Description of elastic scattering in U-matrix method
International Nuclear Information System (INIS)
Edneral, V.F.; Troshin, S.M.; Tyurin, N.E.; Khrustalev, O.A.
1975-01-01
The elastic pp-scattering has been analyzed using a generalized reaction matrix (the U-matrix). A good agreement has been reached with the experimental total cross sections for the (pp) reaction beginning with an energy of 30 GeV and for the dsub(t)(dt)(pp) for four ISR energies [ru
S-matrix description of anomalous large-angle heavy-ion scattering
Energy Technology Data Exchange (ETDEWEB)
Frahn, W E; Hussein, M S [Sao Paulo Univ. (Brazil). Inst. de Fisica; Canto, L F; Donangelo, R [Rio de Janeiro Univ. (Brazil). Inst. de Fisica
1981-10-12
We present a quantitative description of the well-known anomalous features observed in the large-angle scattering of n..cap alpha.. type heavy ions, in particular of the pronounced structures in the backangle excitation function for /sup 16/O + /sup 28/Si. Our treatment is based on the close connection between these anomalies and particular structural deviations of the partial-wave S-matrix from normal strong-absorption behaviour. The properties of these deviations are found to be rather well specified by the data: they are localized within a narrow 'l-window' centered at a critical angular momentum significantly smaller than the grazing value, and have a parity-dependent as well as a parity-independent part. These properties provide important clues as to the physical processes causing the large-angle enhancement.
S-matrix description of anomalus large-angle heavy-ion scattering
International Nuclear Information System (INIS)
Frahn, W.E.; Hussein, M.S.; Canto, L.F.; Donangelo, R.J.
1981-01-01
A quantitative description of the well-known anomalous features observed in the large-angle scattering of n.α type heavy ions, in particular of the pronounced structures in the backangle excitation function or 16 O + 28 Si is presented. This treatment is based on the close connection between these anomalies and particular structural deviations of the partial-wave S-matrix from normal strong-absorption behaviour. The properties of these deviations are found to be rather well specified by the data: they are localized within a narrow 'l-window' centered at a critical angular momentum significantly smaller than the grazing value, and have a parity-dependent as well as a parity-independent part. These properties provide important clues as to the physical processes causing the large-angle enhancement. (Author) [pt
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
Significance of matrix diagonalization in modelling inelastic electron scattering
Energy Technology Data Exchange (ETDEWEB)
Lee, Z. [University of Ulm, Ulm 89081 (Germany); Hambach, R. [University of Ulm, Ulm 89081 (Germany); University of Jena, Jena 07743 (Germany); Kaiser, U.; Rose, H. [University of Ulm, Ulm 89081 (Germany)
2017-04-15
Electron scattering is always applied as one of the routines to investigate nanostructures. Nowadays the development of hardware offers more and more prospect for this technique. For example imaging nanostructures with inelastic scattered electrons may allow to produce component-sensitive images with atomic resolution. Modelling inelastic electron scattering is therefore essential for interpreting these images. The main obstacle to study inelastic scattering problem is its complexity. During inelastic scattering, incident electrons entangle with objects, and the description of this process involves a multidimensional array. Since the simulation usually involves fourdimensional Fourier transforms, the computation is highly inefficient. In this work we have offered one solution to handle the multidimensional problem. By transforming a high dimensional array into twodimensional array, we are able to perform matrix diagonalization and approximate the original multidimensional array with its twodimensional eigenvectors. Our procedure reduces the complicated multidimensional problem to a twodimensional problem. In addition, it minimizes the number of twodimensional problems. This method is very useful for studying multiple inelastic scattering. - Highlights: • 4D problems are involved in modelling inelastic electron scattering. • By means of matrix diagonalization, the 4D problems can be simplified as 2D problems. • The number of 2D problems is minimized by using this approach.
Scattering matrix approach to non-stationary quantum transport
Moskalets, Michael V
2012-01-01
The aim of this book is to introduce the basic elements of the scattering matrix approach to transport phenomena in dynamical quantum systems of non-interacting electrons. This approach admits a physically clear and transparent description of transport processes in dynamical mesoscopic systems promising basic elements of solid-state devices for quantum information processing. One of the key effects, the quantum pump effect, is considered in detail. In addition, the theory for a recently implemented new dynamical source - injecting electrons with time delay much larger than the electron coherence time - is offered. This theory provides a simple description of quantum circuits with such a single-particle source and shows in an unambiguous way that the tunability inherent to the dynamical systems leads to a number of unexpected but fundamental effects.
P-matrix description of charged particles interaction
International Nuclear Information System (INIS)
Babenko, V.A.; Petrov, N.M.
1992-01-01
The paper deals with formalism of the P-matrix description of two charged particles interaction. Separation in the explicit form of the background part corresponding to the purely Coulomb interaction in the P-matrix is proposed. Expressions for the purely Coulomb P-matrix, its poles, residues and purely Coulomb P-matrix approach eigenfunctions are obtained. (author). 12 refs
Matrix-exponential description of radiative transfer
International Nuclear Information System (INIS)
Waterman, P.C.
1981-01-01
By appling the matrix-exponential operator technique to the radiative-transfer equation in discrete form, new analytical solutions are obtained for the transmission and reflection matrices in the limiting cases x >1, where x is the optical depth of the layer. Orthongonality of the eigenvectors of the matrix exponential apparently yields new conditions for determining. Chandrasekhar's characteristic roots. The exact law of reflection for the discrete eigenfunctions is also obtained. Finally, when used in conjuction with the doubling method, the matrix exponential should result in reduction in both computation time and loss of precision
The scattering matrix element of the three body reactive collision
International Nuclear Information System (INIS)
Morsy, M.W.; Hilal, A.A.; El-Sabagh, M.A.
1980-08-01
The optical model approximation has been applied to a previously derived set of coupled equations representing the dynamics of the three-body reactive scattering. The Schroedinger equation obtained describing the scattering problem has then been solved by inserting the effective mass approximation. The asymptotic requirements for both the entrance and exit channels, respectively, have been supplied to give the scattering matrix element of the reactive collision. (author)
Hierarchy of Poisson brackets for elements of a scattering matrix
International Nuclear Information System (INIS)
Konopelchenko, B.G.; Dubrovsky, V.G.
1984-01-01
The infinite family of Poisson brackets [Ssub(i1k1) (lambda 1 ), Ssub(i2k2) (lambda 2 )]sub(n) (n=0, 1, 2, ...) between the elements of a scattering matrix is calculated for the linear matrix spectral problem. (orig.)
Time delay correlations in chaotic scattering and random matrix approach
International Nuclear Information System (INIS)
Lehmann, N.; Savin, D.V.; Sokolov, V.V.; Sommers, H.J.
1994-01-01
We study the correlations in the time delay a model of chaotic resonance scattering based on the random matrix approach. Analytical formulae which are valid for arbitrary number of open channels and arbitrary coupling strength between resonances and channels are obtained by the supersymmetry method. The time delay correlation function, through being not a Lorentzian, is characterized, similar to that of the scattering matrix, by the gap between the cloud of complex poles of the S-matrix and the real energy axis. 28 refs.; 4 figs
Quasinormal-Mode Expansion of the Scattering Matrix
Directory of Open Access Journals (Sweden)
Filippo Alpeggiani
2017-06-01
Full Text Available It is well known that the quasinormal modes (or resonant states of photonic structures can be associated with the poles of the scattering matrix of the system in the complex-frequency plane. In this work, the inverse problem, i.e., the reconstruction of the scattering matrix from the knowledge of the quasinormal modes, is addressed. We develop a general and scalable quasinormal-mode expansion of the scattering matrix, requiring only the complex eigenfrequencies and the far-field properties of the eigenmodes. The theory is validated by applying it to illustrative nanophotonic systems with multiple overlapping electromagnetic modes. The examples demonstrate that our theory provides an accurate first-principles prediction of the scattering properties, without the need for postulating ad hoc nonresonant channels.
Hanle-Zeeman Scattering Matrix for Magnetic Dipole Transitions
Energy Technology Data Exchange (ETDEWEB)
Megha, A.; Sampoorna, M.; Nagendra, K. N.; Sankarasubramanian, K., E-mail: megha@iiap.res.in, E-mail: sampoorna@iiap.res.in, E-mail: knn@iiap.res.in, E-mail: sankar@iiap.res.in [Indian Institute of Astrophysics, Koramangala, Bengaluru 560 034 (India)
2017-06-01
The polarization of the light that is scattered by the coronal ions is influenced by the anisotropic illumination from the photosphere and the magnetic field structuring in the solar corona. The properties of the coronal magnetic fields can be well studied by understanding the polarization properties of coronal forbidden emission lines that arise from magnetic dipole ( M 1) transitions in the highly ionized atoms that are present in the corona. We present the classical scattering theory of the forbidden lines for a more general case of arbitrary-strength magnetic fields. We derive the scattering matrix for M 1 transitions using the classical magnetic dipole model of Casini and Lin and applying the scattering matrix approach of Stenflo. We consider a two-level atom model and neglect collisional effects. The scattering matrix so derived is used to study the Stokes profiles formed in coronal conditions in those regions where the radiative excitations dominate collisional excitations. To this end, we take into account the integration over a cone of an unpolarized radiation from the solar disk incident on the scattering atoms. Furthermore, we also integrate along the line of sight to calculate the emerging polarized line profiles. We consider radial and dipole magnetic field configurations and spherically symmetric density distributions. For our studies we adopt the atomic parameters corresponding to the [Fe xiii] 10747 Å coronal forbidden line. We also discuss the nature of the scattering matrix for M 1 transitions and compare it with that for the electric dipole ( E 1) transitions.
Enhanced Resource Descriptions Help Learning Matrix Users.
Roempler, Kimberly S.
2003-01-01
Describes the Learning Matrix digital library which focuses on improving the preparation of math and science teachers by supporting faculty who teach introductory math and science courses in two- and four-year colleges. Suggests it is a valuable resource for school library media specialists to support new science and math teachers. (LRW)
Comparison of matrix methods for elastic wave scattering problems
International Nuclear Information System (INIS)
Tsao, S.J.; Varadan, V.K.; Varadan, V.V.
1983-01-01
This article briefly describes the T-matrix method and the MOOT (method of optimal truncation) of elastic wave scattering as they apply to A-D, SH- wave problems as well as 3-D elastic wave problems. Two methods are compared for scattering by elliptical cylinders as well as oblate spheroids of various eccentricity as a function of frequency. Convergence, and symmetry of the scattering cross section are also compared for ellipses and spheroidal cavities of different aspect ratios. Both the T-matrix approach and the MOOT were programmed on an AMDHL 470 computer using double precision arithmetic. Although the T-matrix method and MOOT are not always in agreement, it is in no way implied that any of the published results using MOOT are in error
Matrix product state description of Halperin states
Crépel, V.; Estienne, B.; Bernevig, B. A.; Lecheminant, P.; Regnault, N.
2018-04-01
Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact matrix product state (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wave functions, the Halperin states. These can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wave-function symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation lengths, which are compared to plasma analogy arguments.
An estimate on the purely imaginary poles of scattering matrix
International Nuclear Information System (INIS)
Bozhkov, Y.D.
1988-12-01
In this work we obtain two estimates (upper and lower) on the number of purely imaginary poles of the scattering matrix for the wave equation in the exterior of a compact smooth obstacle in R n , n ≥ 3 odd. The method of Lax and Phillips is used. (author). 5 refs
The S-matrix for abstract scattering systems
International Nuclear Information System (INIS)
Amrein, W.O.; Pearson, D.B.
1979-01-01
Let S(lambda) be the S-matrix at energy lambda for an abstract scattering system. A bound is derived in terms of the interaction, on integrals of the form ∫ h(lambda)/S(lambda) - I/ 2 sub(HS) dlambda, where /./sub(HS) denotes the Hilbert-Schmidt norm. (Auth.)
Study of the nuclear-coulomb low-energy scattering parameters on the basis of the p-matrix approach
International Nuclear Information System (INIS)
Babenko, V.A.; Petrov, N.M.
1993-01-01
The P-matrix approach application to the description of two charged strongly interacting particles nuclear-Coulomb scattering parameters is considered. The nuclear-Coulomb scattering length and effective range explicit expressions in terms of the P-matrix parameters are found. The nuclear-Coulomb low-energy parameters expansions in powers of small parameter β ≡ R/a b , involving terms with big logarithms, are obtained. The nuclear-Coulomb scattering length and effective range for the square-well and the delta-shell short range potentials are found in an explicit form. (author). 21 refs
Scattering-matrix elements of coated infinite-length cylinders
International Nuclear Information System (INIS)
Manickavasagam, S.; Menguec, M.P.
1998-01-01
The angular variations of scattering-matrix elements of coated cylindrical particles are presented. The sensitivity of different elements for a number of physical parameters are discussed, including size parameter, real and imaginary parts of the refractive index of the outer coat, and the inner core. The numerical predictions are presented for typical index-of-refraction values of cotton fibers. These results show that the physical structure of coated cylinders can be determined from carefully conducted light-scattering experiments. copyright 1998 Optical Society of America
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
Coherent scattering and matrix correction in bone-lead measurements
International Nuclear Information System (INIS)
Todd, A.C.
2000-01-01
The technique of K-shell x-ray fluorescence of lead in bone has been used in many studies of the health effects of lead. This paper addresses one aspect of the technique, namely the coherent conversion factor (CCF) which converts between the matrix of the calibration standards and those of human bone. The CCF is conventionally considered a constant but is a function of scattering angle, energy and the elemental composition of the matrices. The aims of this study were to quantify the effect on the CCF of several assumptions which may not have been tested adequately and to compare the CCFs for plaster of Paris (the present matrix of calibration standards) and a synthetic apatite matrix. The CCF was calculated, using relativistic form factors, for published compositions of bone, both assumed and assessed compositions of plaster, and the synthetic apatite. The main findings of the study were, first, that impurities in plaster, lead in the plaster or bone matrices, coherent scatter from non-bone tissues and the individual subject's measurement geometry are all minor or negligible effects; and, second, that the synthetic apatite matrix is more representative of bone mineral than is plaster of Paris. (author)
Unified description of bound, resonant and scattering states
International Nuclear Information System (INIS)
Konya, B.; Levai, G.; Papp, Z.
2000-01-01
Recently we have introduced a general method for calculating the discrete Hilbert-space basis representation of the Green's operators of those Hamiltonians which have infinite symmetric tridiagonal matrix forms. The elements of this matrix are used in the calculation of the Green's matrix in terms of a three-term recurrence relation and continued fractions. We specified our general approach to the case of the Coulomb problem and the Coulomb-Sturmian basis associated with it. As a further step, we can combine this new way of calculating the Coulomb-Green's matrix with a technique of solving integral equations in discrete Hilbert-space-basis representations. This provides us with a quantum mechanical approximation method which is rather general in the sense that it is equally applicable to solving bound-, resonant- and scattering-state problems with practically any potential of physical relevance. The method is especially suited to problems where Coulomb-like asymptotics have to be treated, but the formalism also contains the case of the free Green's operator as a special case. (author)
Microscopic description of elastic and direct inelastic nucleon scattering off spherical nuclei
Energy Technology Data Exchange (ETDEWEB)
Dupuis, M. [CEA, DAM, DIF, Arpajon (France)
2017-05-15
The purpose of this study is to improve the modeling of nucleon direct inelastic scattering to the continuum using a microscopic and parameter-free approach. For the first time, direct elastic scattering, inelastic scattering to discrete excitations and to the continuum are described within a microscopic approach without adjustable parameters. Proton scattering off {sup 90}Zr and {sup 208}Pb are the reactions used as test case examples of the calculations. The model uses the Melbourne g-matrix and the Random Phase Approximation description of nuclear states, implemented with the Gogny D1S interaction. The relevant optical and transition potentials in a finite nucleus are calculated within a local density approximation. As we use the nuclear matter approach we limit our study to incident energies above 40 MeV. We first checked that this model provides an accurate account of measured cross sections for elastic scattering and inelastic scattering to discrete states. It is then applied to the direct inelastic scattering to the continuum considering all one-phonon excitations predicted within the RPA approach. This accounts for a part of the direct pre-equilibrium emission, often labeled as the one-step direct process in quantum-based approaches. Our approach provides a very accurate description of angular distributions where the one-step process dominates. The impact of collective excitations is shown to be non negligible for energy transfer to the target up to 20 MeV, decreasing as the incident energy increases. For incident energies above 80 MeV, our modeling provides a good account of direct proton emission for an energy transfer to the target up to 30 MeV. However, the proton emission we predict underestimates the measured cross sections for incident energies below 80 MeV. We compare our prediction to those of the phenomenological exciton model to help interpret this result. Directions that may improve our modeling are discussed. (orig.)
Microscopic description of elastic and direct inelastic nucleon scattering off spherical nuclei
Dupuis, M.
2017-05-01
The purpose of this study is to improve the modeling of nucleon direct inelastic scattering to the continuum using a microscopic and parameter-free approach. For the first time, direct elastic scattering, inelastic scattering to discrete excitations and to the continuum are described within a microscopic approach without adjustable parameters. Proton scattering off 90Zr and 208Pb are the reactions used as test case examples of the calculations. The model uses the Melbourne g-matrix and the Random Phase Approximation description of nuclear states, implemented with the Gogny D1S interaction. The relevant optical and transition potentials in a finite nucleus are calculated within a local density approximation. As we use the nuclear matter approach we limit our study to incident energies above 40 MeV. We first checked that this model provides an accurate account of measured cross sections for elastic scattering and inelastic scattering to discrete states. It is then applied to the direct inelastic scattering to the continuum considering all one-phonon excitations predicted within the RPA approach. This accounts for a part of the direct pre-equilibrium emission, often labeled as the one-step direct process in quantum-based approaches. Our approach provides a very accurate description of angular distributions where the one-step process dominates. The impact of collective excitations is shown to be non negligible for energy transfer to the target up to 20 MeV, decreasing as the incident energy increases. For incident energies above 80 MeV, our modeling provides a good account of direct proton emission for an energy transfer to the target up to 30 MeV. However, the proton emission we predict underestimates the measured cross sections for incident energies below 80 MeV. We compare our prediction to those of the phenomenological exciton model to help interpret this result. Directions that may improve our modeling are discussed.
Connection between Dirac and matrix Schroedinger inverse-scattering transforms
International Nuclear Information System (INIS)
Jaulent, M.; Leon, J.J.P.
1978-01-01
The connection between two applications of the inverse scattering method for solving nonlinear equations is established. The inverse method associated with the massive Dirac system (D) : (iσ 3 d/dx - i q 3 σ 1 - q 1 σ 2 + mσ 2 )Y = epsilonY is rediscovered from the inverse method associated with the 2 x 2 matrix Schroedinger equation (S) : Ysub(xx) + (k 2 -Q)Y = 0. Here Q obeys a nonlinear constraint equivalent to a linear constraint on the reflection coefficient for (S). (author)
A mathematical formulation of the Mahaux-Weidenmueller formula for the scattering matrix
International Nuclear Information System (INIS)
Christiansen, T J; Zworski, M
2009-01-01
This paper gives a mathematical exposition of a formula for the scattering matrix for a manifold with infinite cylindrical ends or a waveguide. This formula is well known in the physics literature and we show that a variant of this formula gives the scattering matrix of the mathematics literature. Moreover, we bound the difference between the scattering matrix and an approximation of it computed using a finite rank approximation of the interaction matrix.
Towards an S-matrix Description of Gravitational Collapse
Amati, D; Veneziano, Gabriele
2008-01-01
Extending our previous results on trans-Planckian ($Gs \\gg \\hbar$) scattering of light particles in quantum string-gravity we present a calculation of the corresponding S-matrix from the region of large impact parameters ($b \\gg G\\sqrt{s}>\\lambda_s$) down to the regime where classical gravitational collapse is expected to occur. By solving the semiclassical equations of a previously introduced effective-action approximation, we find that the perturbative expansion around the leading eikonal result diverges at a critical value $b = b_c = O(G\\sqrt{s})$, signalling the onset of a new (black-hole related?) regime. We then discuss the main features of our explicitly unitary S-matrix -- and of the associated effective metric -- down to (and in the vicinity of) $b = b_c$, and present some ideas and results on its extension all the way to the $ b \\to 0$ region. We find that for $b
On the isobaric spin and the scattering matrix
International Nuclear Information System (INIS)
Hategan, Cornel
2002-01-01
The isobaric spin and the scattering matrix are fundamental nuclear physics concepts invented by Werner Heisenberg. The cardinal impact of the Heisenberg concepts on historical developpement of nuclear physics and other quantum and classical physics branches is discussed in this communication. Heisenberg in physics is synonymous to monumental scientific creations, namely: -'Creation of quantum mechanics' (Nobel Prize, 1932), -'Heisenberg relations', or 'Heisenberg inequalities' or 'Uncertainty principle' or 'Indeterminacy principle', - Basis for Copenhagen interpretation of Quantum Mechanics, -'world formula', - Project for a unitary theory representing all existing particles. Heisenberg does signify also important/cardinal contributions to many fields of physics as follows: - hydrodynamical theory of turbulence, (Dissertation, Sommerfeld); - theory of ferromagnetism; - study of cosmic rays; - nuclear physics. Heisenberg has invented two nuclear physics concepts, isobaric spin and scattering matrix which became cornerstones of the two main fields of the nuclear theory, namely, the nuclear structure (nuclear spectroscopy) and the nuclear reactions. This communication intends to illustrate the impact of the Heisenberg concepts on developpement of nuclear physics. (author)
Classical-limit S-matrix for heavy ion scattering
International Nuclear Information System (INIS)
Donangelo, R.J.
