtained in the present calculation has a higher peak and a deeper valley than the previous one, while the positions of the peak and the valley in the two sets of results agree precisely. Thus the calculated resonance energies are the same as those obtained in the previous result. (author)

  13. Multiphonon resonant Raman scattering in the semimagnetic semiconductor Cd1-xMnxTe: Froehlich and deformation potential exciton-phonon interaction

    International Nuclear Information System (INIS)

    Riera, R; Rosas, R; Marin, J L; Bergues, J M; Campoy, G

    2003-01-01

    A theory describing multiphonon resonant Raman scattering (MPRRS) processes in wide-gap diluted magnetic semiconductors is presented, with Cd 1-x Mn x Te as an example. The incident radiation frequency ω l is taken above the fundamental absorption region. The photoexcited electron and hole make real transitions through the LO phonon, when one considers Froehlich (F) and deformation potential (DP) interactions. The strong exchange interaction, typical of these materials, leads to a large spin splitting of the exciton states in the magnetic field. Neglecting Landau quantization, this Zeeman splitting gives rise to the formation of eight bands (two conduction and six valence ones) and ten different exciton states according to the polarization of the incident light. Explicit expressions for the MPRRS intensity of second and third order, the indirect creation and annihilation probabilities, the exciton lifetime, and the probabilities of transition between different exciton states and different types of exciton as a function of ω l and the external magnetic field are presented. The selection rules for all hot exciton transitions via exciton-photon interaction and F and DP exciton-phonon interactions are investigated. The exciton energies, as a function of B, the Mn concentration x, and the temperature T, are compared to a theoretical expression. Graphics for creation and annihilation probabilities, lifetime, and Raman intensity of second and third order are discussed

  14. Critical scattering

    International Nuclear Information System (INIS)

    Stirling, W.G.; Perry, S.C.

    1996-01-01

    We outline the theoretical and experimental background to neutron scattering studies of critical phenomena at magnetic and structural phase transitions. The displacive phase transition of SrTiO 3 is discussed, along with examples from recent work on magnetic materials from the rare-earth (Ho, Dy) and actinide (NpAs, NpSb, USb) classes. The impact of synchrotron X-ray scattering is discussed in conclusion. (author) 13 figs., 18 refs

  15. Measurement of scattering and absorption properties of dust aerosol in a Gobi farmland region of northwestern China – a potential anthropogenic influence

    Directory of Open Access Journals (Sweden)

    J. Bi

    2017-06-01

    Full Text Available We conducted a comprehensive field campaign to explore the optical characteristics of mineral dust in Dunhuang farmland near the Gobi Desert of northwest China during spring of 2012. The day-to-day and diurnal variations of dust aerosol showed prominent features throughout the experiment, primarily attributable to frequent dust events and local anthropogenic emissions. The overall average mass concentrations of the particulate matter with an aerodynamic diameter less than 10 µm (PM10, light scattering coefficient (σsp, 670, absorption coefficient (σap, 670, and single-scattering albedo (SSA670 were 113 ± 169 µg m−3, 53.3 ± 74.8 Mm−1, 3.2 ± 2.4 Mm−1, and 0.913 ± 0.05, respectively, which were comparable to the background levels in the southern United States but smaller than those in the eastern and other northwestern Chinese cities. The anthropogenic dust produced by agricultural cultivations (e.g., land planning, plowing, and disking exerted a significant superimposed effect on high dust concentrations in Dunhuang farmland prior to the growing season (i.e., from 1 April to 10 May. Strong south valley wind and vertical mixing in daytime scavenged the pollution, and the weak northeast mountain wind and stable inversion layer at night favorably accumulated the air pollutants near the surface. In the afternoon (13:00–18:00 LT, local time, mean SSA670 was 0.945 ± 0.04 predominantly from dust particles, whereas finer particles and lower SSA670 values ( ∼  0.90–0.92 were measured at night, suggesting the potential influence by the mixed dust pollutants. During a typical biomass burning event on 4 April 2012, σap, 670 increased from  ∼  2.0 to 4.75 Mm−1 and SSA670 changed from  ∼  0.90 to  ∼  0.83, implying remarkable modification of aerosol absorptive properties induced by human activities. The findings of this study would help to advance an in

  16. Nuclear Data and Measurements Series: The energy dependence of the optical-model potential for fast-neutron scattering from bismuth

    International Nuclear Information System (INIS)

    Smith, A.B.; Guenther, P.T.; Lawson, R.D.

    1987-05-01

    Neutron differential-elastic-scattering cross sections of bismuth were measured at 0.5 MeV intervals from 4.5 to 10.0 MeV. At each incident energy ≥40 differential values were obtained, distributed between 18 0 and 160 0 . The measured data were combined with lower-energy results previously reported from this laboratory, and others available in the literature, to provide a detailed data base extending from 1.5 to 10.0 MeV. This data base was interpreted in terms of the conventional optical-statistical model and also a model inclusive of the surface-peaked real potential predicted by the dispersion relation. Particular attention was given to the energy dependence of the volume-integral-per-nucleon of the real potential, J/sub v/, to see if there was evidence of the Fermi Surface Anomaly. In the range 3.0 to 10.0 MeV the present data indicate that dJ/sub v//dE is essentially constant, with a relatively large negative value of -6.0 to -9.0 fm 3 , depending on the model used in the analysis. Below 3.0 MeV, there is some evidence for a decrease in the magnitude of dJ/dE. However, the effect is very small and it is only when this trend is combined with considerations of the J/sub v/ values needed to give correct bound-state energies that evidence for the Fermi Surface Anomaly emerges. J/sub v/ and the geometry of the optical potentials found for 209 Bi become equal to those needed to explain the high-energy 208 Pb data at about 10.0 MeV. Since dJ/sub v//dE for the latter is smaller in magnitude than for 209 Bi, a change in dJ/sub v//dE is clearly indicated near 10.0 MeV. This may effect the extrapolation of higher-energy and charged-particle potentials into the lower-energy neutron domain. 47 refs., 9 figs

  17. Heavy ion elastic scatterings

    International Nuclear Information System (INIS)

    Mermaz, M.C.

    1984-01-01

    Diffraction and refraction play an important role in particle elastic scattering. The optical model treats correctly and simultaneously both phenomena but without disentangling them. Semi-classical discussions in terms of trajectories emphasize the refractive aspect due to the real part of the optical potential. The separation due to to R.C. Fuller of the quantal cross section into two components coming from opposite side of the target nucleus allows to understand better the refractive phenomenon and the origin of the observed oscillations in the elastic scattering angular distributions. We shall see that the real part of the potential is responsible of a Coulomb and a nuclear rainbow which allows to determine better the nuclear potential in the interior region near the nuclear surface since the volume absorption eliminates any effect of the real part of the potential for the internal partial scattering waves. Resonance phenomena seen in heavy ion scattering will be discussed in terms of optical model potential and Regge pole analysis. Compound nucleus resonances or quasi-molecular states can be indeed the more correct and fundamental alternative

  18. New Insight into the Local Structure of Hydrous Ferric Arsenate Using Full-Potential Multiple Scattering Analysis, Density Functional Theory Calculations, and Vibrational Spectroscopy.

    Science.gov (United States)

    Wang, Shaofeng; Ma, Xu; Zhang, Guoqing; Jia, Yongfeng; Hatada, Keisuke

    2016-11-15

    Hydrous ferric arsenate (HFA) is an important arsenic-bearing precipitate in the mining-impacted environment and hydrometallurgical tailings. However, there is no agreement on its local atomic structure. The local structure of HFA was reprobed by employing a full-potential multiple scattering (FPMS) analysis, density functional theory (DFT) calculations, and vibrational spectroscopy. The FPMS simulations indicated that the coordination number of the As-Fe, Fe-As, or both in HFA was approximately two. The DFT calculations constructed a structure of HFA with the formula of Fe(HAsO 4 ) x (H 2 AsO 4 ) 1-x (OH) y ·zH 2 O. The presence of protonated arsenate in HFA was also evidenced by vibrational spectroscopy. The As and Fe K-edge X-ray absorption near-edge structure spectra of HFA were accurately reproduced by FPMS simulations using the chain structure, which was also a reasonable model for extended X-Ray absorption fine structure fitting. The FPMS refinements indicated that the interatomic Fe-Fe distance was approximately 5.2 Å, consistent with that obtained by Mikutta et al. (Environ. Sci. Technol. 2013, 47 (7), 3122-3131) using wavelet analysis. All of the results suggested that HFA was more likely to occur as a chain with AsO 4 tetrahedra and FeO 6 octahedra connecting alternately in an isolated bidentate-type fashion. This finding is of significance for understanding the fate of arsenic and the formation of ferric arsenate minerals in an acidic environment.

  19. Compton scattering

    International Nuclear Information System (INIS)

    Botto, D.J.; Pratt, R.H.

    1979-05-01

    The current status of Compton scattering, both experimental observations and the theoretical predictions, is examined. Classes of experiments are distinguished and the results obtained are summarized. The validity of the incoherent scattering function approximation and the impulse approximation is discussed. These simple theoretical approaches are compared with predictions of the nonrelativistic dipole formula of Gavrila and with the relativistic results of Whittingham. It is noted that the A -2 based approximations fail to predict resonances and an infrared divergence, both of which have been observed. It appears that at present the various available theoretical approaches differ significantly in their predictions and that further and more systematic work is required

  20. Compton scattering

    Energy Technology Data Exchange (ETDEWEB)

    Botto, D.J.; Pratt, R.H.

    1979-05-01

    The current status of Compton scattering, both experimental observations and the theoretical predictions, is examined. Classes of experiments are distinguished and the results obtained are summarized. The validity of the incoherent scattering function approximation and the impulse approximation is discussed. These simple theoretical approaches are compared with predictions of the nonrelativistic dipole formula of Gavrila and with the relativistic results of Whittingham. It is noted that the A/sup -2/ based approximations fail to predict resonances and an infrared divergence, both of which have been observed. It appears that at present the various available theoretical approaches differ significantly in their predictions and that further and more systematic work is required.