1977-01-01
An integral representation for the classical limit of the quantum mechanical S-matrix is developed and applied to heavy-ion Coulomb excitation and Coulomb-nuclear interference. The method combines the quantum principle of superposition with exact classical dynamics to describe the projectile-target system. A detailed consideration of the classical trajectories and of the dimensionless parameters that characterize the system is carried out. The results are compared, where possible, to exact quantum mechanical calculations and to conventional semiclassical calculations. It is found that in the case of backscattering the classical limit S-matrix method is able to almost exactly reproduce the quantum-mechanical S-matrix elements, and therefore the transition probabilities, even for projectiles as light as protons. The results also suggest that this approach should be a better approximation for heavy-ion multiple Coulomb excitation than earlier semiclassical methods, due to a more accurate description of the classical orbits in the electromagnetic field of the target nucleus. Calculations using this method indicate that the rotational excitation probabilities in the Coulomb-nuclear interference region should be very sensitive to the details of the potential at the surface of the nucleus, suggesting that heavy-ion rotational excitation could constitute a sensitive probe of the nuclear potential in this region. The application to other problems as well as the present limits of applicability of the formalism are also discussed
Scattering matrix for magnetic potentials with Coulomb decay at infinity
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...
Microscopic description of inelastic proton scattering from 88Sr
International Nuclear Information System (INIS)
Kouw, L.R.
1987-01-01
A microscopic description of the 88 Sr(p,p') reaction at 25 and 31 MeV, 200 MeV and 65 MeV is given. In the analysis several excited states are considered. For the nuclear structure of these states wave functions calculated from a one broken-pair model in a 4hw model space are used which give in general a good description of the shape of the transition charge and current densities as measured in (e,e') scattering. Also a macroscopic analysis has been made of some collective transitions. For 24, 31 and 65 MeV the effective HJ and the JLM interaction were employed, the effective Paris interaction was used at 200 MeV and the M3YP interaction at 65 MeV. At 65 and 200 MeV some calibration factors were needed. It is shown that the nonlocality of the distortion potential is closely related to the nonlocality of the transition potential. The influence of a spin-orbit potential and nonlocality in the single-particle potential on the electromagnetic current operator is discussed. In an impulse approximation of the electromagnetic coupling the presence of these terms would lead to violation of charge conservation. Starting from a Lagrangian formulation a current operator is derived that conserves explicitly electric charge. (Auth.)
Rui, Wei; Tao, Chao; Liu, Xiaojun
2017-09-18
Acoustic scattering medium is a fundamental challenge for photoacoustic imaging. In this study, we reveal the different coherent properties of the scattering photoacoustic waves and the direct photoacoustic waves in a matrix form. Direct waves show a particular coherence on the antidiagonals of the matrix, whereas scattering waves do not. Based on this property, a correlation matrix filter combining with a time reversal operator is proposed to preserve the direct waves and recover the image behind a scattering layer. Both numerical simulations and photoacoustic imaging experiments demonstrate that the proposed approach effectively increases the image contrast and decreases the background speckles in a scattering medium. This study might improve the quality of photoacoustic imaging in an acoustic scattering environment and extend its applications.
Unified description of scattering and fusion phenomena in heavy-ion collisions
International Nuclear Information System (INIS)
Sahu, Basudeb; Sahu, B. B.; Mallick, G. S.; Agarwalla, S. K.; Shastry, C. S.
2008-01-01
An analytical recursive formula of the partial-wave scattering matrix for the total effective complex potential of nucleus-nucleus collisions is derived to conveniently analyze the data of angular variations of elastic scattering cross sections. Further, another expression of cross sections for the absorption from arbitrarily small intervals is derived. This leads to the explanation of the fusion cross section (σ fus ) data at various incident center-of-mass energies E c.m. by collecting the absorption contributions in the interior region of the effective potential. This concept is akin to that used by Udagawa et al. in the calculation of fusion cross sections in elastic channels. The interaction potential considered in the analysis is energy independent and by virtue of its weakly absorbing character it supports resonance states in different partial-wave trajectories. Consequently, occurrence of these resonances is shown to be the physical origin of the observed oscillatory structure in the variation respect to energy of the quantity D(E c.m. )=d 2 (E c.m. σ fus )/dE c.m. 2 , the second derivative of the product E c.m. σ fus with respect to E c.m. . In this article, we investigate two well-known cases of heavy-ion collisions, namely 12 C+ 208 Pb and 16 O+ 208 Pb, and obtain simultaneous and very successful explanations of cross sections for elastic scattering and fusion and the results of D(E c.m. ). These results obtained by using a somewhat novel and convenient method demonstrate the unified description of scattering and fusion for interacting heavy-ion systems
Theory of the particle matrix elements for Helium atom scattering in surfaces
International Nuclear Information System (INIS)
Khater, A.; Toennies, J.P.
2000-01-01
Full text.A brief review is presented for the recent development of the theory of the particle transition matrix elements, basic to the cross section for Helium and inert particle scattering at thermal energies in solid surfaces. the Jackson and Mott matrix elements are presented and discussed for surface scattering processes, habitually classified as elastic and inelastic. Modified transition matrix elements, introduced originally to account for the cut-off effects, are presented in a direct and simple manner. the Debye-Waller factor is introduced and discussed. A recent calculation for the particle transition matrix elements is presented for the specular and inelastic transition matrix elements and the corresponding inelastic scattering cross section is compared in detail to experimental data. the specular and inelastic transition matrix elements are found to be intrinsically similar owing to the intermediate role of a proposed virtual particle squeezed state near the surface
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
The scattering matrix is non-trivial for weakly coupled P(phi)2 models
International Nuclear Information System (INIS)
Osterwalder, K.; Seneor, R.
1976-01-01
It is shown that for sufficiently small coupling constant lambda the lambdaP(phi) 2 quantum field theory models have a scattering matrix which is different from 1. The other method is to write the scattering matrix elements as polynomials in lambda, whose coefficients, though themselves functions of lamda, are uniformly bounded for lambda sufficiently small. The first order term in that expansion is the one given by perturbation theory. (Auth.)
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
Liu, Jia; Zhang, Yongming; Zhang, Qixing; Wang, Jinjun
2018-03-01
The complete scattering matrix for cement dust was measured as a function of scattering angle from 5° to 160° at a wavelength of 532 nm, as a representative of mineral dust of anthropogenic origin in urban areas. Other related characteristics of cement dust, such as particle size distribution, chemical composition, refractive index, and micromorphology, were also analyzed. For this objective, a newly improved apparatus was built and calibrated using water droplets. Measurements of water droplets were in good agreement with Lorenz-Mie calculations. To facilitate the direct applicability of measurements for cement dust in radiative transfer calculation, the synthetic scattering matrix was computed and defined over the full scattering angle range from 0° to 180°. The scattering matrices for cement dust and typical natural mineral dusts were found to be similar in trends and angular behaviors. Angular distributions of all matrix elements were confined to rather limited domains. To promote the application of light-scattering matrix in atmospheric observation and remote sensing, discrimination methods for various atmospheric particulates (cement dust, soot, smolder smoke, and water droplets) based on the angular distributions of their scattering matrix elements are discussed. The ratio -F12/F11 proved to be the most effective discrimination method when a single matrix element is employed; aerosol identification can be achieved based on -F12/F11 values at 90° and 160°. Meanwhile, the combinations of -F12/F11 with F22/F11 (or (F11 - F22)/(F11 + F22)) or -F12/F11 with F44/F11 at 160° can be used when multiple matrix elements at the same scattering angle are selected.
Direct determination of scattering time delays using the R-matrix propagation method
International Nuclear Information System (INIS)
Walker, R.B.; Hayes, E.F.
1989-01-01
A direct method for determining time delays for scattering processes is developed using the R-matrix propagation method. The procedure involves the simultaneous generation of the global R matrix and its energy derivative. The necessary expressions to obtain the energy derivative of the S matrix are relatively simple and involve many of the same matrix elements required for the R-matrix propagation method. This method is applied to a simple model for a chemical reaction that displays sharp resonance features. The test results of the direct method are shown to be in excellent agreement with the traditional numerical differentiation method for scattering energies near the resonance energy. However, for sharp resonances the numerical differentiation method requires calculation of the S-matrix elements at many closely spaced energies. Since the direct method presented here involves calculations at only a single energy, one is able to generate accurate energy derivatives and time delays much more efficiently and reliably
Scattering of long folded strings and mixed correlators in the two-matrix model
International Nuclear Information System (INIS)
Bourgine, J.-E.; Hosomichi, K.; Kostov, I.; Matsuo, Y.
2008-01-01
We study the interactions of Maldacena's long folded strings in two-dimensional string theory. We find the amplitude for a state containing two long folded strings to come and go back to infinity. We calculate this amplitude both in the worldsheet theory and in the dual matrix model, the matrix quantum mechanics. The matrix model description allows to evaluate the amplitudes involving any number of long strings, which are given by the mixed trace correlators in an effective two-matrix model
S-matrix formulation of thermodynamics with N-body scatterings
Energy Technology Data Exchange (ETDEWEB)
Lo, Pok Man [University of Wroclaw, Institute of Theoretical Physics, Wroclaw (Poland); Extreme Matter Institute EMMI, GSI, Darmstadt (Germany)
2017-08-15
We apply a phase space expansion scheme to incorporate the N-body scattering processes in the S-matrix formulation of statistical mechanics. A generalized phase shift function suitable for studying the thermal contribution of N → N processes is motivated and examined in various models. Using the expansion scheme, we revisit how the hadron resonance gas model emerges from the S-matrix framework, and consider an example of structureless scattering in which the phase shift function can be exactly worked out. Finally we analyze the influence of dynamics on the phase shift function in a simple example of 3- and 4-body scattering. (orig.)
Meromorphic extension of the scattering matrix for long range two-body problems
International Nuclear Information System (INIS)
Gerard, C.; Martinez, A.
1989-01-01
We prove the existence of a meromorphic extension of the scattering matrix for long range potentials analytic at infinity. This extension exists as a bounded operator on some Gevrey spaces on S n-1 , with critical depending on the rate of decay of the potential at infinity. We use a semi-stationary definition of the scattering operator due to Isozaki-Kitada, using time independent modifiers. We show that the poles of the scattering matrix coincide with the resonances of the Hamiltonian [fr
Convergent J-matrix calculation of the Poet-Temkin model of electron-hydrogen scattering
International Nuclear Information System (INIS)
Konovalov, D.A.; McCarthy, I.E.
1994-01-01
It is shown that the Poet-Temkin model of electron-hydrogen scattering could be solved to any required accuracy using the J-matrix method. The convergence in the basis size is achieved to an accuracy of better than 2% with the inclusion of 37 basis L 2 functions. Previously observed pseudoresonances in the J-matrix calculation naturally disappear with an increase in basis size. No averaging technique is necessary to smooth the convergent J-matrix results. (Author)
Semiclassical description of scattering with internal degrees of freedom
International Nuclear Information System (INIS)
Cruz-Barrios, S.; Gomez-Camacho, J.
1998-01-01
The scattering of systems with internal degrees of freedom is studied in the semi-classical approximation. It is found that a special set of states, named coherent internal states, are specially relevant for the semi-classical treatment. A classical trajectory is defined for each coherent internal state. The semi-classical expressions obtained satisfy the superposition principle and are valid for arbitrary coupling strength. (orig.)
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)
A unified BFKL/DGLAP description of deep inelastic scattering
International Nuclear Information System (INIS)
Kwiecinski, J.; Stasto, A. M.; Martin, A. D.
1997-01-01
We introduce a coupled pair of evolution equations for the unintegrated gluon distribution and the sea quark distribution which incorporate both the resummed leading ln(1/x) BFKL contributions and the resummed leading ln(Q 2 ) DGLAP contributions. We solve these unified equations in the perturbative QCD domain. With only two physically motivated parameters we obtain an excellent description of the HERA F 2 data
Real space multiple scattering description of alloy phase stability
International Nuclear Information System (INIS)
Turchi, P.E.A.; Sluiter, M.
1992-01-01
This paper presents a brief overview of the advanced methodology which has been recently developed to study phase stability properties of substitutional alloys, including order-disorder phenomena and structural transformations. The approach is based on the real space version of the Generalized Perturbation Method first introduced by Ducastelle and Gautier, within the Korringa-Kohn-Rostoker multiple scattering formulation of the Coherent Potential Approximation. Temperature effects are taken into account with a generalized meanfield approach, namely the Cluster Variation Method. The viability and the predictive power of such a scheme will be illustrated by a few examples, among them: the ground state properties of alloys, in particular the ordering tendencies for a series of equiatomic bcc-based alloys, the computation of alloy phase diagrams with the case of fcc and bcc-based Ni-Al alloys, the calculation of antiphase boundary energies and interfacial energies, and the stability of artificial ordered superlattices
J-matrix method of scattering in one dimension: The nonrelativistic theory
International Nuclear Information System (INIS)
Alhaidari, A.D.; Bahlouli, H.; Abdelmonem, M.S.
2009-01-01
We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a basis that supports a tridiagonal matrix representation for the reference wave operator. Contrary to our expectation, the 1D formulation reveals a rich and highly nontrivial structure compared to the 3D formulation. Examples are given to demonstrate the utility and accuracy of the method. It is hoped that this formulation constitutes a viable alternative to the classical treatment of 1D scattering problem and that it will help unveil new and interesting applications.
Delayed coherent quantum feedback from a scattering theory and a matrix product state perspective
Guimond, P.-O.; Pletyukhov, M.; Pichler, H.; Zoller, P.
2017-12-01
We study the scattering of photons propagating in a semi-infinite waveguide terminated by a mirror and interacting with a quantum emitter. This paradigm constitutes an example of coherent quantum feedback, where light emitted towards the mirror gets redirected back to the emitter. We derive an analytical solution for the scattering of two-photon states, which is based on an exact resummation of the perturbative expansion of the scattering matrix, in a regime where the time delay of the coherent feedback is comparable to the timescale of the quantum emitter’s dynamics. We compare the results with numerical simulations based on matrix product state techniques simulating the full dynamics of the system, and extend the study to the scattering of coherent states beyond the low-power limit.
International Nuclear Information System (INIS)
Rinkel, J.; Dinten, J.M.; Tabary, J.
2004-01-01
The use of focused anti-scatter grids on digital radiographic systems with two-dimensional detectors produces acquisitions with a decreased scatter to primary ratio and thus improved contrast and resolution. Simulation software is of great interest in optimizing grid configuration according to a specific application. Classical simulators are based on complete detailed geometric descriptions of the grid. They are accurate but very time consuming since they use Monte Carlo code to simulate scatter within the high-frequency grids. We propose a new practical method which couples an analytical simulation of the grid interaction with a radiographic system simulation program. First, a two dimensional matrix of probability depending on the grid is created offline, in which the first dimension represents the angle of impact with respect to the normal to the grid lines and the other the energy of the photon. This matrix of probability is then used by the Monte Carlo simulation software in order to provide the final scattered flux image. To evaluate the gain of CPU time, we define the increasing factor as the increase of CPU time of the simulation with as opposed to without the grid. Increasing factors were calculated with the new model and with classical methods representing the grid with its CAD model as part of the object. With the new method, increasing factors are shorter by one to two orders of magnitude compared with the second one. These results were obtained with a difference in calculated scatter of less than five percent between the new and the classical method. (authors)
Quark bags, P-matrix and nucleon-nucleon scattering
International Nuclear Information System (INIS)
Narodetskij, I.M.
1984-01-01
This paper is an extended version of the talk given at IX European Conference on Few Body Problems in Physics, Tbilisi, 1984. It reviews recent developments of the quark compound bag (QCB) model including explicit examples of the QCB nucleon-nucleon potentials, description of the deuteron properties, calculation of the six quark admixture in the deuteron and applications to the three-nucleon system
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.
Kundrát, Vojtech; Kaspar, Jan; Procházka, Jirí
2010-01-01
The standard description of common influence of both the Coulomb and hadronic elastic scattering in the proton - proton elastic collisions at high energies with the help of West and Yennie complete amplitude is shown to be theoretically inconsistent. The approach being based on the eikonal model amplitude removes these troubles. The preference of its applica- tion to the analysis of experimental data and in obtaining the predictions of contemporary models for proton - proton high energy elastic hadronic scattering are discussed.
Formal scattering theory approach to S-matrix relations in supersymmetric quantum mechanics
International Nuclear Information System (INIS)
Amado, R.D.; Cannata, F.; Dedonder, J.P.
1988-01-01
Combining the methods of scattering theory and supersymmetric quantum mechanics we obtain relations between the S matrix and its supersymmetric partner. These relations involve only asymptotic quantities and do not require knowledge of the dynamical details. For example, for coupled channels with no threshold differences the relations involve the asymptotic normalization constant of the bound state removed by supersymmetry
Solution of the scattering T matrix equation in discrete complex momentum space
International Nuclear Information System (INIS)
Rawitscher, G.H.; Delic, G.
1984-01-01
The scattering solution to the Lippmann-Schwinger equation is expanded into a set of spherical Bessel functions of complex wave numbers, K/sub j/, with j = 1,2 , . . . , M. The value of each K/sub j/ is determined from the condition that the spherical Bessel function smoothly matches onto an asymptotically outgoing spherical Hankel (or Coulomb) function of the correct physical wave number at a matching point R. The spherical Bessel functions thus determined are Sturmian functions, and they form a complete set in the interval 0 to R. The coefficients of the expansion of the scattering function are determined by matrix inversion of a linear set of algebraic equations, which are equivalent to the solution of the T-matrix equation in complex momentum space. In view of the presence of a matching radius, no singularities are encountered for the Green's functions, and the inclusion of Coulomb potentials offers no computational difficulties. Three numerical examples are performed in order to illustrate the convergence of the elastic scattering matrix S with M. One of these consists of a set of coupled equations which describe the breakup of a deuteron as it scatters from the nucleus on 58 Ni. A value of M of 15 or less is found sufficient to reproduce the exact S matrix element to an accuracy of four figures after the decimal point
Classical versus quantum structure of the scattering probability matrix: Chaotic waveguides
Czech Academy of Sciences Publication Activity Database
Luna-Acosta, G. A.; Méndez-Bermúdez, J. A.; Šeba, Petr; Pichugin, K. N.
2002-01-01
Roč. 65, č. 4 (2002), 046605/1-046605/8 ISSN 1063-651X Grant - others:CONACYT(MX) 26163-E Institutional research plan: CEZ:AV0Z1010914 Keywords : scattering matrix * waveguids Subject RIV: BE - Theoretical Physics Impact factor: 2.397, year: 2002
Off-shell two-particle scattering amplitude in the P-matrix approach
International Nuclear Information System (INIS)
Babenko, V.A.; Petrov, N.M.
1988-01-01
A generalization of the P-matrix approach which makes it possible to describe the interaction of two particles off the energy shell is proposed. Explicit separation in the wave function of a part corresponding to free motion yields a compact expression for the off-shell scattering amplitude and gives directly a method for separable expansion of the amplitude
Directory of Open Access Journals (Sweden)
E DU
2014-01-01
Full Text Available We developed a model to describe polarized photon scattering in biological tissues. In this model, tissues are simplified to a mixture of scatterers and surrounding medium. There are two types of scatterers in the model: solid spheres and infinitely long solid cylinders. Variables related to the scatterers include: the densities and sizes of the spheres and cylinders, the orientation and angular distribution of cylinders. Variables related to the surrounding medium include: the refractive index, absorption coefficient and birefringence. In this paper, as a development we introduce an optical activity effect to the model. By comparing experiments and Monte Carlo simulations, we analyze the backscattering Mueller matrix patterns of several tissue-like media, and summarize the different effects coming from anisotropic scattering and optical properties. In addition, we propose a possible method to extract the optical activity values for tissues. Both the experimental and simulated results show that, by analyzing the Mueller matrix patterns, the microstructure and optical properties of the medium can be obtained. The characteristic features of Mueller matrix patterns are potentially powerful tools for studying the contrast mechanisms of polarization imaging for medical diagnosis.