  1. Diffraction in nuclear scattering

    International Nuclear Information System (INIS)

    Wojciechowski, H.

    1986-01-01

    The elastic scattering amplitudes for charged and neutral particles have been decomposed into diffractive and refractive parts by splitting the nuclear elastic scattering matrix elements into components responsible for these effects. It has been shown that the pure geometrical diffractive effect which carries no information about the nuclear interaction is always predominant at forward angle of elastic angular distributions. This fact suggests that for strongly absorbed particles only elastic cross section at backward angles, i.e. the refractive cross section, can give us basic information about the central nuclear potential. 12 refs., 4 figs., 1 tab. (author)

  2. Group theory approach to scattering

    International Nuclear Information System (INIS)

    Wu, J.

    1985-01-01

    For certain physical systems, there exists a dynamical group which contains the operators connecting states with the same energy but belonging to potentials with different strengths. This group is called the potential group of that system. The SO(2,1) potential groups structure is introduced to describe physical systems with mixed spectra, such as Morse and Poeschl-teller potentials. The discrete spectrum describes bound states and the continuous spectrum describes bound states and the continuous spectrum describes scattering states. A solvable class of one-dimensional potentials given by Natanzon belongs to this structure with an SO(2,2) potential group. The potential group structure provides us with an algebraic procedure generating the recursion relations for the scattering matrix, which can be formulated in a purely algebraic fashion, divorced from any differential realization. This procedure, when applied to the three-dimensional scattering problem with SO(3,1) symmetry, generates the scattering matrix of the Coulomb problem. Preliminary phenomenological models for elastic scattering in a heavy-ion collision are constructed on the basis. The results obtained here can be regarded as an important extension of the group theory techniques to scattering problems similar to that developed for bound state problems

  3. Elastic scattering

    International Nuclear Information System (INIS)

    Leader, Elliot

    1991-01-01

    With very few unexplained results to challenge conventional ideas, physicists have to look hard to search for gaps in understanding. An area of physics which offers a lot more than meets the eye is elastic and diffractive scattering where particles either 'bounce' off each other, emerging unscathed, or just graze past, emerging relatively unscathed. The 'Blois' workshops provide a regular focus for this unspectacular, but compelling physics, attracting highly motivated devotees

  4. Semiclassical scattering theory

    International Nuclear Information System (INIS)

    Di Salvo, A.

    1985-01-01

    It is intended to write the semiclassical scattering amplitude as a sum of terms, each of them being associated to trajectory. First of all the classical equations of motion are studied, considering both the analytical (real and complex) solutions and a certain type of singular solutions, which behave similary to the difracted rays in optics; in particular, in the case of a central nuclear potential, classical effects like rainbow and orbiting and also wave effects like diffraction and direct reflection are singled out. Successively, considering the Debye expansion of the scattering amplitude relative to a central nuclear potential, and evaluating asymptotically each term by means of the saddle point technique, the decay exponents and difraction coefficients relative to such a potential are determined

  5. Neutron scattering

    International Nuclear Information System (INIS)

    1991-02-01

    The annual report on hand gives an overview of the research work carried out in the Laboratory for Neutron Scattering (LNS) of the ETH Zuerich in 1990. Using the method of neutron scattering, it is possible to examine in detail the static and dynamic properties of the condensed material. In accordance with the multidisciplined character of the method, the LNS has for years maintained a system of intensive co-operation with numerous institutes in the areas of biology, chemistry, solid-state physics, crystallography and materials research. In 1990 over 100 scientists from more than 40 research groups both at home and abroad took part in the experiments. It was again a pleasure to see the number of graduate students present, who were studying for a doctorate and who could be introduced into the neutron scattering during their stay at the LNS and thus were in the position to touch on central ways of looking at a problem in their dissertation using this modern experimental method of solid-state research. In addition to the numerous and interesting ways of formulating the questions to explain the structure, nowadays the scientific programme increasingly includes particularly topical studies in connection with high temperature-supraconductors and materials research

  6. Scattering theory

    CERN Document Server

    Friedrich, Harald

    2016-01-01

    This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is k...

  7. Nonstationary interference and scattering from random media

    International Nuclear Information System (INIS)

    Nazikian, R.

    1991-12-01

    For the small angle scattering of coherent plane waves from inhomogeneous random media, the three dimensional mean square distribution of random fluctuations may be recovered from the interferometric detection of the nonstationary modulational structure of the scattered field. Modulational properties of coherent waves scattered from random media are related to nonlocal correlations in the double sideband structure of the Fourier transform of the scattering potential. Such correlations may be expressed in terms of a suitability generalized spectral coherence function for analytic fields

  8. Scattering of accelerated wave packets

    Science.gov (United States)

    Longhi, S.; Horsley, S. A. R.; Della Valle, G.

    2018-03-01

    Wave-packet scattering from a stationary potential is significantly modified when the wave packet is subject to an external time-dependent force during the interaction. In the semiclassical limit, wave-packet motion is simply described by Newtonian equations, and the external force can, for example, cancel the potential force, making a potential barrier transparent. Here we consider wave-packet scattering from reflectionless potentials, where in general the potential becomes reflective when probed by an accelerated wave packet. In the particular case of the recently introduced class of complex Kramers-Kronig potentials we show that a broad class of time-dependent forces can be applied without inducing any scattering, while there is a breakdown of the reflectionless property when there is a broadband distribution of initial particle momentum, involving both positive and negative components.

  9. Diffractive scattering

    CERN Document Server

    De Wolf, E.A.

    2002-01-01

    We discuss basic concepts and properties of diffractive phenomena in soft hadron collisions and in deep-inelastic scattering at low Bjorken-x. The paper is not a review of the rapidly developing field but presents an attempt to show in simple terms the close inter-relationship between the dynamics of high-energy hadronic and deep-inelastic diffraction. Using the saturation model of Golec-Biernat and Wusthoff as an example, a simple explanation of geometrical scaling is presented. The relation between the QCD anomalous multiplicity dimension and the Pomeron intercept is discussed.

  10. Diffractive Scattering

    International Nuclear Information System (INIS)

    Wolf, E.A. de

    2002-01-01

    We discuss basic concepts and properties of diffractive phenomena in soft hadron collisions and in deep-inelastic scattering at low Bjorken - x. The paper is not a review of the rapidly developing field but presents an attempt to show in simple terms the close inter-relationship between the dynamics of high-energy hadronic and deep-inelastic diffraction. Using the saturation model of Golec-Biernat and Wuesthoff as an example, a simple explanation of geometrical scaling is presented. The relation between the QCD anomalous multiplicity dimension and the Pomeron intercept is discussed. (author)

  11. Scattering of charged particles

    International Nuclear Information System (INIS)

    Barrachina, R.O.; Macek, J.H.

    1989-01-01

    Different methods of avoiding the known difficulties of the Coulomb potential scattering theory are reviewed. Mulherin and Zinnes' [J. Math. Phys. 11, 1402 (1976)] ''distorted'' free waves and van Haeringen's [J. Math. Phys. 17, 995 (1976)] Coulomb asymptotic states are considered. The equivalence of both approaches on the energy shell is shown. Actually the possibility of deriving the first method within van Haeringen's formalism by means of a distorted wave procedure is demonstrated

  12. Correlation in atomic scattering

    International Nuclear Information System (INIS)

    McGuire, J.H.

    1987-01-01

    Correlation due to the Coulomb interactions between electrons in many-electron targets colliding with charged particles is formulated, and various approximate probability amplitudes are evaluated. In the limit that the electron-electron, 1/r/sub i//sub j/, correlation interactions are ignored or approximated by central potentials, the independent-electron approximation is obtained. Two types of correlations, or corrections to the independent-electron approximation due to 1/r/sub i//sub j/ terms, are identified: namely, static and scattering correlation. Static correlation is that contained in the asymptotic, e.g., bound-state, wave functions. Scattering correlation, arising from correlation in the scattering operator, is new and is considered in some detail. Expressions for a scattering correlation amplitude, static correlation or rearrangement amplitude, and independent-electron or direct amplitude are derived at high collision velocity and compared. At high velocities the direct and rearrangement amplitudes dominate. At very high velocities, ν, the rearrangement amplitude falls off less rapidly with ν than the direct amplitude which, however, is dominant as electron-electron correlation tends to zero. Comparisons with experimental observations are discussed

  13. Neutron scattering. Lectures

    International Nuclear Information System (INIS)

    Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner

    2012-01-01

    The following topics are dealt with: Neutron scattering in contemporary research, neutron sources, symmetry of crystals, diffraction, nanostructures investigated by small-angle neutron scattering, the structure of macromolecules, spin dependent and magnetic scattering, structural analysis, neutron reflectometry, magnetic nanostructures, inelastic scattering, strongly correlated electrons, dynamics of macromolecules, applications of neutron scattering. (HSI)

  14. Acoustic phonon limited mobility in two-dimensional semiconductors: Deformation potential and piezoelectric scattering in monolayer MoS2 from first principles

    DEFF Research Database (Denmark)

    Kaasbjerg, Kristen; Thygesen, Kristian Sommer; Jauho, Antti-Pekka

    2013-01-01

    model, analytic expressions and the coupling strengths for the deformation potential and piezoelectric interactions are established. We furthermore show that the deformation potential interaction has contributions from both normal and umklapp processes and that the latter contribution is only weakly...