Wapenaar, C.P.A.; Slob, E.C.; Snieder, R.
2010-01-01
We have analyzed the far-field approximation of the Green's function representation for seismic interferometry. By writing each of the Green's functions involved in the correlation process as a superposition of a direct wave and a scattered wave, the Green's function representation is rewritten as a
Solution of the inverse scattering problem at fixed energy with non-physical S matrix elements
International Nuclear Information System (INIS)
Eberspaecher, M.; Amos, K.; Apagyi, B.
1999-12-01
The quantum mechanical inverse elastic scattering problem is solved with the modified Newton-Sabatier method. A set of S matrix elements calculated from a realistic analytic optical model potential serves as input data. It is demonstrated that the quality of the inversion potential can be improved by including non-physical S matrix elements to half, quarter and eighth valued partial waves if the original set does not contain enough information to determine the interaction potential. We demonstrate that results can be very sensitive to the choice of those non-physical S matrix values both with the analytic potential model and in a real application in which the experimental cross section for the symmetrical scattering system of 12 C+ 12 C at E=7.998 MeV is analyzed
Directory of Open Access Journals (Sweden)
A. Gogoi
2011-09-01
Full Text Available Scattering properties of bentonite clay particles were investigated at 543.5 nm incident laser wavelength by using a designed and fabricated light scattering setup. The scattering samples were held in front of a laser beam by using a transparent cylindrical thermosetting epoxy matrix.
Neutron-deuteron scattering calculations with W-matrix representation of the two-body input
International Nuclear Information System (INIS)
Bartnik, E.A.; Haberzettl, H.; Januschke, T.; Kerwath, U.; Sandhas, W.
1987-05-01
Employing the W-matrix representation of the partial-wave T matrix introduced by Bartnik, Haberzettl, and Sandhas, we show for the example of the Malfliet-Tjon potentials I and III that the single-term separable part of the W-matrix representation, when used as input in three-nucleon neutron-deuteron scattering calculations, is fully capable of reproducing the exact results obtained by Kloet and Tjon. This approximate two-body input not only satisfies the two-body off-shell unitarity relation but, moreover, it also contains a parameter which may be used in optimizing the three-body data. We present numerical evidence that there exists a variational (minimum) principle for the determination of the three-body binding energy which allows one to choose this parameter also in the absence of an exact reference calculation. Our results for neutron-deuteron scattering show that it is precisely this choice of the parameter which provides optimal scattering data. We conclude that the W-matrix approach, despite its simplicity, is a remarkably efficient tool for high-quality three-nucleon calculations. (orig.)
Resonant Raman scattering in ion-beam-synthesized Mg2Si in a silicon matrix
International Nuclear Information System (INIS)
Baleva, M.; Zlateva, G.; Atanassov, A.; Abrashev, M.; Goranova, E.
2005-01-01
Resonant Raman scattering by ion beam synthesized in silicon matrix Mg 2 Si phase is studied. The samples are prepared with the implantation of 24 Mg + ions with dose 4x10 17 cm -2 and with two different energies 40 and 60 keV into (100)Si substrates. The far infrared spectra are used as criteria for the formation of the Mg 2 Si phase. The Raman spectra are excited with different lines of Ar + laser, with energies of the lines lying in the interval from 2.40 to 2.75 eV. The resonant scattering can be investigated using these laser lines, as far as according to the Mg 2 Si band structure, there are direct gaps with energies in the same region. The energy dependences of the scattered intensities in the case of the scattering by the allowed F 2g and the forbidden LO-type modes are experimentally obtained and theoretically interpreted. On the base of the investigation energies of the interband transitions in the Mg 2 Si are determined. It is found also that the resonant Raman scattering appears to be a powerful tool for characterization of a material with inclusions in it. In the particular case it is concluded that the Mg 2 Si phase is present in the form of a surface layer in the sample, prepared with implantation energy 40 keV and as low-dimensional precipitates, embedded in the silicon matrix, in the sample, prepared with the higher implantation energy
The matrix element for radiative Bhabha scattering in the forward direction
International Nuclear Information System (INIS)
Kleiss, R.
1993-09-01
We present an approximation to the matrix element for the process e + e - →e + e - γ, appropriate to the situation where one or both of the fermions are scattered over very small angles. The leading terms in the situation where all scattering angles are small contains not only terms quadratic in the electron mass, but also quartic and even sextic terms must be included. Special attention is devoted to the numerical stability of the resultant expression. Its relation to several existing formulae is discussed. (orig.)
Description of backward maxima in α-particle elastic scattering on 12C and 40Ca nuclei
International Nuclear Information System (INIS)
Zelenskaya, N.S.; Teplov, I.B.; Yushchenko, T.A.
1981-01-01
The backward maxima in the cross section are described presenting the elastic scattering amplitude as a sum of an optical (potential) amplitude and an addition associated with exchange processes. The use of the simplified distorted wave variant (the eikonal) approximation with cutoff in integration over the interior of the nucleus for calculation of the matrix elements of exchange processes is numerically justified. The microscopic description allows not only to describe the backward maxima for both nuclei but as well to improve the agreement with the experiment in a wide angular range and to obtain a correct general behaviour of the excitation functions at the largest angles. Comparison of the microscopic and phenomenological reflection coefficients shows that these coefficients cannot be described in terms of a single phenomenological model [ru
Simplified expressions of the T-matrix integrals for electromagnetic scattering.
Somerville, Walter R C; Auguié, Baptiste; Le Ru, Eric C
2011-09-01
The extended boundary condition method, also called the null-field method, provides a semianalytic solution to the problem of electromagnetic scattering by a particle by constructing a transition matrix (T-matrix) that links the scattered field to the incident field. This approach requires the computation of specific integrals over the particle surface, which are typically evaluated numerically. We introduce here a new set of simplified expressions for these integrals in the commonly studied case of axisymmetric particles. Simplifications are obtained using the differentiation properties of the radial functions (spherical Bessel) and angular functions (associated Legendre functions) and integrations by parts. The resulting simplified expressions not only lead to faster computations, but also reduce the risks of loss of precision and provide a simpler framework for further analytical work.
A S-matrix-like approximation in the charged particle scattering by the hydrogen atom
International Nuclear Information System (INIS)
Mignaco, J.A.; Tort, A.C.
1979-01-01
The Born approximation for charged particle scattering by the hydrogen atom is unfit at low energies. From a S-matrix-like consideration on the dominance of the neighbour singularities, the calculation of other contributions is suggested. The inclusion of bound states is made, following Eden's and his colaborators' ideas, which are described by their interest and likeness with procedures in the intermediate energy physics. (Author) [pt
Higher order spin-dependent terms in D0-brane scattering from the matrix model
International Nuclear Information System (INIS)
McArthur, I.N.
1998-01-01
The potential describing long-range interactions between D0-branes contains spin-dependent terms. In the matrix model, these should be reproduced by the one-loop effective action computed in the presence of a non-trivial fermionic background ψ. The v 3 ψ 2 /r 8 term in the effective action has been computed by Kraus and shown to correspond to a spin-orbit interaction between D0-branes, and the ψ 8 /r 11 term in the static potential has been obtained by Barrio et al. In this paper, the v 2 ψ 4 /r 9 term is computing in the matrix model and compared with the corresponding results of Morales et al. obtained using string theoretic methods. The technique employed is adapted to the underlying supersymmetry of the matrix model, and should be useful in the calculation of spin-dependent effects in more general Dp-brane scatterings. (orig.)
The impact of ice particle roughness on the scattering phase matrix
International Nuclear Information System (INIS)
Baum, Bryan A.; Yang Ping; Hu Yongxiang; Feng Qian
2010-01-01
The goal of this study is to explore the influence of ice particle habit (or shape) and surface roughness on the scattering phase matrix. As an example, reported here are the results for two wavelengths: 0.67 and 1.61 μm. For this effort, a database of single-scattering properties has been computed for a set of habits including hexagonal plates, hollow and solid columns, hollow and solid 3D bullet rosettes, droxtals, aggregates of solid columns, and aggregates of plates. The database provides properties for each of the habits at 101 wavelengths between 0.45 and 2.24 μm for smooth, moderately roughened, and severely roughened particles. At each wavelength, the scattering properties are provided at 233 discrete particle diameters ranging from 2 to 10,000 μm. A single particle size distribution from a very cold ice cloud sampled during the CRYSTAL-FACE field campaign (T cld =-76 o C) is used to illustrate the influence of habit and roughness on the phase matrix. In all, four different habit mixtures are evaluated. The nonzero elements of the phase matrix are shown to be quite sensitive to the assumed habit, particularly in the case of -P 12 /P 11 that is associated with the degree of linear polarization of scattered radiation. Surface roughness is shown to smooth out maxima in the scattering phase function and in the other elements of the phase matrix, consistent with other studies. To compare with the theoretical simulations of the phase matrix for smooth and roughened particles, a full year of cloud-aerosol lidar with orthogonal polarization (CALIOP) data from 2008 is analyzed to provide global statistics on the values of P 11 and P 22 /P 11 in the backscattering direction. In a comparison of two of the habit mixtures (one used for MODIS Collection 5 and another that incorporates new habits including hollow bullet rosettes and aggregates of plates) with the CALIOP data, the values for P 11 are higher regardless of the degree of particle surface roughness, and the
Reducing the orientation influence of Mueller matrix measurements for anisotropic scattering media
Sun, Minghao; He, Honghui; Zeng, Nan; Du, E.; He, Yonghong; Ma, Hui
2014-09-01
Mueller matrix polarimetry techniques contain rich micro-structural information of samples, such as the sizes and refractive indices of scatterers. Recently, Mueller matrix imaging methods have shown great potentials as powerful tools for biomedical diagnosis. However, the orientations of anisotropic fibrous structures in tissues have prominent influence on Mueller matrix measurements, resulting in difficulties for extracting micro-structural information effectively. In this paper, we apply the backscattering Mueller matrix imaging technique to biological samples with different microstructures, such as chicken heart muscle, bovine skeletal muscle, porcine liver and fat tissues. Experimental results show that the directions of the muscle fibers have prominent influence on the Mueller matrix elements. In order to reduce the orientation influence, we adopt the rotation-independent MMT and RLPI parameters, which were proposed in our previous studies, to the tissue samples. Preliminary results in this paper show that the orientation-independent parameters and their statistic features are helpful for analyzing the tissues to obtain their micro-structural properties. Since the micro-structure variations are often related to the pathological changes, the method can be applied to microscope imaging techniques and used to detect abnormal tissues such as cancer and other lesions for diagnosis purposes.
Covariance Matrix of a Double-Differential Doppler-Broadened Elastic Scattering Cross Section
Arbanas, G.; Becker, B.; Dagan, R.; Dunn, M. E.; Larson, N. M.; Leal, L. C.; Williams, M. L.
2012-05-01
Legendre moments of a double-differential Doppler-broadened elastic neutron scattering cross section on 238U are computed near the 6.67 eV resonance at temperature T = 103 K up to angular order 14. A covariance matrix of these Legendre moments is computed as a functional of the covariance matrix of the elastic scattering cross section. A variance of double-differential Doppler-broadened elastic scattering cross section is computed from the covariance of Legendre moments. Notice: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.
Modern approaches for the theoretical description of multiparticle scattering and nuclear reactions
International Nuclear Information System (INIS)
Kukulin, V. I.; Rubtsova, O. A.
2012-01-01
A review of novel approaches to solution of multiparticle scattering problems in the area above three-body breakup together with the review of new computational technologies which provide very effective and ultrafast realization of the novel approaches with ordinary PC are given. The novel direction presented here is based on two key points: a new formulation of the quantum scattering theory in a discrete Hilbert space of stationary wave packets and the massive-parallel solution of the resulted matrix equations with usage of ultrafast graphic processors (the so called GPU-computations). For the reader’s convenience, a short review of the modern GPU calculations for the medicine, physics, military applications etc. is presented.
Mapping local anisotropy axis for scattering media using backscattering Mueller matrix imaging
He, Honghui; Sun, Minghao; Zeng, Nan; Du, E.; Guo, Yihong; He, Yonghong; Ma, Hui
2014-03-01
Mueller matrix imaging techniques can be used to detect the micro-structure variations of superficial biological tissues, including the sizes and shapes of cells, the structures in cells, and the densities of the organelles. Many tissues contain anisotropic fibrous micro-structures, such as collagen fibers, elastin fibers, and muscle fibers. Changes of these fibrous structures are potentially good indicators for some pathological variations. In this paper, we propose a quantitative analysis technique based on Mueller matrix for mapping local anisotropy axis of scattering media. By conducting both experiments on silk sample and Monte Carlo simulation based on the sphere-cylinder scattering model (SCSM), we extract anisotropy axis parameters from different backscattering Mueller matrix elements. Moreover, we testify the possible applications of these parameters for biological tissues. The preliminary experimental results of human cancerous samples show that, these parameters are capable to map the local axis of fibers. Since many pathological changes including early stage cancers affect the well aligned structures for tissues, the experimental results indicate that these parameters can be used as potential tools in clinical applications for biomedical diagnosis purposes.
The Fourier-grid formalism: philosophy and application to scattering problems using R-matrix theory
International Nuclear Information System (INIS)
Layton, E.G.
1993-01-01
The Fourier-grid (FG) method is a recent L 2 variational treatment of the quantum mechanical eigenvalue problem that does not require the use of a set of basis functions; it is rather a discrete variable representation approach. In this article we restate the FG philosophy in more general terms, examine and compare this method with other approaches to the eigenvalue problem, and begin the development of an FG R-matrix method for scattering. The philosophy of the FG method is to use the simplest representation for each of the kinetic and potential energy operators of the Hamiltonian, and use a generalized Fourier transform to put the matrix elements of one of the above operators in the same representation as the other, so the Hamiltonian has a single representation. (author)
Energy Technology Data Exchange (ETDEWEB)
Singh, Mahi R. [Department of Physics and Astronomy, University of Western Ontario, London N6A 3K7 (Canada); Najiminaini, Mohamadreza; Carson, Jeffrey J. L. [Lawson Health Research Institute, St. Joseph' s Health Care, 268 Grosvenor Street, London N6A 4V2 (Canada); Department of Medical Biophysics, University of Western Ontario, London N6A 3K7 (Canada); Balakrishnan, Shankar [Department of Physics and Astronomy, University of Western Ontario, London N6A 3K7 (Canada); Lawson Health Research Institute, St. Joseph' s Health Care, 268 Grosvenor Street, London N6A 4V2 (Canada); Department of Medical Biophysics, University of Western Ontario, London N6A 3K7 (Canada)
2015-05-14
We have experimentally and theoretically investigated the light-matter interaction in metallic nano-hole array structures. The scattering cross section spectrum was measured for three samples each having a unique nano-hole array radius and periodicity. Each measured spectrum had several peaks due to surface plasmon polaritons. The dispersion relation and the effective dielectric constant of the structure were calculated using transmission line theory and Bloch's theorem. Using the effective dielectric constant and the transfer matrix method, the surface plasmon polariton energies were calculated and found to be quantized. Using these quantized energies, a Hamiltonian for the surface plasmon polaritons was written in the second quantized form. Working with the Hamiltonian, a theory of scattering cross section was developed based on the quantum scattering theory and Green's function method. For both theory and experiment, the location of the surface plasmon polariton spectral peaks was dependant on the array periodicity and radii of the nano-holes. Good agreement was observed between the experimental and theoretical results. It is proposed that the newly developed theory can be used to facilitate optimization of nanosensors for medical and engineering applications.
Solution of the nonlinear inverse scattering problem by T-matrix completion. I. Theory.
Levinson, Howard W; Markel, Vadim A
2016-10-01
We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V. An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T-matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016)10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.
Studies of P-matrix formalism on the basis of the potential description of two-particle interaction
International Nuclear Information System (INIS)
Babenko, V.A.; Petrov, N.M.
1991-01-01
A study is made of mathematical and physical aspects of the P-matrix approach within the framework of the potential description of two particle interaction when the dynamics is based on the nonrelativistic Schroedinger equation. A dispersion formula for the P-matrix is derived correctly, different ways of its expansion by means of which it is possible to develop different methods of an approximate description of the quantities characterizing the two-particle interaction are suggested. 15 refs. (author)
A T-matrix calculation for in-medium heavy-quark gluon scattering
International Nuclear Information System (INIS)
Huggins, K.; Rapp, R.
2012-01-01
The interactions of charm and bottom quarks in a quark-gluon plasma (QGP) are evaluated using a thermodynamic 2-body T-matrix. We specifically focus on heavy-quark (HQ) interactions with thermal gluons with an input potential motivated by lattice-QCD computations of the HQ free energy. The latter is implemented into a field-theoretic ansatz for color-Coulomb and (remnants of) confining interactions. This, in particular, enables to discuss corrections to the potential approach, specifically hard-thermal-loop corrections to the vertices, relativistic corrections deduced from pertinent Feynman diagrams, and a suitable projection on transverse thermal gluons. The resulting potentials are applied to compute scattering amplitudes in different color channels and utilized for a calculation of the corresponding HQ drag coefficient in the QGP. A factor of ∼2-3 enhancement over perturbative results is obtained, mainly driven by the resummation in the attractive color-channels.
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
Evolving and energy dependent optical model description of heavy-ion elastic scattering
International Nuclear Information System (INIS)
Michaelian, K.
1996-01-01
We present the application of a genetic algorithm to the problem of determining an energy dependent optical model description of heavy-ion elastic scattering. The problem requires a search for the global best optical model potential and its energy dependence in a very rugged 12 dimensional parameter space of complex topographical features with many local minima. Random solutions are created in the first generation. The fitness of a solution is related to the χ 2 fit of the calculated differential cross sections with the experimental data. Best fit solutions are evolved through cross over and mutation following the biological example. This genetic algorithm approach combined with local gradient minimization is shown to provide a global, complete and extremely efficient search method, well adapted to complex fitness landscapes. These characteristics, combined with the facility of application, should make it the search method of choice for a wide variety of problems from nuclear physics. (Author)
Lee, KyeoReh; Park, YongKeun
2016-10-31
The word 'holography' means a drawing that contains all of the information for light-both amplitude and wavefront. However, because of the insufficient bandwidth of current electronics, the direct measurement of the wavefront of light has not yet been achieved. Though reference-field-assisted interferometric methods have been utilized in numerous applications, introducing a reference field raises several fundamental and practical issues. Here we demonstrate a reference-free holographic image sensor. To achieve this, we propose a speckle-correlation scattering matrix approach; light-field information passing through a thin disordered layer is recorded and retrieved from a single-shot recording of speckle intensity patterns. Self-interference via diffusive scattering enables access to impinging light-field information, when light transport in the diffusive layer is precisely calibrated. As a proof-of-concept, we demonstrate direct holographic measurements of three-dimensional optical fields using a compact device consisting of a regular image sensor and a diffusor.
International Nuclear Information System (INIS)
Uberall, H.; Gaunaurd, G.C.; Tanglis, E.
1983-01-01
The T-matrix approach, which describes the scattering of acoustic waves (or of other waves) from objects of arbitrary shape and geometry, is here 'married' to the resonance scattering theory in order to obtain the (complex) resonance frequencies of an arbitrary shaped target. For the case of nearly impenetrable targets the partial-wave scattering amplitudes are splitted into terms corresponding to 'internal' resonances, plus an apparently nonresonant background amplitude which, however, contains the broad resonances caused by 'external' diffracted (or Franz-type, creeping) waves, in addition to geometrically reflected and refracted (ray) contributions
WWW scattering matrix database for small mineral particles at 441.6 and 632.8 nm
International Nuclear Information System (INIS)
Volten, H.; Munoz, O.; Hovenier, J.W.; Haan, J.F. de; Vassen, W.; Zande, W.J. van der; Waters, L.B.F.M.
2005-01-01
We present a new extensive database containing experimental scattering matrix elements as functions of the scattering angle measured at 441.6 and 632.8 nm for a large collection of micron-sized mineral particles in random orientation. This unique database is accessible through the World-Wide Web. Size distribution tables of the particles are also provided, as well as other characteristics relevant to light scattering. The database provides the light scattering community with easily accessible information that is useful, for a variety of applications such as testing theoretical methods, and the interpretation of measurements of scattered radiation. To illustrate the use of the database, we consider cometary observations and compare them with (1) cometary analog data from the database, and (2) with results of Mie calculations for homogeneous spheres, having the same refractive index and size distribution as those of the analog data
Das, Nandan Kumar; Dey, Rajib; Chakraborty, Semanti; Panigrahi, Prasanta K.; Meglinski, Igor; Ghosh, Nirmalya
2018-04-01
A number of tissue-like disordered media exhibit local anisotropy of scattering in the scaling behavior. Scaling behavior contains wealth of fractal or multifractal properties. We demonstrate that the spatial dielectric fluctuations in a sample of biological tissue exhibit multifractal anisotropy. Multifractal anisotropy encoded in the wavelength variation of the light scattering Mueller matrix and manifesting as an intriguing spectral diattenuation effect. We developed an inverse method for the quantitative assessment of the multifractal anisotropy. The method is based on the processing of relevant Mueller matrix elements in Fourier domain by using Born approximation, followed by the multifractal analysis. The approach promises for probing subtle micro-structural changes in biological tissues associated with the cancer and precancer, as well as for non-destructive characterization of a wide range of scattering materials.
Ivanov, K. A.; Nikolaev, V. V.; Gubaydullin, A. R.; Kaliteevski, M. A.
2017-10-01
Based on the scattering matrix formalism, we have developed a method of quantization of an electromagnetic field in two-dimensional photonic nanostructures ( S-quantization in the two-dimensional case). In this method, the fields at the boundaries of the quantization box are expanded into a Fourier series and are related with each other by the scattering matrix of the system, which is the product of matrices describing the propagation of plane waves in empty regions of the quantization box and the scattering matrix of the photonic structure (or an arbitrary inhomogeneity). The quantization condition (similarly to the onedimensional case) is formulated as follows: the eigenvalues of the scattering matrix are equal to unity, which corresponds to the fact that the set of waves that are incident on the structure (components of the expansion into the Fourier series) is equal to the set of waves that travel away from the structure (outgoing waves). The coefficients of the matrix of scattering through the inhomogeneous structure have been calculated using the following procedure: the structure is divided into parallel layers such that the permittivity in each layer varies only along the axis that is perpendicular to the layers. Using the Fourier transform, the Maxwell equations have been written in the form of a matrix that relates the Fourier components of the electric field at the boundaries of neighboring layers. The product of these matrices is the transfer matrix in the basis of the Fourier components of the electric field. Represented in a block form, it is composed by matrices that contain the reflection and transmission coefficients for the Fourier components of the field, which, in turn, constitute the scattering matrix. The developed method considerably simplifies the calculation scheme for the analysis of the behavior of the electromagnetic field in structures with a two-dimensional inhomogeneity. In addition, this method makes it possible to obviate
Analytical description of photon beam phase spaces in inverse Compton scattering sources
Directory of Open Access Journals (Sweden)
C. Curatolo
2017-08-01
Full Text Available We revisit the description of inverse Compton scattering sources and the photon beams generated therein, emphasizing the behavior of their phase space density distributions and how they depend upon those of the two colliding beams of electrons and photons. The main objective is to provide practical formulas for bandwidth, spectral density, brilliance, which are valid in general for any value of the recoil factor, i.e. both in the Thomson regime of negligible electron recoil, and in the deep Compton recoil dominated region, which is of interest for gamma-gamma colliders and Compton sources for the production of multi-GeV photon beams. We adopt a description based on the center of mass reference system of the electron-photon collision, in order to underline the role of the electron recoil and how it controls the relativistic Doppler/boost effect in various regimes. Using the center of mass reference frame greatly simplifies the treatment, allowing us to derive simple formulas expressed in terms of rms momenta of the two colliding beams (emittance, energy spread, etc. and the collimation angle in the laboratory system. Comparisons with Monte Carlo simulations of inverse Compton scattering in various scenarios are presented, showing very good agreement with the analytical formulas: in particular we find that the bandwidth dependence on the electron beam emittance, of paramount importance in Thomson regime, as it limits the amount of focusing imparted to the electron beam, becomes much less sensitive in deep Compton regime, allowing a stronger focusing of the electron beam to enhance luminosity without loss of mono-chromaticity. A similar effect occurs concerning the bandwidth dependence on the frequency spread of the incident photons: in deep recoil regime the bandwidth comes out to be much less dependent on the frequency spread. The set of formulas here derived are very helpful in designing inverse Compton sources in diverse regimes, giving a
A 19-state R-matrix investigation of resonances in e--He scattering at low energies. Pt. 4
International Nuclear Information System (INIS)
Fon, W.C.; Lim, K.P.
1993-01-01
The authors have previously reported the 11-state and 19-state R-matrix calculations of 1 1 S-2 3,1 S and 1 1 S-2 3 P differential cross sections at low energies. In this paper, the same R-matrix calculations are extended to obtain the differential cross sections and the electron-photon coincidence parameters λ and |Χ| for the excitation of the ground state helium to the 2 1 P state. Convergence studies are carried out between the 11-state and 19-state R-matrix calculations. Only the 19-state R-matrix results are presented in full at scattering angles of 20 o , 30 o , 60 o , 90 o , 120 o and 140 o from the excitation threshold up to 23.8 eV. (author)
Somerville, W. R. C.; Auguié, B.; Le Ru, E. C.
2013-07-01
We propose, describe, and demonstrate a new numerically stable implementation of the extended boundary-condition method (EBCM) to compute the T-matrix for electromagnetic scattering by spheroidal particles. Our approach relies on the fact that for many of the EBCM integrals in the special case of spheroids, a leading part of the integrand integrates exactly to zero, which causes catastrophic loss of precision in numerical computations. This feature was in fact first pointed out by Waterman in the context of acoustic scattering and electromagnetic scattering by infinite cylinders. We have recently studied it in detail in the case of electromagnetic scattering by particles. Based on this study, the principle of our new implementation is therefore to compute all the integrands without the problematic part to avoid the primary cause of loss of precision. Particular attention is also given to choosing the algorithms that minimise loss of precision in every step of the method, without compromising on speed. We show that the resulting implementation can efficiently compute in double precision arithmetic the T-matrix and therefore optical properties of spheroidal particles to a high precision, often down to a remarkable accuracy (10-10 relative error), over a wide range of parameters that are typically considered problematic. We discuss examples such as high-aspect ratio metallic nanorods and large size parameter (≈35) dielectric particles, which had been previously modelled only using quadruple-precision arithmetic codes.
International Nuclear Information System (INIS)
Kuprikov, V. I.; Pilipenko, V. V.; Soznik, A. P.; Tarasov, V. N.; Shlyakhov, N. A.
2009-01-01
The possibility of constructing such new versions of effective nucleon-nucleon forces that would make it possible to describe simultaneously the cross sections for nucleon-nucleus scattering and quantities characterizing nuclear matter and the structure of finite even-even nuclei is investigated on the basis of a microscopic nucleon-nucleus optical potential that is calculated by using effective Skyrme interaction. A procedure for optimizing the parameters of Skyrme forces by employing fits to specific angular distributions for neutron-nucleus scattering and by simultaneously testing the features of nuclear matter, the binding energy of the target nucleus, and its proton root-mean-square radius is proposed. A number of versions of modified Skyrme forces that ensure a reasonable description of both nucleon-nucleus scattering and the properties of nuclear structure are found on the basis of this procedure.
Microscopic description of 3He - α scattering with density dependent interaction
International Nuclear Information System (INIS)
Moraes, M.M.W. de.
1987-01-01
The elastic scattering for a light nuclear system 3 He - α is analysed within the Generating Coordinates Method using a procedure formulated by Piza and Passos. The same numerical technique is used to describe the bond states and scattering properties. (A.C.A.S.) [pt
Directory of Open Access Journals (Sweden)
Yasuhiro Nakamura
2012-07-01
Full Text Available The present study introduces the four-component scattering power decomposition (4-CSPD algorithm with rotation of covariance matrix, and presents an experimental proof of the equivalence between the 4-CSPD algorithms based on rotation of covariance matrix and coherency matrix. From a theoretical point of view, the 4-CSPD algorithms with rotation of the two matrices are identical. Although it seems obvious, no experimental evidence has yet been presented. In this paper, using polarimetric synthetic aperture radar (POLSAR data acquired by Phased Array L-band SAR (PALSAR on board of Advanced Land Observing Satellite (ALOS, an experimental proof is presented to show that both algorithms indeed produce identical results.
FAIR-DDX, Double Diffusion Cross-Sections Scattering Matrix Generated from ENDF/B-4 or JENDL-2
International Nuclear Information System (INIS)
Minami, Kazuyoshi; Yamano, Naoki
2001-01-01
1 - Description of program or function: FAIR-DDX produces double differential (energy and angle) cross sections (DDX) in the form of group-to-group scattering matrices using the evaluated nuclear data libraries JENDL-2 or ENDF/B-IV. The DDX form is useful for verification of the evaluated data, such as the inelastic scattering, through comparison with the experimental DDX values. 2 - Method of solution: DDX uses the file 4 data (angular distribution of secondary neutrons) and the energy and momentum conservation laws. For continuum region reactions, file 5 (energy spectrum of secondary neutrons) is used. To express the angular distribution of secondary neutrons in group-to-group scattering matrices FAIR-DDX adopts a direct angular representation method. 3 - Restrictions on the complexity of the problem: The maximum number of energy groups is 200
Shan, Xiao; Xiahou, Chengkui; Connor, J N L
2018-01-03
In earlier research, we have demonstrated that broad "hidden" rainbows can occur in the product differential cross sections (DCSs) of state-to-state chemical reactions. Here we ask the question: can pronounced and localized rainbows, rather than broad hidden ones, occur in reactive DCSs? Further motivation comes from recent measurements by H. Pan and K. Liu, J. Phys. Chem. A, 2016, 120, 6712, of a "bulge" in a reactive DCS, which they conjecture is a rainbow. Our theoretical approach uses a "weak" version of Heisenberg's scattering matrix program (wHSMP) introduced by X. Shan and J. N. L. Connor, Phys. Chem. Chem. Phys., 2011, 13, 8392. This wHSMP uses four general physical principles for chemical reactions to suggest simple parameterized forms for the S matrix; it does not employ a potential energy surface. We use a parameterization in which the modulus of the S matrix is a smooth-step function of the total angular momentum quantum number, J, and (importantly) its phase is a cubic polynomial in J. We demonstrate for a Legendre partial wave series (PWS) the existence of pronounced rainbows, supernumerary rainbows, and other interference effects, in reactive DCSs. We find that reactive rainbows can be more complicated in their structure than the familiar rainbows of elastic scattering. We also analyse the angular scattering using Nearside-Farside (NF) PWS theory and NF PWS Local Angular Momentum (LAM) theory, including resummations of the PWS. In addition, we apply full and NF asymptotic (semiclassical) rainbow theories to the PWS - in particular, the uniform Airy and transitional Airy approximations for the farside scattering. This lets us prove that structure in the DCSs are indeed rainbows, supernumerary rainbows as well as other interference effects.
International Nuclear Information System (INIS)
Park, Jeong-Hyuck
2003-01-01
We elaborate the idea that the matrix models equipped with the gauge symmetry provide a natural framework to describe identical particles. After demonstrating the general prescription, we study an exactly solvable harmonic oscillator type gauged matrix model. The model gives a generalization of the Calogero-Sutherland system where the strength of the inverse square potential is not fixed but dynamical bounded by below
A vectorial description of electromagnetic scattering by large bodies of spherical shape
International Nuclear Information System (INIS)
Bourrely, C.; Lemaire, T.; Chiappetta, P.; Centre National de la Recherche Scientifique, 13 - Marseille
1989-10-01
We present a new method to obtain a vectorial solution of Helmholtz equation for large homogeneous scatterers having a cylindrical symmetry and a shape approximately spherical. Limitations of the method for arbitrarily shaped particles are discussed
Electron re-scattering from aligned linear molecules using the R-matrix method
International Nuclear Information System (INIS)
Harvey, A G; Tennyson, J
2009-01-01
Electron re-scattering in a strong laser field provides an important probe of molecular structure and processes. The laser field drives the ionization of the molecule, followed by acceleration and subsequent recollision of the electron with the parent molecular ion, the scattered electrons carry information about the nuclear geometry and electronic states of the molecular ion. It is advantageous in strong field experiments to work with aligned molecules, which introduces extra physics compared to the standard gas-phase, electron-molecule scattering problem. The formalism for scattering from oriented linear molecules is presented and applied to H 2 and CO 2 . Differential cross sections are presented for (re-)scattering by these systems concentrating on the most common, linear alignment. In H 2 these cross sections show significant angular structure which, particularly for a scattering angle of 90 deg., are predicted to vary significantly between re-collisions stimulated by an even or an odd number of photons. In CO 2 these cross sections are zero indicating the necessity of using non-parallel alignment with this molecule.
Agrawal, A. P.; Carnegie, D. W.; Boerner, W.-M.
This paper presents an evaluation of polarimetric rain backscatter measurements collected with coherent dual polarization radar systems in the X (8.9 GHz) and Q (45GHz) bands, the first being operated in a pulsed mode and the second being a FM-CW system. The polarimetric measurement data consisted for each band of fifty files of time-sequential scattering matrix measurements expressed in terms of a linear (H, V) antenna polarization state basis. The rain backscattering takes place in a rain cell defined by the beam widths and down range distances of 275 ft through 325 ft and the scattering matrices were measured far below the hydrometeoric scattering center decorrelation time so that ensemble averaging of time-sequential scattering matrices may be applied. In the data evaluation great care was taken in determining: (1) polarimetric Doppler velocities associated with the motion of descending oscillating raindrops and/or eddies within the moving swaths of coastal rain showers, and (2) also the properties of the associated co/cross-polarization rain clutter nulls and their distributions on the Poincare polarization sphere.
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)
Ordered array of ω particles in β-Ti matrix studied by small-angle X-ray scattering
International Nuclear Information System (INIS)
Šmilauerová, J.; Harcuba, P.; Stráský, J.; Stráská, J.; Janeček, M.; Pospíšil, J.; Kužel, R.; Brunátová, T.; Holý, V.; Ilavský, J.
2014-01-01
Nanosized particles of ω phase in a β-Ti alloy were investigated by small-angle X-ray scattering using synchrotron radiation. We demonstrated that the particles are spontaneously weakly ordered in a three-dimensional cubic array along the 〈100〉-directions in the β-Ti matrix. The small-angle scattering data fit well to a three-dimensional short-range-order model; from the fit we determined the evolution of the mean particle size and mean distance between particles during ageing. The self-ordering of the particles is explained by elastic interaction between the particles, since the relative positions of the particles coincide with local minima of the interaction energy. We performed numerical Monte Carlo simulation of the particle ordering and we obtained a good agreement with the experimental data
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
International Nuclear Information System (INIS)
Chyla, K.; Jarczyk, L.; Maciuk, B.; Zipper, W.
1976-01-01
Alpha particle scattering from 28 Si has been studied at five bombarding energies from 23.5 to 28.5 MeV. iota-dependent resonance absorption has been introduced to the optical model analysis of 28 Si (α,β) 28 Si reaction. (author)
Czech Academy of Sciences Publication Activity Database
Al-Zein, A.; Hlinka, Jiří; Rouquette, J.; Kania, A.; Hehlen, B.
2011-01-01
Roč. 109, č. 12 (2011), 124114/1-124114/5 ISSN 0021-8979 R&D Projects: GA ČR GAP204/10/0616 Institutional research plan: CEZ:AV0Z10100520 Keywords : hyper -Raman scattering * PMN * relaxor * ferroelectric phase transition Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 2.168, year: 2011
On the validity of classical description of scattering of atomic particles at mean energies
International Nuclear Information System (INIS)
Pustovit, A.N.
2004-01-01
The conditions of applicability of the classical theory of atomic particle scattering to the small angle and quasi-small angle approximations in calculations of mean-energy particle deflection angles using power interaction potential are analyzed. The applicability range is shown to be much widened for the quasi-small angle approximation, extending to the ranges of quantum theory applicability [ru
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
Energy Technology Data Exchange (ETDEWEB)
Zhang, Le; Yu, Yu; Zhang, Pengjie, E-mail: lezhang@sjtu.edu.cn [Department of Astronomy, Shanghai Jiao Tong University, Shanghai, 200240 (China)
2017-10-10
Photo- z error is one of the major sources of systematics degrading the accuracy of weak-lensing cosmological inferences. Zhang et al. proposed a self-calibration method combining galaxy–galaxy correlations and galaxy–shear correlations between different photo- z bins. Fisher matrix analysis shows that it can determine the rate of photo- z outliers at a level of 0.01%–1% merely using photometric data and do not rely on any prior knowledge. In this paper, we develop a new algorithm to implement this method by solving a constrained nonlinear optimization problem arising in the self-calibration process. Based on the techniques of fixed-point iteration and non-negative matrix factorization, the proposed algorithm can efficiently and robustly reconstruct the scattering probabilities between the true- z and photo- z bins. The algorithm has been tested extensively by applying it to mock data from simulated stage IV weak-lensing projects. We find that the algorithm provides a successful recovery of the scatter rates at the level of 0.01%–1%, and the true mean redshifts of photo- z bins at the level of 0.001, which may satisfy the requirements in future lensing surveys.
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
Cyclotron resonant scattering feature simulations. II. Description of the CRSF simulation process
Schwarm, F.-W.; Ballhausen, R.; Falkner, S.; Schönherr, G.; Pottschmidt, K.; Wolff, M. T.; Becker, P. A.; Fürst, F.; Marcu-Cheatham, D. M.; Hemphill, P. B.; Sokolova-Lapa, E.; Dauser, T.; Klochkov, D.; Ferrigno, C.; Wilms, J.
2017-05-01
Context. Cyclotron resonant scattering features (CRSFs) are formed by scattering of X-ray photons off quantized plasma electrons in the strong magnetic field (of the order 1012 G) close to the surface of an accreting X-ray pulsar. Due to the complex scattering cross-sections, the line profiles of CRSFs cannot be described by an analytic expression. Numerical methods, such as Monte Carlo (MC) simulations of the scattering processes, are required in order to predict precise line shapes for a given physical setup, which can be compared to observations to gain information about the underlying physics in these systems. Aims: A versatile simulation code is needed for the generation of synthetic cyclotron lines. Sophisticated geometries should be investigatable by making their simulation possible for the first time. Methods: The simulation utilizes the mean free path tables described in the first paper of this series for the fast interpolation of propagation lengths. The code is parallelized to make the very time-consuming simulations possible on convenient time scales. Furthermore, it can generate responses to monoenergetic photon injections, producing Green's functions, which can be used later to generate spectra for arbitrary continua. Results: We develop a new simulation code to generate synthetic cyclotron lines for complex scenarios, allowing for unprecedented physical interpretation of the observed data. An associated XSPEC model implementation is used to fit synthetic line profiles to NuSTAR data of Cep X-4. The code has been developed with the main goal of overcoming previous geometrical constraints in MC simulations of CRSFs. By applying this code also to more simple, classic geometries used in previous works, we furthermore address issues of code verification and cross-comparison of various models. The XSPEC model and the Green's function tables are available online (see link in footnote, page 1).
Two-loop massive operator matrix elements for polarized and unpolarized deep-inelastic scattering
Energy Technology Data Exchange (ETDEWEB)
Bierenbaum, I.; Bluemlein, J.; Klein, S.
2007-06-15
The O({alpha}{sup 2}{sub s}) massive operator matrix elements for unpolarized and polarized heavy flavor production at asymptotic values Q{sup 2} >> m{sup 2} are calculated in Mellin space without applying the integration-by-parts method. (orig.)
A method for accurate computation of elastic and discrete inelastic scattering transfer matrix
International Nuclear Information System (INIS)
Garcia, R.D.M.; Santina, M.D.
1986-05-01
A method for accurate computation of elastic and discrete inelastic scattering transfer matrices is discussed. In particular, a partition scheme for the source energy range that avoids integration over intervals containing points where the integrand has discontinuous derivative is developed. Five-figure accurate numerical results are obtained for several test problems with the TRAMA program which incorporates the porposed method. A comparison with numerical results from existing processing codes is also presented. (author) [pt
Reflection Matrix Method for Controlling Light After Reflection From a Diffuse Scattering Surface
2016-12-22
of Philosophy Kenneth W. Burgi, BS, MS Major, USAF 22 December 2016 DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AFIT...refocusing light through thin films of a turbid medium. When coherent light is trans- mitted through a stationary diffuser (i.e. a turbid medium), a fine...resultant light scatter [14, 15, 21, 23]. Transmission matrices were measured with microscopic objectives and thin films of turbid media, resulting in
International Nuclear Information System (INIS)
Kamphuis, C.; Beekman, F.J.; Van Rijk, P.P.; Viergever, M.A.
1998-01-01
Three-dimensional (3D) iterative maximum likelihood expectation maximization (ML-EM) algorithms for single-photon emission tomography (SPET) are capable of correcting image-degrading effects of non-uniform attenuation, distance-dependent camera response and patient shape-dependent scatter. However, the resulting improvements in quantitation, resolution and signal-to-noise ratio (SNR) are obtained at the cost of a huge computational burden. This paper presents a new acceleration method for ML-EM: dual matrix ordered subsets (DM-OS). DM-OS combines two acceleration methods: (a) different matrices for projection and back-projection and (b) ordered subsets of projections. DM-OS was compared with ML-EM on simulated data and on physical thorax phantom data, for both 180 and 360 orbits. Contrast, normalized standard deviation and mean squared error were calculated for the digital phantom experiment. DM-OS resulted in similar image quality to ML-EM, even for speed-up factors of 200 compared to ML-EM in the case of 120 projections. The thorax phantom data could be reconstructed 50 times faster (60 projections) using DM-OS with preservation of image quality. ML-EM and DM-OS with scatter compensation showed significant improvement of SNR compared to ML-EM without scatter compensation. Furthermore, inclusion of complex image formation models in the computer code is simplified in the case of DM-OS. It is thus shown that DM-OS is a fast and relatively simple algorithm for 3D iterative scatter compensation, with similar results to conventional ML-EM, for both 180 and 360 acquired data. (orig.)