  15. On the formfactor of the imaginary part and its coupling to the real optical potential for the α-nucleus scattering

    International Nuclear Information System (INIS)

    Freindl, L.; Dabrowski, H.; Grotowski, K.; Planeta, R.; Uniwersytet Jagiellonski, Krakow

    1980-01-01

    The model-independent formfactor of the absorptive α-nucleus potential was calculated and compared with model dependent ones. The coupling between the shapes of the real and imaginary potential is discussed. (author)

  16. On the formfactor of the imaginary parts and its coupling to the real optical potential for the α-nucleus scattering

    International Nuclear Information System (INIS)

    Freindl, L.; Dabrowski, H.; Grotowski, K.; Planeta, R.; Uniwersytet Jagiellonski, Krakow

    1979-01-01

    The model independent formfactor of the absorptive α-nucleus potential is calculated and compared with model dependent ones. The coupling between the shapes of the real and the imaginary potential is discussed. (Author)

  17. Molecular-beam scattering

    International Nuclear Information System (INIS)

    Vernon, M.F.

    1983-07-01

    The molecular-beam technique has been used in three different experimental arrangements to study a wide range of inter-atomic and molecular forces. Chapter 1 reports results of a low-energy (0.2 kcal/mole) elastic-scattering study of the He-Ar pair potential. The purpose of the study was to accurately characterize the shape of the potential in the well region, by scattering slow He atoms produced by expanding a mixture of He in N 2 from a cooled nozzle. Chapter 2 contains measurements of the vibrational predissociation spectra and product translational energy for clusters of water, benzene, and ammonia. The experiments show that most of the product energy remains in the internal molecular motions. Chapter 3 presents measurements of the reaction Na + HCl → NaCl + H at collision energies of 5.38 and 19.4 kcal/mole. This is the first study to resolve both scattering angle and velocity for the reaction of a short lived (16 nsec) electronic excited state. Descriptions are given of computer programs written to analyze molecular-beam expansions to extract information characterizing their velocity distributions, and to calculate accurate laboratory elastic-scattering differential cross sections accounting for the finite apparatus resolution. Experimental results which attempted to determine the efficiency of optically pumping the Li(2 2 P/sub 3/2/) and Na(3 2 P/sub 3/2/) excited states are given. A simple three-level model for predicting the steady-state fraction of atoms in the excited state is included

  18. Bidirectional optical scattering facility

    Data.gov (United States)

    Federal Laboratory Consortium — Goniometric optical scatter instrument (GOSI)The bidirectional reflectance distribution function (BRDF) quantifies the angular distribution of light scattered from a...

  19. Quaternionic potentials and CP-violation

    International Nuclear Information System (INIS)

    Nishi, Celso Chikahiro

    2000-01-01

    Full text follows: In the formulation of Quantum Mechanics by using a non-commutative ring of quaternions, we attempt to solve the Schroedinger equation with quaternionic potentials. Decay processes can easily be modeled by including complex imaginary potentials. Although, it could be explained as a transition between states under action of a perturbation. Purely imaginary quaternionic potentials can be used to describe CP-violation effects. The neutral kaon system, K 0 - K-bar 0 or K L - K S , represents an example of CP-violation phenomenon. The inclusion of quaternionic potentials imply a reformulation of the whole quantum theory. The use of a quaternionic algebra in discussing the Schroedinger equation leads to the lost of time reversal invariance (T), closely connected to CP violation by the well-known CPT theorem. In particular, we study the Schroedinger equation in presence of a quaternionic potential barrier given in terms of V, real potential acting in the region of width a, and jW, purely quaternionic potential acting in the region of width b. Different cases, |W|/V and b/a, are discussed in view of possible deviations of standard Quantum Mechanics. The complex linear Schroedinger equation is solved for stationary states. The explicit solution contains complex and quaternionic transmission/reflection coefficients. A wave packet treatment needs to make a more realistic and physical description. We briefly discuss possible interpretations and remaining questions. (author)

  20. Solution of a simple inelastic scattering problem

    International Nuclear Information System (INIS)

    Knudson, S.K.

    1975-01-01

    Simple examples of elastic scattering, typically from square wells, serve as important pedagogical tools in discussion of the concepts and processes involved in elastic scattering events. An analytic solution of a model inelastic scattering system is presented here to serve in this role for inelastic events. The model and its solution are simple enough to be of pedagogical utility, but also retain enough of the important physical features to include most of the special characteristics of inelastic systems. The specific model chosen is the collision of an atom with a harmonic oscillator, interacting via a repulsive square well potential. Pedagogically important features of inelastic scattering, including its multistate character, convergence behavior, and dependence on an ''inelastic potential'' are emphasized as the solution is determined. Results are presented for various energies and strengths of inelastic scattering, which show that the model is capable of providing an elementary representation of vibrationally inelastic scattering

  1. Neutron scattering. Lectures

    Energy Technology Data Exchange (ETDEWEB)

    Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner [eds.

    2010-07-01

    The following topics are dealt with: Neutron sources, symmetry of crystals, diffraction, nanostructures investigated by small-angle neutron scattering, the structure of macromolecules, spin dependent and magnetic scattering, structural analysis, neutron reflectometry, magnetic nanostructures, inelastic scattering, strongly correlated electrons, dynamics of macromolecules, applications of neutron scattering. (HSI)

  2. Neutron scattering. Lectures

    International Nuclear Information System (INIS)

    Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner

    2013-01-01

    The following topics are dealt with: Neutron sources, symmetry of crystals, nanostructures investigated by small-angle neutron scattering, structure of macromolecules, spin dependent and magnetic scattering, structural analysis, neutron reflectometry, magnetic nanostructures, inelastic neutron scattering, strongly correlated electrons, polymer dynamics, applications of neutron scattering. (HSI)

  3. Neutron scattering. Lectures

    International Nuclear Information System (INIS)

    Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner

    2010-01-01

    The following topics are dealt with: Neutron sources, symmetry of crystals, diffraction, nanostructures investigated by small-angle neutron scattering, the structure of macromolecules, spin dependent and magnetic scattering, structural analysis, neutron reflectometry, magnetic nanostructures, inelastic scattering, strongly correlated electrons, dynamics of macromolecules, applications of neutron scattering. (HSI)

  4. Newtonian versus black-hole scattering

    International Nuclear Information System (INIS)

    Siopsis, G.

    1999-01-01

    We discuss non-relativistic scattering by a Newtonian potential. We show that the gray-body factors associated with scattering by a black hole exhibit the same functional dependence as scattering amplitudes in the Newtonian limit, which should be the weak-field limit of any quantum theory of gravity. This behavior arises independently of the presence of supersymmetry. The connection to two-dimensional conformal field theory is also discussed. copyright 1999 The American Physical Society

  5. Measurement of the spin asymmetry of the beam in the polarized virtual Compton scattering on the proton. Study of the nucleon's energy spectra through the QCD-type potential model

    International Nuclear Information System (INIS)

    Bensafa, I.K.

    2006-05-01

    The first part of this work presents the analysis and results of the VCS-SSA (virtual Compton scattering - single spin asymmetry) experiment at MAMI (Mainz). It was carried out with beam energy 883 MeV and longitudinal polarization (about 80%), at virtual photon four-momentum transfer squared (Q 2 = 0.35 GeV 2 ) to measure the beam asymmetry in the ep → epγ and ep → epπ 0 reactions. The asymmetry obtained in photon (resp. pion) electro-production is between 0-15% (resp. 0-2%). The dispersion relation model for virtual Compton scattering and MAID model (for π 0 ) reproduce the amplitude globally but not completely the shape of the asymmetry. Perhaps this discrepancy is due to an imperfect parameterization of some pion production multipoles (γ * N → πN). The second part is dedicated to the study of the nucleon energy spectrum in ground-state L=0 and excited-state L=1 in the quark model, using the Coulomb + linear potential type (CL) and a relativistic correction. The hyperfine correction is applied to discriminate the nucleon masses. The values of the mass found for the proton and the Δ(1232) are respectively equal to (968 MeV, 1168 MeV), and the masses of the excited states are between 1564 - 1607 MeV. This part is completed by an application of the CL model to an approximate calculation of generalized polarizabilities of the proton. (author)

  6. Neutron scattering. Lectures

    Energy Technology Data Exchange (ETDEWEB)

    Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner (eds.)

    2010-07-01

    The following topics are dealt with: Neutron sources, neutron properties and elastic scattering, correlation functions measured by scattering experiments, symmetry of crystals, applications of neutron scattering, polarized-neutron scattering and polarization analysis, structural analysis, magnetic and lattice excitation studied by inelastic neutron scattering, macromolecules and self-assembly, dynamics of macromolecules, correlated electrons in complex transition-metal oxides, surfaces, interfaces, and thin films investigated by neutron reflectometry, nanomagnetism. (HSI)

  7. Neutron scattering. Lectures

    International Nuclear Information System (INIS)

    Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner

    2010-01-01

    The following topics are dealt with: Neutron sources, neutron properties and elastic scattering, correlation functions measured by scattering experiments, symmetry of crystals, applications of neutron scattering, polarized-neutron scattering and polarization analysis, structural analysis, magnetic and lattice excitation studied by inelastic neutron scattering, macromolecules and self-assembly, dynamics of macromolecules, correlated electrons in complex transition-metal oxides, surfaces, interfaces, and thin films investigated by neutron reflectometry, nanomagnetism. (HSI)

  8. Realistic non-local potentials from inverse scattering theory for the3S1−3D1nucleon-nucleon interaction

    Directory of Open Access Journals (Sweden)

    P.H.L. Groenenboom

    1978-03-01

    Full Text Available Rank-three and -four separable3S1−3D1potentials have been constructed which reproduce the experimental phase shifts and a realistic deuteron wave function. The off-shell behaviour has been investigated and triton binding energies were calculated.

  9. On exact solutions of scattering problems

    International Nuclear Information System (INIS)

    Nikishov, P.Yu.; Plekhanov, E.B.; Zakhariev, B.N.

    1982-01-01

    Examples illustrating the quality of the reconstruction of potentials from single-channel scattering data by using exactly solvable models are given. Simple exact solutions for multi-channel systems with non-degenerated resonance singularities of the scattering matrix are derived

  10. On three-particle scattering theory

    International Nuclear Information System (INIS)

    Kuz'michev, V.E.