Campagnola, Paul J.; Tilbury, Karissa B.; Campbell, Kirby R.; Eliceiri, Kevin W.; Patankar, Manish
2017-02-01
Ovarian cancer remains the most deadly gynecological cancer with a poor aggregate survival rate. To improve upon this situation, we utilized collagen-specific Second Harmonic Generation (SHG) imaging microscopy and optical scattering measurements to probe structural differences in the extracellular matrix of normal stroma, benign tumors, endometrioid tumors, and low and high-grade serous (LGS and HGS) tumors. The SHG signatures of the emission directionality and conversion efficiency as well as the optical scattering are related to the organization of collagen on the sub-micron size. The wavelength dependence of these readouts adds additional characterization of the size and distribution of collagen fibrils/fibers relative to the interrogating wavelengths. We found strong wavelength dependent dependencies of these metrics that were different between the different tumors that are related to respective structural attributes in the collagen organization. These sub-resolution determinations are consistent with the dualistic classification of type I and II serous tumors. However, type I endometrioid tumors have strongly differing ECM architecture than the serous malignancies. Moreover, our analyses are further consistent with LGS and benign tumors having similar etiology. We identified optimal wavelengths for the SHG metrics as well as optical scattering measurements. The SHG metrics and optical scattering measurements were then used to form a linear discriminant model to classify the tissues, and we obtained high accuracy ( 90%) between the tissue types. This delineation is superior to current clinical performance and has potential applicability in supplementing histological analysis, understanding the etiology, as well as development of an in vivo screening tool.
Coupled channel folding model description of α scattering from 9Be
International Nuclear Information System (INIS)
Roy, S.; Chatterjee, J.M.; Majumdar, H.; Datta, S.K.; Banerjee, S.R.; Chintalapudi, S.N.
1995-01-01
Alpha scattering from 9 Be at E α = 65 MeV is described in the coupled channel framework with phenomenological as well as folded potentials. The multipole components of the deformed density of 9 Be are derived from Nilsson model wave functions. Reasonably good agreements are obtained for the angular distributions of 3/2 - (g.s.) and 5/2 - (2.43 MeV) states of the ground state band with folded potentials. The deformation predicted by the model corroborates with that derived from the phenomenological analysis with potentials of different geometries
Coupled channel folding model description of {alpha} scattering from {sup 9}Be
Energy Technology Data Exchange (ETDEWEB)
Roy, S.; Chatterjee, J.M.; Majumdar, H. [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700064 (India); Datta, S.K. [Nuclear Science Centre, P.O.10502, New Delhi 110067 (India); Banerjee, S.R. [Variable Energy Cyclotron Centre, 1/AF Bidhannagar, Calcutta 700064 (India); Chintalapudi, S.N. [Inter-University Consortium, Department of Atomic Energy Facilities, Bidhannagar, Calcutta 700064 (India)
1995-09-01
Alpha scattering from {sup 9}Be at {ital E}{sub {alpha}}= 65 MeV is described in the coupled channel framework with phenomenological as well as folded potentials. The multipole components of the deformed density of {sup 9}Be are derived from Nilsson model wave functions. Reasonably good agreements are obtained for the angular distributions of 3/2{sup {minus}}(g.s.) and 5/2{sup {minus}}(2.43 MeV) states of the ground state band with folded potentials. The deformation predicted by the model corroborates with that derived from the phenomenological analysis with potentials of different geometries.
A new description of high energy antiproton (proton)-proton elastic scattering
International Nuclear Information System (INIS)
Barshay, S.; Technion-Israel Inst. of Tech., Haifa. Dept. of Physics); Goldberg, J.
1987-01-01
We develop a generalization of the geometric picture for high-energy antiproton (proton)-proton elastic scattering. The eikonal at each impact parameter is considered to have fluctuations about an average value, and is thus characterized by a distribution. A connection to parton branching is made through the specific form of the distribution function for the eikonal. A unified physical theory with significant fluctuations accurately describes the anti p(p)-p data at both √s = 546 GeV and 53 GeV. The fluctuation parameter is remarkably well given by that directly observed in multiparticle production. (orig.)
New description of high energy antiproton (proton)-proton elastic scattering
Energy Technology Data Exchange (ETDEWEB)
Barshay, S; Goldberg, J
1987-10-15
We develop a generalization of the geometric picture for high-energy antiproton (proton)-proton elastic scattering. The eikonal at each impact parameter is considered to have fluctuations about an average value, and is thus characterized by a distribution. A connection to parton branching is made through the specific form of the distribution function for the eikonal. A unified physical theory with significant fluctuations accurately describes the anti p(p)-p data at both ..sqrt..s = 546 GeV and 53 GeV. The fluctuation parameter is remarkably well given by that directly observed in multiparticle production.
Matrix transformation relation for the radial integrals of lepton scattering processes
International Nuclear Information System (INIS)
Sud, K.K.; Soto Vargas, C.W.; Sharma, D.K.
1988-01-01
The radial integrals of many physical problems involving products of initial- and final-state wave functions and the Coulomb interaction are expressible in terms of special cases of generalized hypergeometric functions. In the present work, the generalized hypergeometric functions become elements of a gamma vector which, by means of a partial differential equation and a matrix transformation relation, can be used in calculating the gamma vector in physical regions where the hypergeometric functions are nonconvergent or very slowly converging. Our matrix transformation relation contains the special cases of Gauss' hypergeometric functions 2 F 1 , Appell's hypergeometric functions F 2 , and Lauricella's functions L F transformation relations. The use of contiguous relations along with the transformation relations presented in this paper will facilitate the calculation of physical processes involving such radial integrals
Fokker-Planck description of the scattering of radio frequency waves at the plasma edge
International Nuclear Information System (INIS)
Hizanidis, Kyriakos; Kominis, Yannis; Tsironis, Christos; Ram, Abhay K.
2010-01-01
In magnetic fusion devices, radio frequency (rf) waves in the electron cyclotron (EC) and lower hybrid (LH) range of frequencies are being commonly used to modify the plasma current profile. In ITER, EC waves are expected to stabilize the neoclassical tearing mode (NTM) by providing current in the island region [R. Aymar et al., Nucl. Fusion 41, 1301 (2001)]. The appearance of NTMs severely limits the plasma pressure and leads to the degradation of plasma confinement. LH waves could be used in ITER to modify the current profile closer to the edge of the plasma. These rf waves propagate from the excitation structures to the core of the plasma through an edge region, which is characterized by turbulence--in particular, density fluctuations. These fluctuations, in the form of blobs, can modify the propagation properties of the waves by refraction. In this paper, the effect on rf due to randomly distributed blobs in the edge region is studied. The waves are represented as geometric optics rays and the refractive scattering from a distribution of blobs is formulated as a Fokker-Planck equation. The scattering can have two diffusive effects--one in real space and the other in wave vector space. The scattering can modify the trajectory of rays into the plasma and it can affect the wave vector spectrum. The refraction of EC waves, for example, could make them miss the intended target region where the NTMs occur. The broadening of the wave vector spectrum could broaden the wave generated current profile. The Fokker-Planck formalism for diffusion in real space and wave vector space is used to study the effect of density blobs on EC and LH waves in an ITER type of plasma environment. For EC waves the refractive effects become important since the distance of propagation from the edge to the core in ITER is of the order of a meter. The diffusion in wave vector space is small. For LH waves the refractive effects are insignificant but the diffusion in wave vector space is
Unified description of H-atom-induced chemicurrents and inelastic scattering.
Kandratsenka, Alexander; Jiang, Hongyan; Dorenkamp, Yvonne; Janke, Svenja M; Kammler, Marvin; Wodtke, Alec M; Bünermann, Oliver
2018-01-23
The Born-Oppenheimer approximation (BOA) provides the foundation for virtually all computational studies of chemical binding and reactivity, and it is the justification for the widely used "balls and springs" picture of molecules. The BOA assumes that nuclei effectively stand still on the timescale of electronic motion, due to their large masses relative to electrons. This implies electrons never change their energy quantum state. When molecules react, atoms must move, meaning that electrons may become excited in violation of the BOA. Such electronic excitation is clearly seen for: ( i ) Schottky diodes where H adsorption at Ag surfaces produces electrical "chemicurrent;" ( ii ) Au-based metal-insulator-metal (MIM) devices, where chemicurrents arise from H-H surface recombination; and ( iii ) Inelastic energy transfer, where H collisions with Au surfaces show H-atom translation excites the metal's electrons. As part of this work, we report isotopically selective hydrogen/deuterium (H/D) translational inelasticity measurements in collisions with Ag and Au. Together, these experiments provide an opportunity to test new theories that simultaneously describe both nuclear and electronic motion, a standing challenge to the field. Here, we show results of a recently developed first-principles theory that quantitatively explains both inelastic scattering experiments that probe nuclear motion and chemicurrent experiments that probe electronic excitation. The theory explains the magnitude of chemicurrents on Ag Schottky diodes and resolves an apparent paradox--chemicurrents exhibit a much larger isotope effect than does H/D inelastic scattering. It also explains why, unlike Ag-based Schottky diodes, Au-based MIM devices are insensitive to H adsorption.
Directory of Open Access Journals (Sweden)
Li Mianquan
2016-04-01
Full Text Available The polarization feature of a fully Polarimetric Phased-Array Radar (PPAR antenna varies according to the beam-scanning angle, thereby introducing two problems on the target Polarization Scattering Matrix (PSM measurement. First, the antenna polarization basis is defined within the vertical cross-section of an electromagnetic wave propagation direction, and the polarization basis of each beam direction angle is not identical, resulting in the PSM of a fixed-posture target observed by PPAR being not identical for different beam-scanning angles. Second, the cross polarization of the PPAR antenna increases with increasing beamscanning angle, resulting in a crosstalk among the elements of PSM observed by PPAR. This study focuses on the analysis of the abovementioned two aspects of the effect of beam scanning on target PSM observed by PPAR. The results will establish a more accurate observation of the equation for the precision PSM measurement of PPAR.
A quark-parton description of the deep inelastic scattering processes
International Nuclear Information System (INIS)
Bajpai, R.P.
1977-01-01
A consistent description of various deep inelastic processes in a quark-parton model is presented. The valence quark probability distribution and the form of core quark probability distribution is fixed from the deep inelastic electroproduction data. Langacker and Suzuki prescription is used to fix the p and n quark core distribution. The differential excitation of quark currents similar to the Harari model of e + e - annihilation process is invoked in deep inelastic electroproduction and neutrino reactions. An effective phenomenological form of the weak currents associated with new quarks and the associated nucleon structure is determined. (author)
Directory of Open Access Journals (Sweden)
Haug Joachim T
2012-08-01
Full Text Available Abstract Background Leanchoilia superlata is one of the best known arthropods from the middle Cambrian Burgess Shale of British Columbia. Here we re-describe the morphology of L. superlata and discuss its possible autecology. The re-description follows a standardized scheme, the descriptive matrix approach, designed to provide a template for descriptions of other megacheiran species. Results Our findings differ in several respects from previous interpretations. Examples include a more slender body; a possible hypostome; a small specialised second appendage, bringing the number of pairs of head appendages to four; a further sub-division of the great appendage, making it more similar to that of other megacheirans; and a complex joint of the exopod reflecting the arthropod’s swimming capabilities. Conclusions Different aspects of the morphology, for example, the morphology of the great appendage and the presence of a basipod with strong median armature on the biramous appendages indicate that L. superlata was an active and agile necto-benthic predator (not a scavenger or deposit feeder as previously interpreted.
Ambiguities in the description of nucleon transfer in deep inelastic scattering
International Nuclear Information System (INIS)
Dworzecka, M.; Zielinska-Pfabe, M.; Griffin, J.J.
1986-01-01
Here the authors discuss certain ambiguities which are in the description of (N,Z) evolution in heavy ion collisions by means of nucleon exchange models. Such descriptions have been formulated either in terms of Markovian Master (MM) equations (or its approximate version in the form of Fokker-Planck equation) in terms of transition rates per unit time, or in terms of Random Walk (RW) on the energy surface in terms of transition probabilities per nucleon exchanged. In a series of papers they have shown that the RW is the useful tool in studying probability distributions of particle numbers (protons and neutrons) as a function of energy loss. The authors purpose was to compare the implications of different (often competing) physical mechanisms for specific features of the (N-Z) distribution. One result of that analysis was that not all of the kinetic energy loss could be attributed to the nucleon transfer process assumed; rather, an additional step had to be allowed in the random walk in which no nucleon is transferred, but kinetic energy is lost nonetheless. Only then could the total width, σ/sub A/ 2 , of the (N-Z) distribution (as a function of energy loss) be made to conform with the experimental data. Conversely requiring this conformance yielded a specific value of the average relative probability for this additional non-transfer step
International Nuclear Information System (INIS)
Wong, C.F.; Light, J.C.
1984-01-01
Based on the R-matrix approach of Schneider et al. [J. Phys. B 12, L 365 (1979)] to reactive electron-molecule scattering, a new propagative R-matrix method (PRMM) is presented which is more appropriate for polyatomic systems. The new method should be useful in other calculations where complicated integrals need to be propagated. We also introduce an effective R-matrix model (ERMM) in which the usual resonance parameters (potential and width) can be used as input in model R-matrix calculations. The PRMM and ERMM have been applied to the electron-N 2 system and the electron-F 2 system. The results agree very well with previous calculations for both vibrationally inelastic scattering and dissociative attachment when identical potentials and parameters are used
International Nuclear Information System (INIS)
Wolschke, U.
1986-08-01
Estelle is a formal method of description, which was developed based on an extended state transition model for the specification of communication records and services. Regardless of the field of application, there are problems common to all systems in distributed systems, i.e. in communication systems as in process computer systems, which are to be specified. These include real time problems, such as waiting for events, reactions to expected events and those occurring at the correct time, reacting to unexpected events or those not occurring at the correct time, transmitting and receiving data and the synchronisation of process going on simultaneously. This work examines, using the example of a process computer-controlled neutron scatter experiment, whether Estelle is suitable for the specification of distributed real time systems in this field of application. (orig.) [de
Phan, Quoc-Hung; Lo, Yu-Lung
2017-04-01
A surface plasmon resonance (SPR)-enhanced method is proposed for measuring the circular dichroism (CD), circular birefringence (CB), and degree of polarization (DOP) of turbid media using a Stokes–Mueller matrix polarimetry technique. The validity of the analytical model is confirmed by means of numerical simulations. The simulation results show that the proposed detection method enables the CD and CB properties to be measured with a resolution of 10 ? 4 refractive index unit (RIU) and 10 ? 5 ?? RIU , respectively, for refractive indices in the range of 1.3 to 1.4. The practical feasibility of the proposed method is demonstrated by detecting the CB/CD/DOP properties of glucose–chlorophyllin compound samples containing polystyrene microspheres. It is shown that the extracted CB value decreases linearly with the glucose concentration, while the extracted CD value increases linearly with the chlorophyllin concentration. However, the DOP is insensitive to both the glucose concentration and the chlorophyllin concentration. Consequently, the potential of the proposed SPR-enhanced Stokes–Mueller matrix polarimetry method for high-resolution CB/CD/DOP detection is confirmed. Notably, in contrast to conventional SPR techniques designed to detect relative refractive index changes, the SPR technique proposed in the present study allows absolute measurements of the optical properties (CB/CD/DOP) to be obtained.
Polarized micro-Raman scattering characterization of Mg2Si nanolayers in (001) Si matrix
International Nuclear Information System (INIS)
Zlateva, G; Atanassov, A; Baleva, M; Nikolova, L; Abrashev, M V
2007-01-01
An orientational growth of the Mg 2 Si lattice relative to the Si lattice is considered assuming minimum mismatch of their lattice parameters. The Raman scattering cross-sections are calculated for the four possible orientations of the Mg 2 Si lattice positioned in this way. The integral intensity ratios for the F 2g mode of Mg 2 Si in different polarization configurations, obtained from the experimental spectra, are compared with the calculated ratios. It is found that the Mg 2 Si nanolayer's morphology is sensitive to the implantation energy, which determines both the peak Mg concentration in the initial implantation profile and its position in the sample depth. At a peak concentration of the order of the stoichiometric concentration, the layers are highly oriented. When the peak concentration is higher and the peak is placed closer to the surface, the layers are polycrystalline
International Nuclear Information System (INIS)
Bando, H.; Krenciglowa, E.M.
1976-01-01
The role of 2p1h correlations in 17 O is studied within a multiple-scattering formalism. An accurate, energy-dependent reaction matrix with orthogonalized plane-wave intermediate states is used to assess the relative importance of particle-particle and particle-hole correlations in the 17 O energies. The effect of energy dependence of the reaction matrix is closely examined. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Chen, Lin; Qiu, Shunli; Liu, Pinyang; Xiong, Feifei; Lu, Jianjie; Liu, Yuefeng; Li, Guopeng; Liu, Yiran; Ren, Fei; Xiao, Yunqing; Gao, Lei; Zhao, Qiushuang; Ding, Bin; Li, Yuan [School of Nuclear Science and Technology, Lanzhou University, 730000 (China); Key Laboratory of Special Function Materials and Structure Design, Ministry of Education, Lanzhou University, 730000 (China); Guo, Yanling, E-mail: guoyanling@lzu.edu.cn [School of Nuclear Science and Technology, Lanzhou University, 730000 (China); Key Laboratory of Special Function Materials and Structure Design, Ministry of Education, Lanzhou University, 730000 (China); Chen, Ximeng, E-mail: chenxm@lzu.edu.cn [School of Nuclear Science and Technology, Lanzhou University, 730000 (China); Key Laboratory of Special Function Materials and Structure Design, Ministry of Education, Lanzhou University, 730000 (China)
2016-11-30
Highlights: • We first observe that negative-ion fractions present no variation with the doping concentration, which is very different from the results of low energy Li neutralization from doped Si samples. • Our work shows that the affinity levels and collision time significantly counteract the band gap effect on negative ion formation. The work will improve our understanding on electron transfer on semiconductor surfaces associated with doping. • In addition, we build a complete theoretical framework to quantitatively calculate the negative-ion fractions. • Our work is related to charge transfer on semiconductor surfaces, which will be of interest to a broad audience due to the wide necessity of the knowledge of charge exchange on semiconductor surfaces in different fields. - Abstract: Doping has significantly affected the characteristics and performance of semiconductor electronic devices. In this work, we study the charge transfer processes for 8.5–22.5 keV C{sup −} and F{sup −} ions scattering on H{sub 2}O-terminated p-type Si(100) surfaces with two different doping concentrations. We find that doping has no influence on negative-ion formation for fast collisions in this relatively high energy range. Moreover, we build a model to calculate negative ion fractions including the contribution from positive ions. The calculations support the nonadiabatic feature of charge transfer.
Energy Technology Data Exchange (ETDEWEB)
Rinkel, J.; Dinten, J.M.; Tabary, J
2004-07-01
The use of focused anti-scatter grids on digital radiographic systems with two-dimensional detectors produces acquisitions with a decreased scatter to primary ratio and thus improved contrast and resolution. Simulation software is of great interest in optimizing grid configuration according to a specific application. Classical simulators are based on complete detailed geometric descriptions of the grid. They are accurate but very time consuming since they use Monte Carlo code to simulate scatter within the high-frequency grids. We propose a new practical method which couples an analytical simulation of the grid interaction with a radiographic system simulation program. First, a two dimensional matrix of probability depending on the grid is created offline, in which the first dimension represents the angle of impact with respect to the normal to the grid lines and the other the energy of the photon. This matrix of probability is then used by the Monte Carlo simulation software in order to provide the final scattered flux image. To evaluate the gain of CPU time, we define the increasing factor as the increase of CPU time of the simulation with as opposed to without the grid. Increasing factors were calculated with the new model and with classical methods representing the grid with its CAD model as part of the object. With the new method, increasing factors are shorter by one to two orders of magnitude compared with the second one. These results were obtained with a difference in calculated scatter of less than five percent between the new and the classical method. (authors)
Quantum Optical Multiple Scattering
DEFF Research Database (Denmark)
Ott, Johan Raunkjær
. In the first part we use a scattering-matrix formalism combined with results from random-matrix theory to investigate the interference of quantum optical states on a multiple scattering medium. We investigate a single realization of a scattering medium thereby showing that it is possible to create entangled...... states by interference of squeezed beams. Mixing photon states on the single realization also shows that quantum interference naturally arises by interfering quantum states. We further investigate the ensemble averaged transmission properties of the quantized light and see that the induced quantum...... interference survives even after disorder averaging. The quantum interference manifests itself through increased photon correlations. Furthermore, the theoretical description of a measurement procedure is presented. In this work we relate the noise power spectrum of the total transmitted or reflected light...