    1977-01-01

    The approach proposed earlier by the author to three-particle scattering theory is discussed. This approach may prove to be useful for studying certain problems in the physics of few-nucleon systems. The corresponding equations for the partial components of the amplitudes and the potentials are obtained in the N-d scattering case

  11. New method for solving multidimensional scattering problem

    International Nuclear Information System (INIS)

    Melezhik, V.S.

    1991-01-01

    A new method is developed for solving the quantum mechanical problem of scattering of a particle with internal structure. The multichannel scattering problem is formulated as a system of nonlinear functional equations for the wave function and reaction matrix. The method is successfully tested for the scattering from a nonspherical potential well and a long-range nonspherical scatterer. The method is also applicable to solving the multidimensional Schroedinger equation with a discrete spectrum. As an example the known problem of a hydrogen atom in a homogeneous magnetic field is analyzed

  12. Cooperative scattering of scalar waves by optimized configurations of point scatterers

    Science.gov (United States)

    Schäfer, Frank; Eckert, Felix; Wellens, Thomas

    2017-12-01

    We investigate multiple scattering of scalar waves by an ensemble of N resonant point scatterers in three dimensions. For up to N = 21 scatterers, we numerically optimize the positions of the individual scatterers, to maximize the total scattering cross section for an incoming plane wave, on the one hand, and to minimize the decay rate associated to a long-lived scattering resonance, on the other. In both cases, the optimum is achieved by configurations where all scatterers are placed on a line parallel to the direction of the incoming plane wave. The associated maximal scattering cross section increases quadratically with the number of scatterers for large N, whereas the minimal decay rate—which is realized by configurations that are not the same as those that maximize the scattering cross section—decreases exponentially as a function of N. Finally, we also analyze the stability of our optimized configurations with respect to small random displacements of the scatterers. These results demonstrate that optimized configurations of scatterers bear a considerable potential for applications such as quantum memories or mirrors consisting of only a few atoms.

  13. Classical trajectory in non-relativistic scattering

    International Nuclear Information System (INIS)

    Williams, A.C.

    1978-01-01

    With the statistical interpretation of quantum mechanics as a guide, the classical trajectory is incorporated into quantum scattering theory. The Feynman path integral formalism is used as a starting point, and classical transformation theory is applied to the phase of the wave function so derived. This approach is then used to derive an expression for the scattering amplitude for potential scattering. It is found that the amplitude can be expressed in an impact parameter representation similar to the Glauber formalism. Connections are then made to the Glauber approximation and to semiclassical approximations derived from the Feynman path integral formalism. In extending this analysis to projectile-nucleus scattering, an approximation scheme is given with the first term being the same as in Glauber's multiple scattering theory. Higher-order approximations, thus, are found to give corrections to the fixed scatterer form of the impulse approximation inherent in the Glauber theory

  14. Scattering and multiple scattering in disordered materials

    International Nuclear Information System (INIS)

    Weaver, R.L.; Butler, W.H.

    1992-01-01

    The papers in this section were presented at a joint session of symposium V on Applications of Multiple Scattering Theory and of Symposium P on Disordered Systems. They show that the ideas of scattering theory can help us to understand a very broad class of phenomena

  15. Regularization method for solving the inverse scattering problem

    International Nuclear Information System (INIS)

    Denisov, A.M.; Krylov, A.S.

    1985-01-01

    The inverse scattering problem for the Schroedinger radial equation consisting in determining the potential according to the scattering phase is considered. The problem of potential restoration according to the phase specified with fixed error in a finite range is solved by the regularization method based on minimization of the Tikhonov's smoothing functional. The regularization method is used for solving the problem of neutron-proton potential restoration according to the scattering phases. The determined potentials are given in the table

  16. Quantum scattering at low energies

    DEFF Research Database (Denmark)

    Derezinski, Jan; Skibsted, Erik

    2009-01-01

    For a class of negative slowly decaying potentials, including V(x):=−γ|x|−μ with 0quantum mechanical scattering theory in the low-energy regime. Using appropriate modifiers of the Isozaki–Kitada type we show that scattering theory is well behaved on the whole continuous spectrum...... of the Hamiltonian, including the energy 0. We show that the modified scattering matrices S(λ) are well-defined and strongly continuous down to the zero energy threshold. Similarly, we prove that the modified wave matrices and generalized eigenfunctions are norm continuous down to the zero energy if we use...... of the kernel of S(λ) experiences an abrupt change from passing from positive energies λ to the limiting energy λ=0 . This change corresponds to the behaviour of the classical orbits. Under stronger conditions one can extract the leading term of the asymptotics of the kernel of S(λ) at its singularities....

  17. Neutron scattering from fractals

    DEFF Research Database (Denmark)

    Kjems, Jørgen; Freltoft, T.; Richter, D.

    1986-01-01

    The scattering formalism for fractal structures is presented. Volume fractals are exemplified by silica particle clusters formed either from colloidal suspensions or by flame hydrolysis. The determination of the fractional dimensionality through scattering experiments is reviewed, and recent small...

  18. Scatter from optical components

    International Nuclear Information System (INIS)

    Stover, J.C.

    1989-01-01

    This book is covered under the following topics: measurement and analysis techniques; BRDF standards, comparisons, and anomalies; scatter measurement of several materials; scatter from contaminations; and optical system contamination: effects, measurement, and control

  19. Classical- and quantum mechanical Coulomb scattering

    International Nuclear Information System (INIS)

    Gratzl, W.

    1987-01-01

    Because in textbooks the quantum mechanical Coulomb scattering is either ignored or treated unsatisfactory, the present work attempts to present a physically plausible, mathematically correct but elementary treatment in a way that it can be used in textbooks and lectures on quantum mechanics. Coulomb scattering is derived as a limiting case of a screened Coulomb potential (finite range) within a time dependent quantum scattering theory. The difference in the asymptotic conditions for potentials of finite versus infinite range leads back to the classical Coulomb scattering. In the classical framework many concepts of the quantum theory can be introduced and are useful in an intuitive understanding of the quantum theory. The differences between classical and quantum scattering theory are likewise useful for didactic purposes. (qui)

  20. Electron scattering from tetrahydrofuran

    International Nuclear Information System (INIS)

    Fuss, M C; Sanz, A G; García, G; Muñoz, A; Oller, J C; Blanco, F; Do, T P T; Brunger, M J; Almeida, D; Limão-Vieira, P

    2012-01-01

    Electron scattering from Tetrahydrofuran (C 4 H 8 O) was investigated over a wide range of energies. Following a mixed experimental and theoretical approach, total scattering, elastic scattering and ionization cross sections as well as electron energy loss distributions were obtained.

  1. Neutron Scattering Software

    Science.gov (United States)

    Home Page | Facilities | Reference | Software | Conferences | Announcements | Mailing Lists Neutron Scattering Banner Neutron Scattering Software A new portal for neutron scattering has just been established sets KUPLOT: data plotting and fitting software ILL/TAS: Matlab probrams for analyzing triple axis data

  2. Magnetic photon scattering

    International Nuclear Information System (INIS)

    Lovesey, S.W.

    1987-05-01

    The report reviews, at an introductory level, the theory of photon scattering from condensed matter. Magnetic scattering, which arises from first-order relativistic corrections to the Thomson scattering amplitude, is treated in detail and related to the corresponding interaction in the magnetic neutron diffraction amplitude. (author)

  3. Polarized Neutron Scattering

    OpenAIRE

    Roessli, B.; Böni, P.

    2000-01-01

    The technique of polarized neutron scattering is reviewed with emphasis on applications. Many examples of the usefulness of the method in various fields of physics are given like the determination of spin density maps, measurement of complex magnetic structures with spherical neutron polarimetry, inelastic neutron scattering and separation of coherent and incoherent scattering with help of the generalized XYZ method.

  4. Elastic and inelastic heavy ion scattering

    International Nuclear Information System (INIS)

    Toepffer, C.; University of the Witwatersrand, Johannesburg; Richter, A.

    1977-02-01

    In the field of elastic and inelastic heavy ion scattering, the following issues are dealt with: semiclassical descriptive approximations, optical potentials, barriers, critical radii and angular momenta, excitation functions and the application to superheavy ions and high energies. (WL) [de

  5. Scattering of Non-Relativistic Charged Particles by Electromagnetic Radiation

    Science.gov (United States)

    Apostol, M.

    2017-11-01

    The cross-section is computed for non-relativistic charged particles (like electrons and ions) scattered by electromagnetic radiation confined to a finite region (like the focal region of optical laser beams). The cross-section exhibits maxima at scattering angles given by the energy and momentum conservation in multi-photon absorption or emission processes. For convenience, a potential scattering is included and a comparison is made with the well-known Kroll-Watson scattering formula. The scattering process addressed in this paper is distinct from the process dealt with in previous studies, where the scattering is immersed in the radiation field.

  6. Direct Calculation of the Scattering Amplitude Without Partial Wave Analysis

    Science.gov (United States)

    Shertzer, J.; Temkin, A.; Fisher, Richard R. (Technical Monitor)

    2001-01-01

    Two new developments in scattering theory are reported. We show, in a practical way, how one can calculate the full scattering amplitude without invoking a partial wave expansion. First, the integral expression for the scattering amplitude f(theta) is simplified by an analytic integration over the azimuthal angle. Second, the full scattering wavefunction which appears in the integral expression for f(theta) is obtained by solving the Schrodinger equation with the finite element method (FEM). As an example, we calculate electron scattering from the Hartree potential. With minimal computational effort, we obtain accurate and stable results for the scattering amplitude.

  7. Some remarks on electron scattering in a laser field

    International Nuclear Information System (INIS)

    Ehlotzky, F.

    1988-01-01

    Potential scattering of electrons in a quantized radiation field is reconsidered. Some remarks are made on the validity of the Kroll-Watson scattering formula and on the close connection of this formula with the classical transition rate of scattering in a radiation field. (17 refs.)

  8. On the algebraic scattering theory for heavy ions

    International Nuclear Information System (INIS)

    Amos, K.; Kiedeldey, H.; Morrison, I.; Allen, L.J.