Sun, B.; Yang, P.; Kattawar, G. W.; Zhang, X.
2017-12-01
The ice cloud single-scattering properties can be accurately simulated using the invariant-imbedding T-matrix method (IITM) and the physical-geometric optics method (PGOM). The IITM has been parallelized using the Message Passing Interface (MPI) method to remove the memory limitation so that the IITM can be used to obtain the single-scattering properties of ice clouds for sizes in the geometric optics regime. Furthermore, the results associated with random orientations can be analytically achieved once the T-matrix is given. The PGOM is also parallelized in conjunction with random orientations. The single-scattering properties of a hexagonal prism with height 400 (in units of lambda/2*pi, where lambda is the incident wavelength) and an aspect ratio of 1 (defined as the height over two times of bottom side length) are given by using the parallelized IITM and compared to the counterparts using the parallelized PGOM. The two results are in close agreement. Furthermore, the integrated single-scattering properties, including the asymmetry factor, the extinction cross-section, and the scattering cross-section, are given in a completed size range. The present results show a smooth transition from the exact IITM solution to the approximate PGOM result. Because the calculation of the IITM method has reached the geometric regime, the IITM and the PGOM can be efficiently employed to accurately compute the single-scattering properties of ice cloud in a wide spectral range.
International Nuclear Information System (INIS)
Queen, N.M.
1978-01-01
This series of lectures on basic scattering theory were given as part of a course for postgraduate high energy physicists and were designed to acquaint the student with some of the basic language and formalism used for the phenomenological description of nuclear reactions and decay processes used for the study of elementary particle interactions. Well established and model independent aspects of scattering theory, which are the basis of S-matrix theory, are considered. The subject is considered under the following headings; the S-matrix, cross sections and decay rates, phase space, relativistic kinematics, the Mandelstam variables, the flux factor, two-body phase space, Dalitz plots, other kinematic plots, two-particle reactions, unitarity, the partial-wave expansion, resonances (single-channel case), multi-channel resonances, analyticity and crossing, dispersion relations, the one-particle exchange model, the density matrix, mathematical properties of the density matrix, the density matrix in scattering processes, the density matrix in decay processes, and the helicity formalism. Some exercises for the students are included. (U.K.)
Energy Technology Data Exchange (ETDEWEB)
Zhuo, Ye [Iowa State Univ., Ames, IA (United States)
2011-01-01
In this thesis, we theoretically study the electromagnetic wave propagation in several passive and active optical components and devices including 2-D photonic crystals, straight and curved waveguides, organic light emitting diodes (OLEDs), and etc. Several optical designs are also presented like organic photovoltaic (OPV) cells and solar concentrators. The first part of the thesis focuses on theoretical investigation. First, the plane-wave-based transfer (scattering) matrix method (TMM) is briefly described with a short review of photonic crystals and other numerical methods to study them (Chapter 1 and 2). Next TMM, the numerical method itself is investigated in details and developed in advance to deal with more complex optical systems. In chapter 3, TMM is extended in curvilinear coordinates to study curved nanoribbon waveguides. The problem of a curved structure is transformed into an equivalent one of a straight structure with spatially dependent tensors of dielectric constant and magnetic permeability. In chapter 4, a new set of localized basis orbitals are introduced to locally represent electromagnetic field in photonic crystals as alternative to planewave basis. The second part of the thesis focuses on the design of optical devices. First, two examples of TMM applications are given. The first example is the design of metal grating structures as replacements of ITO to enhance the optical absorption in OPV cells (chapter 6). The second one is the design of the same structure as above to enhance the light extraction of OLEDs (chapter 7). Next, two design examples by ray tracing method are given, including applying a microlens array to enhance the light extraction of OLEDs (chapter 5) and an all-angle wide-wavelength design of solar concentrator (chapter 8). In summary, this dissertation has extended TMM which makes it capable of treating complex optical systems. Several optical designs by TMM and ray tracing method are also given as a full complement of this
Energy Technology Data Exchange (ETDEWEB)
Behring, A.; Bluemlein, J.; Freitas, A. de [Deutsches Elektronen Synchrotron, DESY, Zeuthen (Germany); Bierenbaum, I. [Universitaet Hamburg, II. Institut fuer Theoretische Physik, Hamburg (Germany); Klein, S. [RWTH Aachen University, Institut fuer Theoretische Teilchenphysik und Kosmologie, Aachen (Germany); Wissbrock, F. [Deutsches Elektronen Synchrotron, DESY, Zeuthen (Germany); Johannes Kepler University, Research Institute for Symbolic Computation (RISC), Linz (Austria); IHES, Bures-sur-Yvette (France)
2014-09-15
We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region Q{sup 2} >> m{sup 2} to 3-loop order in the fixed flavor number scheme and present the corresponding expressions for the massive operator matrix elements needed in the variable flavor number scheme. Explicit expressions are given in Mellin N-space. (orig.)
International Nuclear Information System (INIS)
Kuznichenko, A.V.; Onishchenko, G.M.; Pilipenko, V.V.; Dem'yanova, A.S.; Burtebaev, N.
2003-01-01
The analysis of the cross sections of the 16 O + 16 O nuclei elastic scattering by the energy of 124, 145, 250, 350, 480, 704 and 1120 MeV is carried out on the basis of the phenomenological S-matrix model. It is shown, that by high energy the refraction behavior of the opalescent-type cross sections is well described by the simple smooth dependence of the S-matrix on the angular moment and by the energy E ≤ 480 MeV the opalescent-type structures are strongly effected by the Regge poles and S-matrix zeroes, close to the actual axis. The comparison with the results of the cross sections by the optical model is carried out [ru
Hyperon beta decay and the CKM matrix
International Nuclear Information System (INIS)
Ratcliffe, P.G.
2004-01-01
I shall present a pedagogical discussion of hyperon semileptonic decays, covering some of the historical background, the basics notions of hyperon semileptonic decays, deeply inelastic scattering and the CKM matrix, and the description of SU(2) and SU(3) breaking. I shall also present a prediction for a process under current experimental study. (author)
On the microscopic foundation of scattering theory
International Nuclear Information System (INIS)
Moser, T.
2007-01-01
The aim of the thesis is to give a contribution to the microscopic foundation of scattering theory, i. e. to show, how the asymptotic formalism of scattering theory with objects like the S-matrix as well the initial and final asymptotics ψ in and ψ out can be derived from a microscopic description of the basic system. First the final statistics from a N-particle system through farly distant surfaces is derived. Thereafter we confine us to the 1-particle scattering and apply the final statistics in order to derive the scattering cross section from a microscopical description of the scattering situation. The basing dynamics are Bohm's mechanics, a theory on the motion of point particles, which reproduces all results of nonrelativistic quantum mechanics
Prinari, Barbara; Demontis, Francesco; Li, Sitai; Horikis, Theodoros P.
2018-04-01
The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrödinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.
Energy Technology Data Exchange (ETDEWEB)
Costescu, A [Department of Physics, University of Bucharest, MG11, Bucharest-Magurele 76900 (Romania); Spanulescu, S [Department of Physics, University of Bucharest, MG11, Bucharest-Magurele 76900 (Romania); Stoica, C [Department of Physics, University of Bucharest, MG11, Bucharest-Magurele 76900 (Romania)
2007-08-14
The right expressions of the nonrelativistic K-shell Rayleigh scattering amplitudes and cross-sections are obtained by using the Coulomb Green's function method. Our analytical result does not have the spurious poles that occur in the old nonrelativistic result with retardation (Gavrila and Costescu 1970 Phys. Rev. A 2 1752). Starting from the expression of the second-order S-matrix element for the case of the elastic scattering of photons by K-shell bound electrons, we obtain the correct nonrelativistic Rayleigh angular distribution (valid for photon energies {omega} up to {alpha}Zm) by removing the relativistic higher order terms in {alpha}Z and {omega}/m. The imaginary part of the Rayleigh amplitudes is obtained for any scattering angles in a closed form in terms of elementary functions. Thereby a simple formula for the exact nonrelativistic photoeffect total cross-section is obtained via the optical theorem, giving significantly better predictions than Fischer's nonrelativistic photoeffect formula. Comparing the predictions given by our formulae with the full relativistic numerical calculations of Kissel et al (Phys. Rev. 1980 A 22 1970), and with experimental results, a fairly good agreement within 10% is found for the angular distribution of Rayleigh scattering for photon energies up to 200 keV and both below and above the first resonance.
Directory of Open Access Journals (Sweden)
Fabian Zeitvogel
2016-02-01
Full Text Available We present ScatterJn, an ImageJ (and Fiji plugin for scatterplot-based exploration and analysis of analytical microscopy data. In contrast to commonly used scatterplot tools, it handles more than two input images (or image stacks, respectively by creating a matrix of pairwise scatterplots. The tool offers the possibility to manually classify pixels by selecting regions of datapoints in the scatterplots as well as in the spatial domain. We demonstrate its functioning using a set of elemental maps acquired by SEM-EDX mapping of a soil sample. The plugin is available at https://savannah.nongnu.org/projects/scatterjn.
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.
Martinek, Tomas; Duboué-Dijon, Elise; Timr, Štěpán; Mason, Philip E.; Baxová, Katarina; Fischer, Henry E.; Schmidt, Burkhard; Pluhařová, Eva; Jungwirth, Pavel
2018-06-01
We present a combination of force field and ab initio molecular dynamics simulations together with neutron scattering experiments with isotopic substitution that aim at characterizing ion hydration and pairing in aqueous calcium chloride and formate/acetate solutions. Benchmarking against neutron scattering data on concentrated solutions together with ion pairing free energy profiles from ab initio molecular dynamics allows us to develop an accurate calcium force field which accounts in a mean-field way for electronic polarization effects via charge rescaling. This refined calcium parameterization is directly usable for standard molecular dynamics simulations of processes involving this key biological signaling ion.
International Nuclear Information System (INIS)
Das, Avik; Mazumder, S.; Sen, D.; Yalmali, V.; Shah, J.G.
2014-01-01
Nuclear power plants generate many kinds of hazardous nuclear waste which are needed to be disposed in an eco-friendly manner. Many different waste incarceration techniques have been adapted for managing the nuclear waste of different category of radioactivity. Immobilisation of low and intermediate level radioactive wastes in cement matrix is one of the widely used and cost-effective techniques in waste management. However, loading of nuclear waste in cement matrix can alter the mesoscopic structure of the hydrated cement and hence, it is very important to set the maximum limit of waste loading in cement for providing proper physical isolation to the nuclear waste
International Nuclear Information System (INIS)
Hoffmann, T H; Ruf, M-W; Hotop, H; Zatsarinny, O; Bartschat, K; Allan, M
2010-01-01
In a joint experimental and theoretical effort, we carried out a detailed study of electron scattering from Kr atoms in the energy range of the low-lying Kr - (4p 5 5s 2 ) Feshbach resonances. Absolute angle-differential cross sections for elastic electron scattering were measured over the energy range 9.3-10.3 eV with an energy width of about 13 meV at scattering angles between 10 deg. and 180 deg. Using several sets of elastic scattering phase shifts, a detailed analysis of the sharp Kr - (4p 5 5s 2 2 P 3/2 ) resonance was carried out, resulting in a resonance width of Γ 3/2 3.6(2) meV. By direct comparison with the position of the Ar - (3p 5 4s 2 2 P 3/2 ) resonance, the energy for the Kr - (4p 5 5s 2 2 P 3/2 ) resonance was determined as E 3/2 = 9.489(3) eV. A Fano-type fit of the higher lying Kr - (4p 5 5s 2 2 P 1/2 ) resonance yielded the resonance parameters Γ 1/2 = 33(5) meV and E 1/2 = 10.126(4) eV. In order to obtain additional insights, B-spline R-matrix calculations were performed for both the elastic and the inelastic cross sections above the threshold for 4p 5 5s excitation. They provide the total and angle-differential cross sections for excitation of long-lived and short-lived levels of the 4p 5 5s configuration in Kr and branching ratios for the decay of the Kr - (4p 5 5s 2 2 P 1/2 ) resonance into the three available exit channels. The results are compared with selected experimental data.
Energy Technology Data Exchange (ETDEWEB)
Castro, A., E-mail: acastro@bifi.es [Institute for Biocomputation and Physics of Complex Systems (BIFI) and Zaragoza Scientific Center for Advanced Modelling (ZCAM), University of Zaragoza, 50018 Zaragoza (Spain); Isla, M. [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47005 Valladolid (Spain); Martinez, Jose I. [Departamento de Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid, ES-28049 Madrid (Spain); Alonso, J.A. [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47005 Valladolid (Spain)
2012-05-03
Graphical abstract: Two trajectories for the collision of a proton with the Lithium tetramer. On the left, the proton is scattered away, and a Li{sub 2} molecule plus two isolated Lithium atoms result. On the right, the proton is captured and a LiH molecule is created. Highlights: Black-Right-Pointing-Pointer Scattering of a proton with Lithium clusters described from first principles. Black-Right-Pointing-Pointer Description based on non-adiabatic molecular dynamics. Black-Right-Pointing-Pointer The electronic structure is described with time-dependent density-functional theory. Black-Right-Pointing-Pointer The method allows to discern reaction channels depending on initial parameters. - Abstract: We have employed non-adiabatic molecular dynamics based on time-dependent density-functional theory to characterize the scattering behavior of a proton with the Li{sub 4} cluster. This technique assumes a classical approximation for the nuclei, effectively coupled to the quantum electronic system. This time-dependent theoretical framework accounts, by construction, for possible charge transfer and ionization processes, as well as electronic excitations, which may play a role in the non-adiabatic regime. We have varied the incidence angles in order to analyze the possible reaction patterns. The initial proton kinetic energy of 10 eV is sufficiently high to induce non-adiabatic effects. For all the incidence angles considered the proton is scattered away, except in one interesting case in which one of the Lithium atoms captures it, forming a LiH molecule. This theoretical formalism proves to be a powerful, effective and predictive tool for the analysis of non-adiabatic processes at the nanoscale.
International Nuclear Information System (INIS)
Resler, D.A.
1987-03-01
The specific purpose of this work is to provide a better understanding of the 14 C level structure; the general purpose is to provide the details for using shell model calculations in R-matrix analyses. Using the TOF facilities of the Ohio University Accelerator Laboratory, the elastic and first 3 inelastic differential scattering cross sections for 13 C + n were measured at 69 energies for 4.5 ≤ E/sub n/ ≤ 11 MeV. A multiple scattering code was developed which provided a simulation of the experimental scattering process allowing accurate corrections to the small inelastic data. The integrated 13 C(n,α) 10 Be cross section is estimated. The sequential 2n-decay of 14 C states populated by 13 C + n was observed. A shell model code was developed. Normal and nonnormal parity calculations were made for the lithium isotopes using a new two-body interaction. The results for 5 Li predict the 2s/sub 1/2/ and 1d/sub 5/2/ single-particle states to be located below the 3/2 + state. Similar calculations were made for 13 C, 13 N, and 14 C. Results for 13 C and 13 N show for E/sub x/ 7 Li and 14 C, 2 h-barω calculations were done. Shell model calculations generated the R-matrix parameters for the elastic and first 3 inelastic channels of 13 C + n. After adjusting some energies, the predicted structure generally agrees with experiment for E/sub n/ 13 C + n data were refit to replace R 0 background terms by more realistic broad states and to get better agreement with model calculations. R-matrix fitting of the full data set produced new 14 C level information. For E/sub n/ > 4 MeV (E/sub x/ > 12 MeV), 5 states are given definite J/sup π/ assignments; 3, tentative assignments. 122 refs., 91 figs., 30 tabs
Energy Technology Data Exchange (ETDEWEB)
Pensky, H.M.H.
2000-07-01
For realistic numerical simulations of the stress-strain behaviour of structures, models are necessary which describe elastic-inelastic and scattering material behaviour. The developed models simulate elastic, viscoplastic and anisotropic damage material phenomena. An approach is proposed for covering stochastic material beahviour by correspondingly distributed parameters of the deterministic material model. Numerical simulations of biaxial material tests and structural tests demonstrate the range of applicability. (orig.) [German] Die realitaetsnahe numerische Simulation des Spannungs-Verformungsverhaltens von Bauteilen erfordert Modelle zur Beschreibung inelastischen und streuenden Materialverhaltens. Die hier entwickelten Modelle beschreiben elastische, viskoplastische und anisotrope Schaedigungsphaenomene des Materialverhaltens. Desweiteren wird ein Konzept vorgestellt, mit dem streuendes Materialverhalten mit streuenden Materialparametersaetzen deterministischer Stoffmodelle beschreibbar ist. Numerische Simulationen von Werkstoff- und Bauteilversuchen veranschaulichen den Anwendungsbereich der Modelle. (orig.)
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.
International Nuclear Information System (INIS)
Maekawa, T.; Tanaka, H.; Uchida, M.; Igami, H.
2003-01-01
General properties of scattering matrix, which governs the mode conversion process between electron Bernstein (B) waves and external electromagnetic (EM) waves in the presence of steep density gradient, are theoretically analyzed. Based on the analysis, polarization adjustment of incident EM waves for optimal mode conversion to B waves is possible and effective for a range of density gradient near the upper hybrid resonance, which are not covered by the previously proposed schemes of perpendicular injection of X mode and oblique injection of O mode. Furthermore, the analysis shows that the polarization of the externally emitted EM waves from B waves is uniquely related to the optimized polarization of incident EM waves for B wave heating and that the mode conversion rate is the same for the both processes of emission and the injection with the optimized polarization
International Nuclear Information System (INIS)
Tyynelae, Jani; Nousiainen, Timo; Goeke, Sabine; Muinonen, Karri
2009-01-01
We study the applicability of the discrete-dipole approximation by modeling centimeter (C-band) radar echoes for hydrometeors, and compare the results to exact theories. We use ice and water particles of various shapes with varying water-content to investigate how the backscattering, extinction, and absorption cross sections change as a function of particle radius. We also compute radar parameters, such as the differential reflectivity, the linear depolarization ratio, and the copolarized correlation coefficient. We find that using discrete-dipole approximation (DDA) to model pure ice and pure water particles at the C-band, is a lot more accurate than particles containing both ice and water. For coated particles, a large grid-size is recommended so that the coating is modeled adequately. We also find that the absorption cross section is significantly less accurate than the scattering and backscattering cross sections. The accuracy of DDA can be increased by increasing the number of dipoles, but also by using the filtered coupled dipole-option for the polarizability. This halved the relative errors in cross sections.
P-matrix approach and three-nucleon problem
International Nuclear Information System (INIS)
Babenko, V.A.; Petrov, N.M.; Teneva, G.N.
1993-01-01
The paper deals with the P-matrix approach application to the three strongly interacting particles systems description. On the basis of the obtained off-energy-shell scattering amplitude separable expansion in the P-matrix approach the low-energy three-particle quantities were calculated in the case of square-well potential. The results of calculations show good convergence of the calculated three-particle quantities. (author). 12 refs., 1 tab
A Modal Description of Multiport Antennas
Directory of Open Access Journals (Sweden)
Jonathan J. Lynch
2011-01-01
Full Text Available This paper presents a modal description of multiport antennas that leads directly to a rigorous network representation and simple quadratic expressions for gain, efficiency, and effective area. The analysis shows that the transmitting and receiving properties of an element antenna array are exactly described by a 2×2 element scattering matrix together with a set of orthonormal mode functions and accounts for effects such as mutual coupling, scattering, reflection, and losses. The approach is quite general, only requiring that the antenna be finite and reciprocal. The scattering network description simplifies accounting of power flow while retaining a close connection to the physical antenna characteristics. The orthonormal mode functions provide a complete basis for radiated and received fields, facilitating beamforming. The theory provides rigorous definitions of input-output signals and links them to the underlying electromagnetics in a straightforward manner.
Li, Ming
In this dissertation, a set of numerical simulation tools are developed under previous work to efficiently and accurately study one-dimensional (1D), two-dimensional (2D), 2D slab and three-dimensional (3D) photonic crystal structures and their defects effects by means of spectrum (transmission, reflection, absorption), band structure (dispersion relation), and electric and/or magnetic fields distribution (mode profiles). Further more, the lasing property and spontaneous emission behaviors are studied when active gain materials are presented in the photonic crystal structures. First, the planewave based transfer (scattering) matrix method (TMM) is described in every detail along with a brief review of photonic crystal history (Chapter 1 and 2). As a frequency domain method, TMM has the following major advantages over other numerical methods: (1) the planewave basis makes Maxwell's Equations a linear algebra problem and there are mature numerical package to solve linear algebra problem such as Lapack and Scalapack (for parallel computation). (2) Transfer (scattering) matrix method make 3D problem into 2D slices and link all slices together via the scattering matrix (S matrix) which reduces computation time and memory usage dramatically and makes 3D real photonic crystal devices design possible; and this also makes the simulated domain no length limitation along the propagation direction (ideal for waveguide simulation). (3) It is a frequency domain method and calculation results are all for steady state, without the influences of finite time span convolution effects and/or transient effects. (4) TMM can treat dispersive material (such as metal at visible light) naturally without introducing any additional computation; and meanwhile TMM can also deal with anisotropic material and magnetic material (such as perfectly matched layer) naturally from its algorithms. (5) Extension of TMM to deal with active gain material can be done through an iteration procedure with gain
DEFF Research Database (Denmark)
Wagner, Stephan; Legros, Samuel; Löschner, Katrin
2015-01-01
content by asymmetric flow-field flow fractionation coupled to a multi-angle light scattering detector and an inductively coupled plasma mass spectrometer. Following the proposed generic procedure SiO2-ENPs were separated from a tomato soup. Two potential sample preparation methods were tested these being...... quality criteria for method development is urgently needed for standardized and systematic development of procedures for separation of ENPs from a complex matrix. The chosen analytical technique was shown to be suitable for detecting SiO2-ENPs in a complex food matrix like tomato soup and may therefore...
International Nuclear Information System (INIS)
Nagadi, M.M.; Howell, C.R.; Tornow, W.; Weisel, G.J.; Al-Ohali, M.A.; Braun, R.T.; Setze, H.R.; Chen Zemin; Walter, R.L.; Delaroche, J.P.; Romain, P.
2003-01-01
Differential cross sections σ(θ) and analyzing powers A y (θ) have been measured for neutron scattering from 27 Al and 59 Co at 15 MeV at the Triangle Universities Nuclear Laboratory using standard time-of-flight techniques. In addition, σ(θ) was measured for 59 Co at 10, 12, 14, 17, and 19 MeV . Two large databases covering the energy range from 0.1 to 80 MeV were formed for these nuclei from this new data and previously published data, including that for the total cross section σ T . These sets of data were analyzed using spherical dispersive optical-model (DOM) potentials, as well as coupled-channels model (CCM) potentials. The 59 Co DOM gives good agreement with the σ(θ) data, except in the region of the first minimum. It also gives a reasonable description of our A y (θ) measurement. The 27 Al DOM gives good agreement with the data, except for σ(θ) at backward angles below 9.4 MeV and for σ T , for which there is up to 5% disagreement in the 10-50 MeV range. Compared to the DOM, the 59 Co CCM calculations give improved agreement with the σ(θ) data, especially at the first minimum. The σ T calculations agree with the data to within about 3% above 1.0 MeV . The three-level CCM calculations for 27 Al give excellent agreement with the entire database
DISCUS, Neutron Single to Double Scattering Ratio in Inelastic Scattering Experiment by Monte-Carlo
International Nuclear Information System (INIS)
Johnson, M.W.
1993-01-01
1 - Description of problem or function: DISCUS calculates the ratio of once-scattered to twice-scattered neutrons detected in an inelastic neutron scattering experiment. DISCUS also calculates the flux of once-scattered neutrons that would have been observed if there were no absorption in the sample and if, once scattered, the neutron would emerge without further re-scattering or absorption. Three types of sample geometry are used: an infinite flat plate, a finite flat plate or a finite length cylinder. (The infinite flat plate is included for comparison with other multiple scattering programs.) The program may be used for any sample for which the scattering law is of the form S(/Q/, omega). 2 - Method of solution: Monte Carlo with importance sampling is used. Neutrons are 'forced' both into useful angular trajectories, and useful energy bins. Biasing of the collision point according to the point of entry of the neutron into the sample is also utilised. The first and second order scattered neutron fluxes are calculated in independent histories. For twice-scattered neutron histories a square distribution in Q-omega space is used to sample the neutron coming from the first scattering event, whilst biasing is used for the second scattering event. (A square distribution is used so as to obtain reasonable inelastic-inelastic statistics.) 3 - Restrictions on the complexity of the problem: Unlimited number of detectors. Max. size of (Q, omega) matrix is 39*149. Max. number of points in momentum space for the scattering cross section is 199
International Nuclear Information System (INIS)
Eriksson, Karl-Erik
2009-01-01
The measurement process of quantum mechanics is analysed in the scattering theory of quantum field theory. A matrix of bilinear forms of the scattering amplitudes (the R-matrix) is used as the basic descriptive tool. The measurement process is viewed as a final-state interaction described through a series of linear stochastic mappings of the R-matrix, not changing the observable to be measured. The unknown details of the measurement apparatus enter through the stochasticity of the mappings. Although linear in terms of the R-matrix, the mappings are nonlinear in the density matrix, which is obtainable from the R-matrix through normalization. The eigenstates of the observable are the attractors of the mapping process. This result, known from previous generalizations of quantum mechanics, is obtained here within linear quantum mechanics. The conclusion is that the measurement process can be understood within relativistic quantum field theory itself without any generalization or metatheory.
Giddings, Steven B
2010-01-01
We investigate the hypothesized existence of an S-matrix for gravity, and some of its expected general properties. We first discuss basic questions regarding existence of such a matrix, including those of infrared divergences and description of asymptotic states. Distinct scattering behavior occurs in the Born, eikonal, and strong gravity regimes, and we describe aspects of both the partial wave and momentum space amplitudes, and their analytic properties, from these regimes. Classically the strong gravity region would be dominated by formation of black holes, and we assume its unitary quantum dynamics is described by corresponding resonances. Masslessness limits some powerful methods and results that apply to massive theories, though a continuation path implying crossing symmetry plausibly still exists. Physical properties of gravity suggest nonpolynomial amplitudes, although crossing and causality constrain (with modest assumptions) this nonpolynomial behavior, particularly requiring a polynomial bound in c...
Matrix model and time-like linear dila ton matter
International Nuclear Information System (INIS)
Takayanagi, Tadashi
2004-01-01
We consider a matrix model description of the 2d string theory whose matter part is given by a time-like linear dilaton CFT. This is equivalent to the c=1 matrix model with a deformed, but very simple Fermi surface. Indeed, after a Lorentz transformation, the corresponding 2d spacetime is a conventional linear dila ton background with a time-dependent tachyon field. We show that the tree level scattering amplitudes in the matrix model perfectly agree with those computed in the world-sheet theory. The classical trajectories of fermions correspond to the decaying D-boranes in the time-like linear dilaton CFT. We also discuss the ground ring structure. Furthermore, we study the properties of the time-like Liouville theory by applying this matrix model description. We find that its ground ring structure is very similar to that of the minimal string. (author)
Chemical shift of neutron resonances and some ideas on neutron resonances and scattering theory
International Nuclear Information System (INIS)
Ignatovich, V.K.; )
2002-01-01
The dependence of positions of neutron resonances in nuclei in condensed matter on chemical environment is considered. A possibility of theoretical description of neutron resonances, different from R-matrix theory is investigated. Some contradictions of standard scattering theory are discussed and a new approach without these contradictions is formulated [ru
Germer, Thomas A
2017-11-20
We measured the Mueller matrix bidirectional reflectance distribution function (BRDF) of a sintered polytetrafluoroethylene (PTFE) sample over the scattering hemisphere for six incident angles (0°-75° in 15° steps) and for four wavelengths (351 nm, 532 nm, 633 nm, and 1064 nm). The data for each wavelength were fit to a phenomenological description for the Mueller matrix BRDF, which is an extension of the bidirectional surface scattering modes developed by Koenderink and van Doorn [J. Opt. Soc. Am. A.15, 2903 (1998)JOAOD60740-323210.1364/JOSAA.15.002903] for unpolarized BRDF. This description is designed to be complete, to obey the appropriate reciprocity conditions, and to provide a full description of the Mueller matrix BRDF as a function of incident and scattering directions for each wavelength. The description was further extended by linearizing the surface scattering mode coefficients with wavelength. This data set and its parameterization provides a comprehensive on-demand description of the reflectance properties for this commonly used diffuse reflectance reference material over a wide range of wavelengths.
On the microscopic foundation of scattering theory; Zur mikroskopischen Begruendung der Streutheorie
Energy Technology Data Exchange (ETDEWEB)
Moser, T.
2007-02-26
The aim of the thesis is to give a contribution to the microscopic foundation of scattering theory, i. e. to show, how the asymptotic formalism of scattering theory with objects like the S-matrix as well the initial and final asymptotics {psi}{sub in} and {psi}{sub out} can be derived from a microscopic description of the basic system. First the final statistics from a N-particle system through farly distant surfaces is derived. Thereafter we confine us to the 1-particle scattering and apply the final statistics in order to derive the scattering cross section from a microscopical description of the scattering situation. The basing dynamics are Bohm's mechanics, a theory on the motion of point particles, which reproduces all results of nonrelativistic quantum mechanics.
Strong factor in the SO(2,3) S matrix
International Nuclear Information System (INIS)
Amado, R.D.; Sparrow, D.A.
1986-01-01
The group theoretic S matrix of Alhassid, Iachello, and Wu is factorable into a product of Coulomb and strong factors. The strong factor is examined with a view to relating it to more fa- miliar potential and phase shift descriptions. We find simple approximate expressions for the phase shifts which are very accurate for heavy-ion-type applications. For peripheral scattering it is possible to obtain simple expressions relating the strong factor to an effective potential
International Nuclear Information System (INIS)
Efimov, G.V.; Ivanov, M.A.; Rusetskij, A.G.
1989-01-01
The S-wave πN-scattering lengths and the (pπ - )-atom lifetime are in the quark confinement model. Nucleon is treated as a quark-diquark system. The fulfillment of the Weinberg-Tomozawa relations is checked. The agreement is achieved with the experiment and with the results obtained within other approaches. 32 refs.; 5 figs.; 2 tabs
Complex Masses in the S-Matrix
International Nuclear Information System (INIS)
Rupp, G.; Coito, S.; Beveren, E. van
2010-01-01
Most excited hadrons have multiparticle strong decay modes, which can often be described as resulting from intermediate states containing one or two resonances. In a theoretical approach, such a description in terms of quasi-two-particle initial and final states leads to unitarity violations, because of the complex masses of the involved resonances. In the present paper, an empirical algebraic procedure is presented to restore unitarity of the S-matrix while preserving its symmetry. Preliminary results are presented in a first application to S-wave ππ scattering, in the framework of the Resonance-Spectrum Expansion. (author)
S-matrix analysis of the baryon electric charge correlation
Lo, Pok Man; Friman, Bengt; Redlich, Krzysztof; Sasaki, Chihiro
2018-03-01
We compute the correlation of the net baryon number with the electric charge (χBQ) for an interacting hadron gas using the S-matrix formulation of statistical mechanics. The observable χBQ is particularly sensitive to the details of the pion-nucleon interaction, which are consistently incorporated in the current scheme via the empirical scattering phase shifts. Comparing to the recent lattice QCD studies in the (2 + 1)-flavor system, we find that the natural implementation of interactions and the proper treatment of resonances in the S-matrix approach lead to an improved description of the lattice data over that obtained in the hadron resonance gas model.
The genus Aeromonas is one of several medically significant genera that have gained prominence due to their evolving taxonomy and controversial role in human diseases. In this study, matrix-assisted laser desorption/ionization-mass spectrometry (MALDI-MS) was used to analyze the...
Electron-translation effects in heavy-ion scattering
International Nuclear Information System (INIS)
Heinz, U.; Greiner, W.; Mueller, B.
1981-01-01
The origin and importance of electron-translation effects within a molecular description of electronic excitations in heavy-ion collisions is investigated. First, a fully consistent quantum-mechanical description of the scattering process is developed; the electrons are described by relativistic molecular orbitals, while the nuclear motion is approximated nonrelativistically. Leaving the quantum-mechanical level by using the semiclassical approximation for the nuclear motion, a set of coupled differential equations for the occupation amplitudes of the molecular orbitals is derived. In these coupled-channel equations the spurious asymptotic dynamical couplings are corrected for by additional matrix elements stemming from the electron translation. Hence, a molecular description of electronic excitations in heavy-ion scattering has been achieved, which is free from the spurious asymptotic couplings of the conventional perturbated stationary-state approach. The importance of electron-translation effects for continuum electrons and positrons is investigated. To this end an algorithm for the description of continuum electrons is proposed, which for the first time should allow for the calculation of angular distributions for delta electrons. Finally, the practical consequences of electron-translation effects are studied by calculating the corrected coupling matrix elements for the Pb-Cm system and comparing the corresponding K-vacancy probabilities with conventional calculations. We critically discuss conventional methods for cutting off the coupling matrix elements in coupled-channel calculations
Rayleigh scattering in an emitter-nanofiber-coupling system
Tang, Shui-Jing; Gao, Fei; Xu, Da; Li, Yan; Gong, Qihuang; Xiao, Yun-Feng
2017-04-01
Scattering is a general process in both fundamental and applied physics. In this paper, we investigate Rayleigh scattering of a solid-state-emitter coupled to a nanofiber, by S -matrix-like theory in k -space description. Under this model, both Rayleigh scattering and dipole interaction are studied between a two-level artificial atom embedded in a nanocrystal and fiber modes (guided and radiation modes). It is found that Rayleigh scattering plays a critical role in the transport properties and quantum statistics of photons. On the one hand, Rayleigh scattering produces the transparency in the optical transmitted field of the nanofiber, accompanied by the change of atomic phase, population, and frequency shift. On the other hand, the interference between two kinds of scattering fields by Rayleigh scattering and dipole transition modifies the photon statistics (second-order autocorrelation function) of output fields, showing a strong wavelength dependence. This study provides guidance for the solid-state emitter acting as a single-photon source and can be extended to explore the scattering effect in many-body physics.
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...
International Nuclear Information System (INIS)
Stechel, E.B.; Walker, R.B.; Light, J.C.
1977-01-01
In an extension of previous work (R.B. Walker, J.C. Light and A. Altenberger-Siczek, J. Chem. Phys. 64, 1166(1976)), equations for the accurate quantum mechanical treatment of three body rearrangement collisions are presented in the R-matrix language. These equations describe how the solutions to Schrodinger's equation in three separate regions of configuration space (each containing one asymptotic atom + diatom arrangement) are matched smoothly to each other. The symmetry of the matching equations is discussed in detail. Within the R-matrix formalism, unitary S-matrices may be constructed for arbitrary atom-diatom mass combinations and for small target wave function basis expansions. Applications of this method to the three dimensional H + H 2 (labelled nuclei) exchange reaction are reported, and comparison is made to prior work
How to calculate the Coulomb scattering amplitude
International Nuclear Information System (INIS)
Grosse, H.; Narnhofer, H.; Thirring, W.
1974-01-01
The derivation of scattering amplitudes for Coulomb scattering is discussed. A derivation of the S-matrix elements for a dense set of states in momentum space is given in the framework of time dependent scattering theory. The convergence of the S-matrix is studied. A purely algebraic derivation of the S-matrix elements and phase shifts is also presented. (HFdV)
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
Brunel, Marc; Shen, Huanhuan; Coetmellec, Sebastien; Lebrun, Denis
2012-03-10
We present a new model to predict diffraction patterns of femtosecond pulses through complex optical systems. The model is based on the extension of an ABCD matrix formalism combined with generalized Huygens-Fresnel transforms (already used in the CW regime) to the femtosecond regime. The model is tested to describe femtosecond digital in-line holography experiments realized in situ through a cylindrical Plexiglas pipe. The model allows us to establish analytical relations that link the holographic reconstruction process to the experimental parameters of the pipe and of the incident beam itself. Simulations and experimental results are in good concordance. Femtosecond digital in-line holography is shown to allow significant coherent noise reduction, and this model will be particularly efficient to describe a wide range of optical geometries. More generally, the model developed can be easily used in any experiment where the knowledge of the precise evolution of femtosecond transverse patterns is required.
Influence of alloy disorder scattering on the hole mobility of SiGe nanowires
Energy Technology Data Exchange (ETDEWEB)
Martinez-Blanque, Celso; Ruiz, Francisco G., E-mail: franruiz@ugr.es; Godoy, Andres, E-mail: agodoy@ugr.es; Marin, Enrique G.; Donetti, Luca; Gámiz, Francisco [Dpto. de Electrónica y Tecnología de Computadores, Facultad de Ciencias, Universidad de Granada, Av. Fuentenueva S/N, 18071 Granada (Spain)
2014-12-28
In this work, we analyze the influence of the alloy disorder (AD) scattering on the low-field hole mobility of Si{sub 1-x}Ge{sub x} nanowires (NWs). To do it, the electrostatic description is achieved through a self-consistent solution of the Poisson equation and the six-band k⋅p method in the cross section of the NW. The momentum relaxation time approximation is used to calculate the hole mobility, including alloy disorder and phonon scattering mechanisms, and the use of approximations to calculate the overlap integrals for the scattering matrix elements is discussed. We study the influence of the alloy disorder scattering on the total mobility compared to the phonon contribution, for different values of the AD scattering parameter proposed in the literature, and analyze the performance of SiGe NWs as a function of the Ge molar fraction for both low and high inversion charge densities.
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.)
International Nuclear Information System (INIS)
Guzey, V.; Teckentrup, T.
2006-01-01
We develop the minimal model of a new leading order parametrization of generalized parton distributions (GPDs) introduced by Polyakov and Shuvaev. The model for GPDs H and E is formulated in terms of the forward quark distributions, the Gegenbauer moments of the D-term, and the forward limit of the GPD E. The model is designed primarily for small and medium-size values of x B , x B ≤0.2. We examine two different models of the t dependence of the GPDs: the factorized exponential model and the nonfactorized Regge-motivated model. Using our model, we successfully described the deeply virtual Compton scattering (DVCS) cross section measured by H1 and ZEUS, the moments of the beam-spin A LU sinφ , the beam-charge A C cosφ , and the transversely polarized target A UT sinφcosφ DVCS asymmetries measured by HERMES and A LU sinφ measured by CLAS. The data on A C cosφ prefer the Regge-motivated model of the t dependence of the GPDs. The data on A UT sinφcosφ indicate that the u and d quarks carry only a small fraction of the proton total angular momentum
Duboué-Dijon, Elise; Mason, Philip E; Fischer, Henry E; Jungwirth, Pavel
2018-04-05
Magnesium and zinc dications possess the same charge and have an almost identical size, yet they behave very differently in aqueous solutions and play distinct biological roles. It is thus crucial to identify the origins of such different behaviors and to assess to what extent they can be captured by force-field molecular dynamics simulations. In this work, we combine neutron scattering experiments in a specific mixture of H 2 O and D 2 O (the so-called null water) with ab initio molecular dynamics simulations to probe the difference in the hydration structure and ion-pairing properties of chloride solutions of the two cations. The obtained data are used as a benchmark to develop a scaled-charge force field for Mg 2+ that includes electronic polarization in a mean field way. We show that using this electronic continuum correction we can describe aqueous magnesium chloride solutions well. However, in aqueous zinc chloride specific interaction terms between the ions need to be introduced to capture ion pairing quantitatively.
Symmetries and Interactions in Matrix String Theory
Hacquebord, F.H.
1999-01-01
This PhD-thesis reviews matrix string theory and recent developments therein. The emphasis is put on symmetries, interactions and scattering processes in the matrix model. We start with an introduction to matrix string theory and a review of the orbifold model that flows out of matrix string theory
The kinematic algebras from the scattering equations
International Nuclear Information System (INIS)
Monteiro, Ricardo; O’Connell, Donal
2014-01-01
We study kinematic algebras associated to the recently proposed scattering equations, which arise in the description of the scattering of massless particles. In particular, we describe the role that these algebras play in the BCJ duality between colour and kinematics in gauge theory, and its relation to gravity. We find that the scattering equations are a consistency condition for a self-dual-type vertex which is associated to each solution of those equations. We also identify an extension of the anti-self-dual vertex, such that the two vertices are not conjugate in general. Both vertices correspond to the structure constants of Lie algebras. We give a prescription for the use of the generators of these Lie algebras in trivalent graphs that leads to a natural set of BCJ numerators. In particular, we write BCJ numerators for each contribution to the amplitude associated to a solution of the scattering equations. This leads to a decomposition of the determinant of a certain kinematic matrix, which appears naturally in the amplitudes, in terms of trivalent graphs. We also present the kinematic analogues of colour traces, according to these algebras, and the associated decomposition of that determinant
Belitsky, A. V.