    1989-01-01

    Algebraic potentials from SO(3,1) and SO(3,2) representations of scattering functions are deduced by matching to scattering functions obtained by fitting 12 C- 12 C elastic scattering differential cross-sections. Their variations with energy suggest a simple mapping between algebraic and coordinate space interactions. 13 refs., 5 figs., 2 tabs

  9. Symmetry effects in neutron scattering from isotopically enriched Se isotopes

    Energy Technology Data Exchange (ETDEWEB)

    Lachkar, J.; Haouat, G.; McEllistrem, M. T.; Patin, Y.; Sigaud, J.; Cocu, F.

    1975-06-01

    Differential cross sections for neutron elastic and inelastic scattering from {sup 76}Se, {sup 78}Se, {sup 80}Se and {sup 82}Se, have been measured at 8-MeV incident neutron energy and from {sup 76}Se and {sup 82}Se at 6- and 10-MeV incident energies. The differences observed in the elastic scattering cross sections are interpretable as the effects of isospin term in the scattering potentials. A full analysis of the elastic scattering data are presented.

  10. Rayleigh scattering from ions near threshold

    International Nuclear Information System (INIS)

    Roy, S.C.; Gupta, S.K.S.; Kissel, L.; Pratt, R.H.

    1988-01-01

    Theoretical studies of Rayleigh scattering of photons from neon atoms with different degrees of ionization, for energies both below and above the K-edges of the ions, are presented. Some unexpected structures both in Rayleigh scattering and in photoionization from neutral and weakly ionized atoms, very close to threshold, have been reported. It has recently been realized that some of the predicted structures may have a nonphysical origin and are due to the limitation of the independent-particle model and also to the use of a Coulombic Latter tail. Use of a K-shell vacancy potential - in which an electron is assumed to be removed from the K-shell - in calculating K-shell Rayleigh scattering amplitudes removes some of the structure effects near threshold. We present in this work a discussion of scattering angular distributions and total cross sections, obtained utilizing vacancy potentials, and compare these predictions with those previously obtained in other potential model. (author) [pt

  11. Inelastic scattering of fast electrons by crystals

    International Nuclear Information System (INIS)

    Allen, L.J.; Josefsson, T.W.

    1995-01-01

    Generalized fundamental equations for electron diffraction in crystals, which include the effect of inelastic scattering described by a nonlocal interaction, are derived. An expression is obtained for the cross section for any specific type of inelastic scattering (e.g. inner-shell ionization, Rutherford backscattering). This result takes into account all other (background) inelastic scattering in the crystal leading to absorption from the dynamical Bragg-reflected beams, in practice mainly due to thermal diffuse scattering. There is a contribution to the cross section from all absorbed electrons, which form a diffuse background, as well as from the dynamical electrons. The approximations involved, assuming that the interactions leading to inelastic scattering can be described by a local potential are discussed, together with the corresponding expression for the cross section. It is demonstrated by means of an example for K-shell electron energy loss spectroscopy that nonlocal effects can be significant. 47 refs., 4 figs

  12. Quantum scattering theory on the momentum lattice

    International Nuclear Information System (INIS)

    Rubtsova, O. A.; Pomerantsev, V. N.; Kukulin, V. I.

    2009-01-01

    A new approach based on the wave-packet continuum discretization method recently developed by the present authors for solving quantum-mechanical scattering problems for atomic and nuclear scattering processes and few-body physics is described. The formalism uses the complete continuum discretization scheme in terms of the momentum stationary wave-packet basis, which leads to formulation of the scattering problem on a lattice in the momentum space. The solution of the few-body scattering problem can be found in the approach from linear matrix equations with nonsingular matrix elements, averaged on energy over lattice cells. The developed approach is illustrated by the solution of numerous two- and three-body scattering problems with local and nonlocal potentials below and well above the three-body breakup threshold.

  13. Variable phase approach to potential scattering

    CERN Document Server

    Calogero, Francesco

    1967-01-01

    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

  14. Features of the non-collinear one-phonon anomalous light scattering controlled by elastic waves with elevated linear losses: potentials for multi-frequency parallel spectrum analysis of radio-wave signals.

    Science.gov (United States)

    Shcherbakov, Alexandre S; Arellanes, Adan Omar

    2017-12-01

    During subsequent development of the recently proposed multi-frequency parallel spectrometer for precise spectrum analysis of wideband radio-wave signals, we study potentials of new acousto-optical cells exploiting selected crystalline materials at the limits of their capabilities. Characterizing these wide-aperture cells is non-trivial due to new features inherent in the chosen regime of an advanced non-collinear one-phonon anomalous light scattering by elastic waves with significantly elevated acoustic losses. These features can be observed simpler in uniaxial, tetragonal, and trigonal crystals possessing linear acoustic attenuation. We demonstrate that formerly studied additional degree of freedom, revealed initially for multi-phonon regimes of acousto-optical interaction, can be identified within the one-phonon geometry as well and exploited for designing new cells. We clarify the role of varying the central acoustic frequency and acoustic attenuation using the identified degree of freedom. Therewith, we are strongly restricted by a linear regime of acousto-optical interaction to avoid the origin of multi-phonon processes within carrying out a multi-frequency parallel spectrum analysis of radio-wave signals. Proof-of-principle experiments confirm the developed approaches and illustrate their applicability to innovative technique for an advanced spectrum analysis of wideband radio-wave signals with the improved resolution in an extended frequency range.

  15. Scattering with polarized neutrons

    International Nuclear Information System (INIS)

    Schweizer, J.

    2007-01-01

    In the history of neutron scattering, it was shown very soon that the use of polarized neutron beams brings much more information than usual scattering with unpolarized neutrons. We shall develop here the different scattering methods that imply polarized neutrons: 1) polarized beams without polarization analysis, the flipping ratio method; 2) polarized beams with a uniaxial polarization analysis; 3) polarized beams with a spherical polarization analysis. For all these scattering methods, we shall give examples of the physical problems which can been solved by these methods, particularly in the field of magnetism: investigation of complex magnetic structures, investigation of spin or magnetization densities in metals, insulators and molecular compounds, separation of magnetic and nuclear scattering, investigation of magnetic properties of liquids and amorphous materials and even, for non magnetic material, separation between coherent and incoherent scattering. (author)

  16. Neutron scattering and magnetism

    International Nuclear Information System (INIS)

    Mackintosh, A.R.

    1983-01-01

    Those properties of the neutron which make it a unique tool for the study of magnetism are described. The scattering of neutrons by magnetic solids is briefly reviewed, with emphasis on the information on the magnetic structure and dynamics which is inherent in the scattering cross-section. The contribution of neutron scattering to our understanding of magnetic ordering, excitations and phase transitions is illustrated by experimental results on a variety of magnetic crystals. (author)

  17. Introduction to neutron scattering

    Energy Technology Data Exchange (ETDEWEB)

    Fischer, W E [Paul Scherrer Inst. (PSI), Villigen (Switzerland)

    1996-11-01

    We give here an introduction to the theoretical principles of neutron scattering. The relationship between scattering- and correlation-functions is particularly emphasized. Within the framework of linear response theory (justified by the weakness of the basic interaction) the relation between fluctuation and dissipation is discussed. This general framework explains the particular power of neutron scattering as an experimental method. (author) 4 figs., 4 refs.

  18. Scattering from black holes

    International Nuclear Information System (INIS)

    Futterman, J.A.H.; Handler, F.A.; Matzner, R.A.

    1987-01-01

    This book provides a comprehensive treatment of the propagation of waves in the presence of black holes. While emphasizing intuitive physical thinking in their treatment of the techniques of analysis of scattering, the authors also include chapters on the rigorous mathematical development of the subject. Introducing the concepts of scattering by considering the simplest, scalar wave case of scattering by a spherical (Schwarzschild) black hole, the book then develops the formalism of spin weighted spheroidal harmonics and of plane wave representations for neutrino, electromagnetic, and gravitational scattering. Details and results of numerical computations are given. The techniques involved have important applications (references are given) in acoustical and radar imaging

  19. Quantum theory of scattering

    CERN Document Server

    Wu Ta You

    1962-01-01

    This volume addresses the broad formal aspects and applications of the quantum theory of scattering in atomic and nuclear collisions. An encyclopedic source of pioneering work, it serves as a text for students and a reference for professionals in the fields of chemistry, physics, and astrophysics. The self-contained treatment begins with the general theory of scattering of a particle by a central field. Subsequent chapters explore particle scattering by a non-central field, collisions between composite particles, the time-dependent theory of scattering, and nuclear reactions. An examinati

  20. Cross plane scattering correction

    International Nuclear Information System (INIS)

    Shao, L.; Karp, J.S.

    1990-01-01

    Most previous scattering correction techniques for PET are based on assumptions made for a single transaxial plane and are independent of axial variations. These techniques will incorrectly estimate the scattering fraction for volumetric PET imaging systems since they do not take the cross-plane scattering into account. In this paper, the authors propose a new point source scattering deconvolution method (2-D). The cross-plane scattering is incorporated into the algorithm by modeling a scattering point source function. In the model, the scattering dependence both on axial and transaxial directions is reflected in the exponential fitting parameters and these parameters are directly estimated from a limited number of measured point response functions. The authors' results comparing the standard in-plane point source deconvolution to the authors' cross-plane source deconvolution show that for a small source, the former technique overestimates the scatter fraction in the plane of the source and underestimate the scatter fraction in adjacent planes. In addition, the authors also propose a simple approximation technique for deconvolution

  1. Neutrino scattering and the reactor antineutrino anomaly

    Science.gov (United States)

    Garcés, Estela; Cañas, Blanca; Miranda, Omar; Parada, Alexander

    2017-12-01

    Low energy threshold reactor experiments have the potential to give insight into the light sterile neutrino signal provided by the reactor antineutrino anomaly and the gallium anomaly. In this work we analyze short baseline reactor experiments that detect by elastic neutrino electron scattering in the context of a light sterile neutrino signal. We also analyze the sensitivity of experimental proposals of coherent elastic neutrino nucleus scattering (CENNS) detectors in order to exclude or confirm the sterile neutrino signal with reactor antineutrinos.

  2. Pion-pion scattering

    International Nuclear Information System (INIS)

    Kuehnelt, H.

    1975-01-01

    We discuss a few properties of scattering amplitudes proved within the framework of the field theory and their significance in the derivation of quantitative statements. The state of the boundaries for the scattering lengths is to be especially discussed as well as the question as to how far it is possible to exclude various solutions from phase displacement analyses. (orig./LH) [de

  3. Modelling Hyperboloid Sound Scattering

    DEFF Research Database (Denmark)

    Burry, Jane; Davis, Daniel; Peters, Brady

    2011-01-01

    The Responsive Acoustic Surfaces workshop project described here sought new understandings about the interaction between geometry and sound in the arena of sound scattering. This paper reports on the challenges associated with modelling, simulating, fabricating and measuring this phenomenon using...... both physical and digital models at three distinct scales. The results suggest hyperboloid geometry, while difficult to fabricate, facilitates sound scattering....

  4. Incoherent Thomson scattering

    NARCIS (Netherlands)

    Donne, A. J. H.

    1996-01-01

    Thomson scattering is a very powerful diagnostic which is applied at nearly every magnetic confinement device. Depending on the experimental conditions different plasma parameters can be diagnosed. When the wave vector is much larger than the plasma Debye length, the total scattered power is

  5. Concentric layered Hermite scatterers

    Science.gov (United States)

    Astheimer, Jeffrey P.; Parker, Kevin J.

    2018-05-01

    The long wavelength limit of scattering from spheres has a rich history in optics, electromagnetics, and acoustics. Recently it was shown that a common integral kernel pertains to formulations of weak spherical scatterers in both acoustics and electromagnetic regimes. Furthermore, the relationship between backscattered amplitude and wavenumber k was shown to follow power laws higher than the Rayleigh scattering k2 power law, when the inhomogeneity had a material composition that conformed to a Gaussian weighted Hermite polynomial. Although this class of scatterers, called Hermite scatterers, are plausible, it may be simpler to manufacture scatterers with a core surrounded by one or more layers. In this case the inhomogeneous material property conforms to a piecewise continuous constant function. We demonstrate that the necessary and sufficient conditions for supra-Rayleigh scattering power laws in this case can be stated simply by considering moments of the inhomogeneous function and its spatial transform. This development opens an additional path for construction of, and use of scatterers with unique power law behavior.

  6. Introductory theory of neutron scattering

    International Nuclear Information System (INIS)

    Gunn, J.M.F.

    1986-12-01

    The paper comprises a set of six lecture notes which were delivered to the summer school on 'Neutron Scattering at a pulsed source', Rutherford Laboratory, United Kingdom, 1986. The lectures concern the physical principles of neutron scattering. The topics of the lectures include: diffraction, incoherent inelastic scattering, connection with the Schroedinger equation, magnetic scattering, coherent inelastic scattering, and surfaces and neutron optics. (UK)

  7. Diffuse scattering of neutrons

    International Nuclear Information System (INIS)

    Novion, C.H. de.

    1981-02-01

    The use of neutron scattering to study atomic disorder in metals and alloys is described. The diffuse elastic scattering of neutrons by a perfect crystal lattice leads to a diffraction spectrum with only Bragg spreads. the existence of disorder in the crystal results in intensity and position modifications to these spreads, and above all, to the appearance of a low intensity scatter between Bragg peaks. The elastic scattering of neutrons is treated in this text, i.e. by measuring the number of scattered neutrons having the same energy as the incident neutrons. Such measurements yield information on the static disorder in the crystal and time average fluctuations in composition and atomic displacements [fr

  8. Complex scattering dynamics and the quantum Hall effects

    International Nuclear Information System (INIS)

    Trugman, S.A.

    1994-01-01

    We review both classical and quantum potential scattering in two dimensions in a magnetic field, with applications to the quantum Hall effect. Classical scattering is complex, due to the approach of scattering states to an infinite number of dynamically bound states. Quantum scattering follows the classical behavior rather closely, exhibiting sharp resonances in place of the classical bound states. Extended scatterers provide a quantitative explanation for the breakdown of the QHE at a comparatively small Hall voltage as seen by Kawaji et al., and possibly for noise effects

  9. Inelastic Light Scattering Processes

    Science.gov (United States)

    Fouche, Daniel G.; Chang, Richard K.

    1973-01-01

    Five different inelastic light scattering processes will be denoted by, ordinary Raman scattering (ORS), resonance Raman scattering (RRS), off-resonance fluorescence (ORF), resonance fluorescence (RF), and broad fluorescence (BF). A distinction between fluorescence (including ORF and RF) and Raman scattering (including ORS and RRS) will be made in terms of the number of intermediate molecular states which contribute significantly to the scattered amplitude, and not in terms of excited state lifetimes or virtual versus real processes. The theory of these processes will be reviewed, including the effects of pressure, laser wavelength, and laser spectral distribution on the scattered intensity. The application of these processes to the remote sensing of atmospheric pollutants will be discussed briefly. It will be pointed out that the poor sensitivity of the ORS technique cannot be increased by going toward resonance without also compromising the advantages it has over the RF technique. Experimental results on inelastic light scattering from I(sub 2) vapor will be presented. As a single longitudinal mode 5145 A argon-ion laser line was tuned away from an I(sub 2) absorption line, the scattering was observed to change from RF to ORF. The basis, of the distinction is the different pressure dependence of the scattered intensity. Nearly three orders of magnitude enhancement of the scattered intensity was measured in going from ORF to RF. Forty-seven overtones were observed and their relative intensities measured. The ORF cross section of I(sub 2) compared to the ORS cross section of N2 was found to be 3 x 10(exp 6), with I(sub 2) at its room temperature vapor pressure.

  10. New Techniques in Neutron Scattering

    DEFF Research Database (Denmark)

    Birk, Jonas Okkels

    potential performance than any existing facility, however in order to use this pulse structure optimally many existing neutron scattering instruments will need to be redesigned. This defense will concentrate on the design and optimization of the inverse time-of-flight cold neutron spectrometer CAMEA......, simulations and prototyping to optimize the instrument and ensure that it will deliver the predicted performance when constructed. During the design a new prismatic analyser concept that can be of interest to many other neutron spectrometers was developed. The design work was compiled into an instrument......Neutron scattering is an important experimental technique in amongst others solid state physics, biophysics, and engineering. This year construction of European Spallation Source (ESS) was commenced in Lund, Sweeden. The facility will use a new long pulsed source principle to obtain higher...

  11. Quantum scattering at low energies

    DEFF Research Database (Denmark)

    Derezinski, Jan; Skibsted, Erik

    For a class of negative slowly decaying potentials, including with , we study the quantum mechanical scattering theory in the low-energy regime. Using modifiers of the Isozaki--Kitada type we show that scattering theory is well behaved on the {\\it whole} continuous spectrum of the Hamiltonian......, including the energy . We show that the --matrices are well-defined and strongly continuous down to the zero energy threshold. Similarly, we prove that the wave matrices and generalized eigenfunctions are norm continuous down to the zero energy if we use appropriate weighted spaces. These results are used...... from positive energies to the limiting energy . This change corresponds to the behaviour of the classical orbits. Under stronger conditions we extract the leading term of the asymptotics of the kernel of at its singularities; this leading term defines a Fourier integral operator in the sense...

  12. Regularization of the Coulomb scattering problem

    International Nuclear Information System (INIS)

    Baryshevskii, V.G.; Feranchuk, I.D.; Kats, P.B.

    2004-01-01

    The exact solution of the Schroedinger equation for the Coulomb potential is used within the scope of both stationary and time-dependent scattering theories in order to find the parameters which determine the regularization of the Rutherford cross section when the scattering angle tends to zero but the distance r from the center remains finite. The angular distribution of the particles scattered in the Coulomb field is studied on rather a large but finite distance r from the center. It is shown that the standard asymptotic representation of the wave functions is inapplicable in the case when small scattering angles are considered. The unitary property of the scattering matrix is analyzed and the 'optical' theorem for this case is discussed. The total and transport cross sections for scattering the particle by the Coulomb center proved to be finite values and are calculated in the analytical form. It is shown that the effects under consideration can be important for the observed characteristics of the transport processes in semiconductors which are determined by the electron and hole scattering by the field of charged impurity centers

  13. Light scattering studies at UNICAMP

    International Nuclear Information System (INIS)

    Luzzi, R.; Cerdeira, H.A.; Salzberg, J.; Vasconcellos, A.R.; Frota Pessoa, S.; Reis, F.G. dos; Ferrari, C.A.; Algarte, C.A.S.; Tenan, M.A.

    1975-01-01

    Current theoretical studies on light scattering spectroscopy at UNICAMP is presented briefly, such as: inelastic scattering of radiation from a solid state plasma; resonant Ramman scattering; high excitation effects; saturated semiconductors and glasses

  14. A fortran program for elastic scattering of deuterons with an optical model containing tensorial potentials; Programme fortran pour la diffusion elastique de deutons avec un modele optique contenant des termes tensoriels

    Energy Technology Data Exchange (ETDEWEB)

    Raynal, J. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1963-07-01

    The optical model has been applied with success to the elastic scattering of particles of spin 0 and 1/2 and to a lesser degree to that of deuterons. For particles of spin l/2, an LS coupling term is ordinarily used; this term is necessary to obtain a polarization; for deuterons, this coupling has been already introduced, but the possible forms of potentials are more numerous (in this case, scalar products of a second rank spin tensor with a tensor of the same rank in space or momentum can occur). These terms which may be necessary are primarily important for the tensor polarization. This problem is of particular interest at Saclay since a beam of polarized deuterons has become available. The FORTRAN program SPM 037 permits the study of the effect of tensorial potentials constructed from the distance of the deuteron from the target and its angular momentum with respect to it. This report should make possible the use and even the modification of the program. It consists of: a description of the problem and of the notation employed, a presentation of the methods adopted, an indication of the necessary data and how they should be introduced, and finally tables of symbols which are in equivalence or common statements: these tables must be considered when making any modification. (author) [French] Le modele optique a ete applique avec succes a la diffusion elastique des particules de spin nul et 1/2 et dans une moindre mesure a celle des deutons. Pour les particules de spin 1/2, on utilise habituellement un couplage LS, necessaire pour calculer la polarisation; pour les deutons, ce couplage a deja ete introduit, mais les formes de potentiel possibles sont plus nombreuses (intervention de produits scalaires d'un tenseur d'ordre 2 de spin avec un tenseur du meme ordre d'espace ou d'impulsion) et celles qui peuvent etre eventuellement necessaires ont une importance capitale pour la polarisation tensorielle. Ce probleme revet a Saclay un interet

  15. A fortran program for elastic scattering of deuterons with an optical model containing tensorial potentials; Programme fortran pour la diffusion elastique de deutons avec un modele optique contenant des termes tensoriels

    Energy Technology Data Exchange (ETDEWEB)

    Raynal, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1963-07-01

    The optical model has been applied with success to the elastic scattering of particles of spin 0 and 1/2 and to a lesser degree to that of deuterons. For particles of spin l/2, an LS coupling term is ordinarily used; this term is necessary to obtain a polarization; for deuterons, this coupling has been already introduced, but the possible forms of potentials are more numerous (in this case, scalar products of a second rank spin tensor with a tensor of the same rank in space or momentum can occur). These terms which may be necessary are primarily important for the tensor polarization. This problem is of particular interest at Saclay since a beam of polarized deuterons has become available. The FORTRAN program SPM 037 permits the study of the effect of tensorial potentials constructed from the distance of the deuteron from the target and its angular momentum with respect to it. This report should make possible the use and even the modification of the program. It consists of: a description of the problem and of the notation employed, a presentation of the methods adopted, an indication of the necessary data and how they should be introduced, and finally tables of symbols which are in equivalence or common statements: these tables must be considered when making any modification. (author) [French] Le modele optique a ete applique avec succes a la diffusion elastique des particules de spin nul et 1/2 et dans une moindre mesure a celle des deutons. Pour les particules de spin 1/2, on utilise habituellement un couplage LS, necessaire pour calculer la polarisation; pour les deutons, ce couplage a deja ete introduit, mais les formes de potentiel possibles sont plus nombreuses (intervention de produits scalaires d'un tenseur d'ordre 2 de spin avec un tenseur du meme ordre d'espace ou d'impulsion) et celles qui peuvent etre eventuellement necessaires ont une importance capitale pour la polarisation tensorielle. Ce probleme revet a Saclay un interet particulier depuis la mise

  16. Virtual neutron scattering experiments

    DEFF Research Database (Denmark)

    Overgaard, Julie Hougaard; Bruun, Jesper; May, Michael

    2017-01-01

    . In the last week of the course, students travel to a large-scale neutron scattering facility to perform real neutron scattering experiments. Through student interviews and survey answers, we argue, that the virtual training prepares the students to engage more fruitfully with experiments by letting them focus......We describe how virtual experiments can be utilized in a learning design that prepares students for hands-on experiments at large-scale facilities. We illustrate the design by showing how virtual experiments are used at the Niels Bohr Institute in a master level course on neutron scattering...

  17. Scattering on magnetic monopoles

    International Nuclear Information System (INIS)

    Petry, H.R.

    1980-01-01

    The time-dependent scattering theory of charged particles on magnetic monopoles is investigated within a mathematical frame-work, which duely pays attention to the fact that the wavefunctions of the scattered particles are sections in a non-trivial complex line-bundle. It is found that Moeller operators have to be defined in a way which takes into account the peculiar long-range behaviour of the monopole field. Formulas for the scattering matrix and the differential cross-section are derived, and, as a by-product, a momentum space picture for particles, which are described by sections in the underlying complex line-bundle, is presented. (orig.)

  18. Deep inelastic neutron scattering

    International Nuclear Information System (INIS)

    Mayers, J.

    1989-03-01

    The report is based on an invited talk given at a conference on ''Neutron Scattering at ISIS: Recent Highlights in Condensed Matter Research'', which was held in Rome, 1988, and is intended as an introduction to the techniques of Deep Inelastic Neutron Scattering. The subject is discussed under the following topic headings:- the impulse approximation I.A., scaling behaviour, kinematical consequences of energy and momentum conservation, examples of measurements, derivation of the I.A., the I.A. in a harmonic system, and validity of the I.A. in neutron scattering. (U.K.)

  19. Anomalous and resonance small-angle scattering

    International Nuclear Information System (INIS)

    Epperson, J.E.; Thiyagarajan, P.

    1988-01-01

    Significant changes in the small-angle scattered intensity can be induced by making measurements with radiation close to an absorption edge of an appropriate atomic species contained in the sample. These changes can be related quantitatively to the real and imaginary anomalous-dispersion terms for the scattering factor (X-rays) or scattering length (neutrons). The physics inherent in these anomalous-dispersion terms is first discussed before consideration of how they enter the relevant scattering theory. Two major areas of anomalous-scattering research have emerged; macromolecules in solution and unmixing of metallic alloys. Research in each area is reviewed, illustrating both the feasibility and potential of these techniques. All the experimental results reported to date have been obtained with X-rays. However, it is pointed out that the formalism is the same for the analog experiment with neutrons, and a number of suitable isotopes exist which exhibit resonance in an accessible range of energy. Potential applications of resonance small-angle neutron scattering are discussed. (orig.)

  20. Selective scattering in a zigzag graphene nanoribbon

    International Nuclear Information System (INIS)

    Nakabayashi, Jun; Kurihara, Susumu

    2009-01-01

    Electric transport of a zigzag graphene nanoribbon through a step-like potential or a potential barrier is studied by using the recursive Green's function method. The results for a step-like potential show that scattering processes in a zigzag graphene nanoribbon obey a following selection rule: when the number of zigzag chains N is even, electrons in the band m are only scattered into the bands m+2n, where n is an integer. According to this selection rule, a step-like potential blocks the current when the potential height exceeds the incident energy as long as only the low-energy region is treated. Then, replacing a step-like potential with a potential barrier, we also show that it can play the role of a b and-selective filter .

  1. Theoretically unprejudiced fits to proton scattering

    International Nuclear Information System (INIS)

    Kobos, A.M.; Mackintosh, R.S.

    1979-01-01

    By using a spline interpolation method applied to all components of the proton optical potential we have fitted elastic scattering from 40 Ca and from 16 O at a range of energies. The potentials are highly oscillatory and we have shown that similar oscillations are found when the spline fitting procedure is applied to pseudo-data generated from potentials of known l-dependence. Moreover, we show how to find an l-independent potential equivalent to one that is l-dependent and we find that it is oscillatory and that various characteristic features of empirical spline fit potentials can be explained. Thus, by fitting the data with model indenpendt l-independent potentials we have found support for the contention that the nucleon optical potential should be viewed as being l-dependent. This work may be regarded as an example of the kind of physical information that can be gained by pursuing exact fits to proton elastic scattering data

  2. Scattered Radiation Emission Imaging: Principles and Applications

    Directory of Open Access Journals (Sweden)

    M. K. Nguyen

    2011-01-01

    Full Text Available Imaging processes built on the Compton scattering effect have been under continuing investigation since it was first suggested in the 50s. However, despite many innovative contributions, there are still formidable theoretical and technical challenges to overcome. In this paper, we review the state-of-the-art principles of the so-called scattered radiation emission imaging. Basically, it consists of using the cleverly collected scattered radiation from a radiating object to reconstruct its inner structure. Image formation is based on the mathematical concept of compounded conical projection. It entails a Radon transform defined on circular cone surfaces in order to express the scattered radiation flux density on a detecting pixel. We discuss in particular invertible cases of such conical Radon transforms which form a mathematical basis for image reconstruction methods. Numerical simulations performed in two and three space dimensions speak in favor of the viability of this imaging principle and its potential applications in various fields.

  3. Cloaking through cancellation of diffusive wave scattering

    KAUST Repository

    Farhat, Mohamed

    2016-08-10

    A new cloaking mechanism, which makes enclosed objects invisible to diffusive photon density waves, is proposed. First, diffusive scattering from a basic core-shell geometry, which represents the cloaked structure, is studied. The conditions of scattering cancellation in a quasi-static scattering regime are derived. These allow for tailoring the diffusivity constant of the shell enclosing the object so that the fields scattered from the shell and the object cancel each other. This means that the photon flow outside the cloak behaves as if the cloaked object were not present. Diffusive light invisibility may have potential applications in hiding hot spots in infrared thermography or tissue imaging. © 2016 The Author(s) Published by the Royal Society. All rights reserved.

  4. General time-dependent formulation of quantum scattering theory

    International Nuclear Information System (INIS)

    Althorpe, Stuart C.

    2004-01-01

    We derive and explain the key ideas behind a time-dependent formulation of quantum scattering theory, applicable generally to systems with a finite-range scattering potential. The scattering is initiated and probed by plane wave packets, which are localized just outside the range of the potential. The asymptotic limits of conventional scattering theory (initiation in the remote past; detection in the remote future) are not taken. Instead, the differential cross section (DCS) is obtained by projecting the scattered wave packet onto the probe plane wave packets. The projection also yields a time-dependent version of the DCS. Cuts through the wave packet, just as it exits the scattering potential, yield time-dependent and time-independent angular distributions that give a close-up picture of the scattering which complements the DCS. We have previously applied the theory to interpret experimental cross sections of chemical reactions [e.g., S. C. Althorpe, F. Fernandez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. This paper gives the derivation of the theory, and explains its relation to conventional scattering theory. For clarity, the derivation is restricted to spherical-particle scattering, though it may readily be extended to general multichannel systems. We illustrate the theory using a simple application to hard-sphere scattering

  5. Sum rules in classical scattering

    International Nuclear Information System (INIS)

    Bolle, D.; Osborn, T.A.

    1981-01-01

    This paper derives sum rules associated with the classical scattering of two particles. These sum rules are the analogs of Levinson's theorem in quantum mechanics which provides a relationship between the number of bound-state wavefunctions and the energy integral of the time delay of the scattering process. The associated classical relation is an identity involving classical time delay and an integral over the classical bound-state density. We show that equalities between the Nth-order energy moment of the classical time delay and the Nth-order energy moment of the classical bound-state density hold in both a local and a global form. Local sum rules involve the time delay defined on a finite but otherwise arbitrary coordinate space volume S and the bound-state density associated with this same region. Global sum rules are those that obtain when S is the whole coordinate space. Both the local and global sum rules are derived for potentials of arbitrary shape and for scattering in any space dimension. Finally the set of classical sum rules, together with the known quantum mechanical analogs, are shown to provide a unified method of obtaining the high-temperature expansion of the classical, respectively the quantum-mechanical, virial coefficients

  6. Gaussian basis functions for highly oscillatory scattering wavefunctions

    Science.gov (United States)

    Mant, B. P.; Law, M. M.

    2018-04-01

    We have applied a basis set of distributed Gaussian functions within the S-matrix version of the Kohn variational method to scattering problems involving deep potential energy wells. The Gaussian positions and widths are tailored to the potential using the procedure of Bačić and Light (1986 J. Chem. Phys. 85 4594) which has previously been applied to bound-state problems. The placement procedure is shown to be very efficient and gives scattering wavefunctions and observables in agreement with direct numerical solutions. We demonstrate the basis function placement method with applications to hydrogen atom–hydrogen atom scattering and antihydrogen atom–hydrogen atom scattering.

  7. Electron scattering from pyrimidine

    International Nuclear Information System (INIS)

    Colmenares, Rafael; Fuss, Martina C; García, Gustavo; Oller, Juan C; Muñoz, Antonio; Blanco, Francisco; Almeida, Diogo; Limão-Vieira, Paulo

    2014-01-01

    Electron scattering from pyrimidine (C 4 H 4 N 2 ) was investigated over a wide range of energies. Following different experimental and theoretical approaches, total, elastic and ionization cross sections as well as electron energy loss distributions were obtained.

  8. Gravitational Bhabha scattering

    International Nuclear Information System (INIS)

    Santos, A F; Khanna, Faqir C

    2017-01-01

    Gravitoelectromagnetism (GEM) as a theory for gravity has been developed similar to the electromagnetic field theory. A weak field approximation of Einstein theory of relativity is similar to GEM. This theory has been quantized. Traditional Bhabha scattering, electron–positron scattering, is based on quantized electrodynamics theory. Usually the amplitude is written in terms of one photon exchange process. With the development of quantized GEM theory, the scattering amplitude will have an additional component based on an exchange of one graviton at the lowest order of perturbation theory. An analysis will provide the relative importance of the two amplitudes for Bhabha scattering. This will allow an analysis of the relative importance of the two amplitudes as the energy of the exchanged particles increases. (paper)

  9. Applied electromagnetic scattering theory

    CERN Document Server

    Osipov, Andrey A

    2017-01-01

    Besides classical applications (radar and stealth, antennas, microwave engineering), scattering and diffraction are enabling phenomena for some emerging research fields (artificial electromagnetic materials or metamaterials, terahertz technologies, electromagnetic aspects of nano-science). This book is a tutorial for advanced students who need to study diffraction theory. The textbook gives fundamental knowledge about scattering and diffraction of electromagnetic waves and provides some working examples of solutions for practical high-frequency scattering and diffraction problems. The book focuses on the most important diffraction effects and mechanisms influencing the scattering process and describes efficient and physically justified simulation methods - physical optics (PO) and the physical theory of diffraction (PTD) - applicable in typical remote sensing scenarios. The material is presented in a comprehensible and logical form, which relates the presented results to the basic principles of electromag...

  10. Scattering by bound nucleons

    International Nuclear Information System (INIS)

    Tezuka, Hirokazu.

    1984-10-01

    Scattering of a particle by bound nucleons is discussed. Effects of nucleons that are bound in a nucleus are taken as a structure function. The way how to calculate the structure function is given. (author)

  11. LIDAR Thomson scattering

    International Nuclear Information System (INIS)

    1991-07-01

    This collection contains 21 papers on the application and development of LIDAR (Light Detection and Ranging) Thomson scattering techniques for the determination of spatially resolved electron temperature and density in magnetic confinement experiments, particularly tokamaks. Refs, figs and tabs

  12. Magnetic electron scattering

    International Nuclear Information System (INIS)

    Peterson, G.A.

    1989-01-01

    We briefly review some of the motivations, early results, and techniques of magnetic elastic and inelastic electron-nucleus scattering. We then discuss recent results, especially those acquired at high momentum transfers. 50 refs., 19 figs

  13. Deep inelastic lepton scattering

    International Nuclear Information System (INIS)

    Nachtmann, O.

    1977-01-01

    Deep inelastic electron (muon) nucleon and neutrino nucleon scattering as well as electron positron annihilation into hadrons are reviewed from a theoretical point of view. The emphasis is placed on comparisons of quantum chromodynamics with the data. (orig.) [de

  14. Small angle neutron scattering

    International Nuclear Information System (INIS)

    Bernardini, G.; Cherubini, G.; Fioravanti, A.; Olivi, A.

    1976-09-01

    A method for the analysis of the data derived from neutron small angle scattering measurements has been accomplished in the case of homogeneous particles, starting from the basic theory without making any assumption on the form of particle size distribution function. The experimental scattering curves are interpreted with the aid the computer by means of a proper routine. The parameters obtained are compared with the corresponding ones derived from observations at the transmission electron microscope

  15. Pp scattering at SIN

    International Nuclear Information System (INIS)

    Aprile-Giboni, E.; Cantale, G.; Hausammann, R.

    1983-01-01

    Using the PM1 polarized proton beam at SIN and a polarized target, the elastic pp scattering as well as the inelastic channel pp → π + d have been studied between 400 and 600 MeV. For the elastic reaction, a sufficient number of spin dependent parameters has been measured in order to do a direct reconstruction of the scattering matrix between 38 0 /sub cm/ and 90 0 /sub cm/. 10 references, 6 figures

  16. Iterative numerical solution of scattering problems

    Energy Technology Data Exchange (ETDEWEB)

    Tomio, L; Adhikari, S K

    1995-05-01

    An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10{sup 10} after some-8-10 iterations. (author). 31 refs, 2 tabs.

  17. Iterative numerical solution of scattering problems

    International Nuclear Information System (INIS)

    Tomio, L.; Adhikari, S.K.

    1995-05-01

    An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10 10 after some-8-10 iterations. (author). 31 refs, 2 tabs

  18. Inelastic scattering from amorphous solids

    International Nuclear Information System (INIS)

    Price, D.L.

    1985-08-01

    The potential of inelastic neutron scattering techniques for surveying various aspects of the dynamics of amorphous solids is briefly reviewed. The recent use of the Intense Pulsed Neutron Source to provide detailed information on the optical vibrations of glasses is discussed in more detail. The density of states represents an averaged quantity which gives information about the general characteristics of the structure and bonding. More extensive information can be obtained by studying the detailed wavevector dependence of the dynamic structure factor. 15 refs., 7 figs

  19. Neutron scattering studies of modulated magnetic structures

    Energy Technology Data Exchange (ETDEWEB)

    Aagaard Soerensen, Steen

    1999-08-01

    This report describes investigations of the magnetic systems DyFe{sub 4}Al{sub 8} and MnSi by neutron scattering and in the former case also by X-ray magnetic resonant scattering. The report is divided into three parts: An introduction to the technique of neutron scattering with special emphasis on the relation between the scattering cross section and the correlations between the scattering entities of the sample. The theoretical framework of neutron scattering experiments using polarized beam technique is outlined. The second part describes neutron and X-ray scattering investigation of the magnetic structures of DyFe{sub 4}Al{sub 8}. The Fe sublattice of the compound order at 180 K in a cycloidal structure in the basal plane of the bct crystal structure. At 25 K the ordering of the Dy sublattice shows up. By the element specific technique of X-ray resonant magnetic scattering, the basal plane cycloidal structure was also found for the Dy sublattice. The work also includes neutron scattering studies of DyFe{sub 4}Al{sub 8} in magnetic fields up to 5 T applied along a <110> direction. The modulated structure at the Dy sublattice is quenched by a field lower than 1 T, whereas modulation is present at the Fe sublattice even when the 5 T field is applied. In the third part of the report, results from three small angle neutron experiments on MnSi are presented. At ambient pressure, a MnSi is known to form a helical spin density wave at temperature below 29 K. The application of 4.5 kbar pressure intended as hydrostatic decreased the Neel temperature to 25 K and changed the orientation of the modulation vector. To understand this reorientation within the current theoretical framework, anisotropic deformation of the sample crystal must be present. The development of magnetic critical scattering with an isotropic distribution of intensity has been studied at a level of detail higher than that of work found in the literature. Finally the potential of a novel polarization

  20. On the theory of inelastic scattering of slow electrons by surface excitations: 2. Thin film formalism

    International Nuclear Information System (INIS)

    Nkoma, J.S.

    1982-08-01

    A quantum-mechanical theory for the inelastic scattering of slow electrons (ISSE) by surface excitations in a thin film is developed. The scattered wave function inside the thin film is obtained by solving the inhomogeneous Schroedinger equation, and it is found to contain terms which show that the back scattered intensity is smaller than the forward scattered intensity. A scattering cross-section for forward scattering is derived and is found to be dependent on transmission factors, wavevectors and fluctuations of the scattering potential. (author)