2017-10-01
The Operator Product Expansion for null polygonal Wilson loop in planar maximally supersymmetric Yang-Mills theory runs systematically in terms of multi-particle pentagon transitions which encode the physics of excitations propagating on the color flux tube ending on the sides of the four-dimensional contour. Their dynamics was unraveled in the past several years and culminated in a complete description of pentagons as an exact function of the 't Hooft coupling. In this paper we provide a solution for the last building block in this program, the SU(4) matrix structure arising from internal symmetry indices of scalars and fermions. This is achieved by a recursive solution of the Mirror and Watson equations obeyed by the so-called singlet pentagons and fixing the form of the twisted component in their tensor decomposition. The non-singlet, or charged, pentagons are deduced from these by a limiting procedure.
Directory of Open Access Journals (Sweden)
A.V. Belitsky
2017-10-01
Full Text Available The Operator Product Expansion for null polygonal Wilson loop in planar maximally supersymmetric Yang–Mills theory runs systematically in terms of multi-particle pentagon transitions which encode the physics of excitations propagating on the color flux tube ending on the sides of the four-dimensional contour. Their dynamics was unraveled in the past several years and culminated in a complete description of pentagons as an exact function of the 't Hooft coupling. In this paper we provide a solution for the last building block in this program, the SU(4 matrix structure arising from internal symmetry indices of scalars and fermions. This is achieved by a recursive solution of the Mirror and Watson equations obeyed by the so-called singlet pentagons and fixing the form of the twisted component in their tensor decomposition. The non-singlet, or charged, pentagons are deduced from these by a limiting procedure.
Inversion assuming weak scattering
DEFF Research Database (Denmark)
Xenaki, Angeliki; Gerstoft, Peter; Mosegaard, Klaus
2013-01-01
due to the complex nature of the field. A method based on linear inversion is employed to infer information about the statistical properties of the scattering field from the obtained cross-spectral matrix. A synthetic example based on an active high-frequency sonar demonstrates that the proposed...
Supersymmetry applied to the spectrum edge of random matrix ensembles
International Nuclear Information System (INIS)
Andreev, A.V.; Simons, B.D.; Taniguchi, N.
1994-01-01
A new matrix ensemble has recently been proposed to describe the transport properties in mesoscopic quantum wires. Both analytical and numerical studies have shown that the ensemble of Laguerre or of chiral random matrices provides a good description of scattering properties in this class of systems. Until now only conventional methods of random matrix theory have been used to study statistical properties within this ensemble. We demonstrate that the supersymmetry method, already employed in the study Dyson ensembles, can be extended to treat this class of random matrix ensembles. In developing this approach we investigate both new, as well as verify known statistical measures. Although we focus on ensembles in which T-invariance is violated our approach lays the foundation for future studies of T-invariant systems. ((orig.))
International Nuclear Information System (INIS)
Descouvemont, P; Baye, D
2010-01-01
The different facets of the R-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: (i) The 'calculable' R-matrix method is a calculational tool to derive scattering properties from the Schroedinger equation in a large variety of physical problems. It was developed rather independently in atomic and nuclear physics with too little mutual influence. (ii) The 'phenomenological' R-matrix method is a technique to parametrize various types of cross sections. It was mainly (or uniquely) used in nuclear physics. Both directions are explained by starting from the simple problem of scattering by a potential. They are illustrated by simple examples in nuclear and atomic physics. In addition to elastic scattering, the R-matrix formalism is applied to inelastic and radiative-capture reactions. We also present more recent and more ambitious applications of the theory in nuclear physics.
Polarization phenomena in inelastic scattering
International Nuclear Information System (INIS)
Verhaar, B.J.
1974-01-01
An attempt is made to clarify the principles of inelastic scattering using the distorted wave Born approximation, concentrating on inelastic proton scattering. The principle aspects and merits of the microscopic description and the necessity of including the N-N spin orbit force are discussed. (7 figures) (U.S.)
Electron scattering off nuclei
International Nuclear Information System (INIS)
Gattone, A.O.
1989-01-01
Two recently developed aspects related to the scattering of electrons off nuclei are presented. On the one hand, a model is introduced which emphasizes the relativistic aspects of the problem in the impulse approximation, by demanding strict maintenance of the algebra of the Poincare group. On the other hand, the second model aims at a more sophisticated description of the nuclear response in the case of collective excitations. Basically, it utilizes the RPA formalism with a new development which enables a more careful treatment of the states in the continuum as is the case for the giant resonances. Applications of both models to the description of elastic scattering, inelastic scattering to discrete levels, giant resonances and the quasi-elastic region are discussed. (Author) [es
Zhan, Hanyu; Voelz, David G.
2016-12-01
The polarimetric bidirectional reflectance distribution function (pBRDF) describes the relationships between incident and scattered Stokes parameters, but the familiar surface-only microfacet pBRDF cannot capture diffuse scattering contributions and depolarization phenomena. We propose a modified pBRDF model with a diffuse scattering component developed from the Kubelka-Munk and Le Hors et al. theories, and apply it in the development of a method to jointly estimate refractive index, slope variance, and diffuse scattering parameters from a series of Stokes parameter measurements of a surface. An application of the model and estimation approach to experimental data published by Priest and Meier shows improved correspondence with measurements of normalized Mueller matrix elements. By converting the Stokes/Mueller calculus formulation of the model to a degree of polarization (DOP) description, the estimation results of the parameters from measured DOP values are found to be consistent with a previous DOP model and results.
Hanle effect at forward scattering in excited media
International Nuclear Information System (INIS)
Veklenko, B.A.
2001-01-01
One introduces a new method to calculate matrix of density of quantized electromagnetic field interacting with environment with kinetic processes in the medium. This method alongside with the accurate account of photon-photon quantum correlators has a number of symmetry features essentially facilitating summing up of appearing Feynman diagrams. Forward scattering of resonance radiation by gas two-level atoms within magnetic field was studied as a supplement. It is shown that inadequacy of semiclassical description of this coherent process in the excited media using unique tensor factor of refraction follows from quantum electrodynamics. One more function depending on frequency of irradiation and on concentration of excited atoms should be introduced [ru
Thermal-neutron multiple scattering: critical double scattering
International Nuclear Information System (INIS)
Holm, W.A.
1976-01-01
A quantum mechanical formulation for multiple scattering of thermal-neutrons from macroscopic targets is presented and applied to single and double scattering. Critical nuclear scattering from liquids and critical magnetic scattering from ferromagnets are treated in detail in the quasielastic approximation for target systems slightly above their critical points. Numerical estimates are made of the double scattering contribution to the critical magnetic cross section using relevant parameters from actual experiments performed on various ferromagnets. The effect is to alter the usual Lorentzian line shape dependence on neutron wave vector transfer. Comparison with corresponding deviations in line shape resulting from the use of Fisher's modified form of the Ornstein-Zernike spin correlations within the framework of single scattering theory leads to values for the critical exponent eta of the modified correlations which reproduce the effect of double scattering. In addition, it is shown that by restricting the range of applicability of the multiple scattering theory from the outset to critical scattering, Glauber's high energy approximation can be used to provide a much simpler and more powerful description of multiple scattering effects. When sufficiently close to the critical point, it provides a closed form expression for the differential cross section which includes all orders of scattering and has the same form as the single scattering cross section with a modified exponent for the wave vector transfer
The Performance Analysis Based on SAR Sample Covariance Matrix
Directory of Open Access Journals (Sweden)
Esra Erten
2012-03-01
Full Text Available Multi-channel systems appear in several fields of application in science. In the Synthetic Aperture Radar (SAR context, multi-channel systems may refer to different domains, as multi-polarization, multi-interferometric or multi-temporal data, or even a combination of them. Due to the inherent speckle phenomenon present in SAR images, the statistical description of the data is almost mandatory for its utilization. The complex images acquired over natural media present in general zero-mean circular Gaussian characteristics. In this case, second order statistics as the multi-channel covariance matrix fully describe the data. For practical situations however, the covariance matrix has to be estimated using a limited number of samples, and this sample covariance matrix follow the complex Wishart distribution. In this context, the eigendecomposition of the multi-channel covariance matrix has been shown in different areas of high relevance regarding the physical properties of the imaged scene. Specifically, the maximum eigenvalue of the covariance matrix has been frequently used in different applications as target or change detection, estimation of the dominant scattering mechanism in polarimetric data, moving target indication, etc. In this paper, the statistical behavior of the maximum eigenvalue derived from the eigendecomposition of the sample multi-channel covariance matrix in terms of multi-channel SAR images is simplified for SAR community. Validation is performed against simulated data and examples of estimation and detection problems using the analytical expressions are as well given.
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)
Carey, Ralph; Lucchese, Robert R.; Gianturco, F. A.
2013-05-01
We present scattering calculations of electron collisions with the platinum-containing compound cis-diamminedichloroplatinum (CDDP), commonly known as cisplatin, between 0.5 eV and 6 eV, and the corresponding isolated Pt atom from 0.1 eV to 10 eV. We find evidence of resonances in e--CDDP scattering, using an ab initio description of the target. We computed scattering matrix elements from equations incorporating exchange and polarization effects through the use of the static-exchange plus density functional correlation potential. Additionally, we made use of a purely local adiabatic model potential that allows Siegert eigenstates to be calculated, thereby allowing inspection of the possible resonant scattering wave functions. The total cross section for electron scattering from (5d10) 1S Pt displays a large magnitude, monotonic decay from the initial collision energies, with no apparent resonance scattering features in any scattering symmetry. By contrast, the e--CDDP scattering cross section shows a small feature near 3.8 eV, which results from a narrow, well localized resonance of b2 symmetry. These findings are then related to the possible electron-mediated mechanism of the action of CDDP on DNA replication as suggested by recent experiments.
International Nuclear Information System (INIS)
Brown, T.W.
2010-11-01
The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super- Yang-Mills. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich- Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Brown, T.W.
2010-11-15
The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super- Yang-Mills. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich- Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces. (orig.)
Small angle neutron scattering and small angle X-ray scattering ...
Indian Academy of Sciences (India)
Abstract. The morphology of carbon nanofoam samples comprising platinum nanopar- ticles dispersed in the matrix was characterized by small angle neutron scattering (SANS) and small angle X-ray scattering (SAXS) techniques. Results show that the structure of pores of carbon matrix exhibits a mass (pore) fractal nature ...
Chaotic scattering and quantum dynamics
International Nuclear Information System (INIS)
Doron, Eyal.
1992-11-01
The main concern of this thesis is the application of the semiclassical approximation to quantum chaotic scattering systems. We deal with two separate, although interconnected, subjects. The first subject dealt with is the semiclassical characterization of the fluctuations of the S matrix. A particular important parameter is the magnetic field B, and we show how the correlation length and line shape of S matrix elements under a change of B may be derived. An effect which is present in many physical wave systems is absorption of energy flux. We show how absorption affects both the reflectivity and the scattering phase and time delay of a scattering system. In the second part of the thesis, we show how the formalism and results obtained from chaotic scattering can be applied to the investigation of closed chaotic systems, and in particular to chaotic billiards. The semiclassical expansion for billiards is presented. In the last part of the thesis we deal with the statistics of S matrices of chaotic scattering systems. The main message of this work is that scattering matrix, and its classical counterpart the Poincare Scattering Map can be used to yield a powerful formulation of the quantum mechanical dynamics of bounded systems. (author)
Detection of explosives by neutron scattering
International Nuclear Information System (INIS)
Brooks, F.D.; Buffler, A.; Allie, M.S.; Nchodu, M.R.; Bharuth-Ram, K.
1998-01-01
For non-intrusive detection of hidden explosives or other contraband such as narcotics a fast neutron scattering analysis (FNSA) technique is proposed. An experimental arrangement uses a collimated, pulsed beam of neutrons directed at the sample. Scattered neutrons are detected by liquid scintillation counters at different scattering angles. A scattering signature is derived from two-parameter data, counts vs pulse height and time-of-flight measured for each element (H, C, N or O) at each of two scattering angles and two neutron energies. The elemental signatures are very distinctive and constitute a good response matrix for unfolding elemental components from the scattering signatures measured for different compounds
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
Pion-Skyrmion scattering: collective coordinates at work
International Nuclear Information System (INIS)
Peskin, M.E.
1985-06-01
It is argued that the Skryme model, and more generally, the picture of the nucleon as a chiral soliton, can give a qualitatively correct picture of pion-nucleon scattering, considering both group-theoretic and more scheme-dependent results. The properties of the nucleon and its excited states in large-N quantum chromodynamics are discussed qualitatively. Then the pion-nucleon S-matrix is reduced. It is found that the model succeeds at the first level of calculation in producing many of the features of pion-nucleon scattering which are revealed by experiment, but that many aspects of the description need to be better understood, including the treatment of nonleading corrections near threshold and the inclusion of inelastic channels. 22 refs., 8 figs
Franklin, Joel N
2003-01-01
Mathematically rigorous introduction covers vector and matrix norms, the condition-number of a matrix, positive and irreducible matrices, much more. Only elementary algebra and calculus required. Includes problem-solving exercises. 1968 edition.
Directory of Open Access Journals (Sweden)
Robert de Mello Koch
2017-05-01
Full Text Available We study the worldsheet S-matrix of a string attached to a D-brane in AdS5×S5. The D-brane is either a giant graviton or a dual giant graviton. In the gauge theory, the operators we consider belong to the su(2|3 sector of the theory. Magnon excitations of open strings can exhibit both elastic (when magnons in the bulk of the string scatter and inelastic (when magnons at the endpoint of an open string participate scattering. Both of these S-matrices are determined (up to an overall phase by the su(2|22 global symmetry of the theory. In this note we study the S-matrix for inelastic scattering. We show that it exhibits poles corresponding to boundstates of bulk and boundary magnons. A crossing equation is derived for the overall phase. It reproduces the crossing equation for maximal giant gravitons, in the appropriate limit. Finally, scattering in the su(2 sector is computed to two loops. This two loop result, which determines the overall phase to two loops, will be useful when a unique solution to the crossing equation is to be selected.
Effects of quark structure on NN scattering: relevance to current data and bag models
International Nuclear Information System (INIS)
Lomon, E.L.
1984-01-01
The applicability of the R-matrix method to the transition from asymptotic freedom to confinement depends on the overlap of the regions in which asymptotic freedom is a good approximation and the region well described by hadronic field theory. This enables a quantitative description of hadron-hadron interactions at low and intermediate energies. ''Compound'' and ''Cloudy'' bag models and the P-matrix method are shown to be special or approximate versions of the R-matrix method in its f-matrix form. The f-matrix condition is applied to S-state nucleon-nucleon scattering where it (i) overcomes the deficiencies of the P-matrix applications, (ii) shows that some of the bag models which have had some success in describing mesons and baryons are inconsistent when applied to nucleon-nucleon scattering, and (iii) that the bag models which are consistent with that data predict inelastic resonant structures of 50-100 MeV width at barycentric energies between 2.3 GeV and 3.5 GeV
On the limits of the effective description of hyperbolic materials in the presence of surface waves
International Nuclear Information System (INIS)
Tschikin, Maria; Biehs, Svend-Age; Messina, Riccardo; Ben-Abdallah, Philippe
2013-01-01
Here, we address the question of the validity of an effective description for hyperbolic metamaterials in the near-field region. We show that the presence of localized modes such as surface waves drastically limits the validity of the effective description, and requires revisiting the concept of homogenization in the near-field. We demonstrate, from exact scattering matrix calculations for multilayer hyperbolic structures, that one can find surface modes in spectral regions where the effective approach predicts hyperbolic modes only. Hence, the presence of surface modes which are not accounted for in the effective description can lead to physical misinterpretations in the description of hyperbolic materials and their related properties. In particular, we discuss in detail how the choice of the topmost layer affects the validity of the effective medium approach for calculating the local density of states and the super-Planckian thermal radiation. (paper)
Theory of atom displacements induced by fast electron elastic scattering in solids
International Nuclear Information System (INIS)
Cruz, C. M.; Pinera, I.; Abreu, Y.; Leyva, A.
2006-01-01
Present contribution deals with the theoretical description of the conditions favoring the occurrence of single fast electron elastic scattering in solids, leading to the displacement of atoms from their crystalline sites. Firstly, the Moliere-Bethe-Goudsmit-Saunderson theory of Multiple Electron Scattering is applied, determining the limiting angle θ l over which the single electron elastic scattering prevails over the multiple one, leading to the evaluation of the total macroscopic cross-section for single electron elastic scattering on the basis of the Mott-Rutherford differential cross-section. On the basis of single electron elastic scattering by atoms in the solid matrix, it was determined the relative number of Atom Displacements produced by the Gamma Radiation as a primary act, as well as the energy and linear momentum of the ejected atoms. The statistical distributions of single electron elastic scattering and of those inducing Atom Displacements at different electron initial energies in comparison with the others electron inelastic scattering channels are discussed, where the statistical sampling methods on the basis of the rejection one where applied simulating different practical situations. (Full text)
Analytic nuclear scattering theories
International Nuclear Information System (INIS)
Di Marzio, F.; University of Melbourne, Parkville, VIC
1999-01-01
A wide range of nuclear reactions are examined in an analytical version of the usual distorted wave Born approximation. This new approach provides either semi analytic or fully analytic descriptions of the nuclear scattering processes. The resulting computational simplifications, when used within the limits of validity, allow very detailed tests of both nuclear interaction models as well as large basis models of nuclear structure to be performed
International Nuclear Information System (INIS)
Hempel, M.; Haeussler, F.; Eichhorn, E.
1993-01-01
Neutron small angle scatter (NSAS) is suitable for characterising matrix non-homogeneousness in many materials. The description of amorphous materials (distribution of clusters, defect structures, boundary surfaces, e.g.: Between pores and the solid matrix etc.) is possible, in principle, by NSAS. This method is non-destructive to the extent that no pretreatment of samples is necessary, which significantly affects the microstructure to be examined. The process of NSAS itself produces no changes in the sample regarding the target of the examination. Thus the progress of hydratisation in concrete can be observed by successive NSAS measurements in time. (orig./HP) [de
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
Analytical transition-matrix treatment of electric multipole polarizabilities of hydrogen-like atoms
International Nuclear Information System (INIS)
Kharchenko, V.F.
2015-01-01
The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the case of the bound system formed by the Coulomb interaction the corresponding inhomogeneous integral equation determining an off-shell scattering function, which consistently describes virtual multiple scattering, can be solved exactly analytically for all electric multipole polarizabilities. Our method allows to reproduce the known Dalgarno–Lewis formula for electric multipole polarizabilities of the hydrogen atom in the ground state and can also be applied to determine the polarizability of the atom in excited bound states. - Highlights: • A new description for electric polarization of hydrogen-like atoms. • Expression for multipole polarizabilities in terms of off-shell scattering functions. • Derivation of integral equation determining the off-shell scattering function. • Rigorous analytic solving the integral equations both for ground and excited states. • Study of contributions of virtual multiple scattering to electric polarizabilities
Scattering theory of stochastic electromagnetic light waves.
Wang, Tao; Zhao, Daomu
2010-07-15
We generalize scattering theory to stochastic electromagnetic light waves. It is shown that when a stochastic electromagnetic light wave is scattered from a medium, the properties of the scattered field can be characterized by a 3 x 3 cross-spectral density matrix. An example of scattering of a spatially coherent electromagnetic light wave from a deterministic medium is discussed. Some interesting phenomena emerge, including the changes of the spectral degree of coherence and of the spectral degree of polarization of the scattered field.
Transient radiative transfer in a scattering slab considering polarization.
Yi, Hongliang; Ben, Xun; Tan, Heping
2013-11-04
The characteristics of the transient and polarization must be considered for a complete and correct description of short-pulse laser transfer in a scattering medium. A Monte Carlo (MC) method combined with a time shift and superposition principle is developed to simulate transient vector (polarized) radiative transfer in a scattering medium. The transient vector radiative transfer matrix (TVRTM) is defined to describe the transient polarization behavior of short-pulse laser propagating in the scattering medium. According to the definition of reflectivity, a new criterion of reflection at Fresnel surface is presented. In order to improve the computational efficiency and accuracy, a time shift and superposition principle is applied to the MC model for transient vector radiative transfer. The results for transient scalar radiative transfer and steady-state vector radiative transfer are compared with those in published literatures, respectively, and an excellent agreement between them is observed, which validates the correctness of the present model. Finally, transient radiative transfer is simulated considering the polarization effect of short-pulse laser in a scattering medium, and the distributions of Stokes vector in angular and temporal space are presented.
DEFF Research Database (Denmark)
Wigram, Anthony Lewis
2003-01-01
Descriptive research is described by Lathom-Radocy and Radocy (1995) to include Survey research, ex post facto research, case studies and developmental studies. Descriptive research also includes a review of the literature in order to provide both quantitative and qualitative evidence of the effect...... starts will allow effect size calculations to be made in order to evaluate effect over time. Given the difficulties in undertaking controlled experimental studies in the creative arts therapies, descriptive research methods offer a way of quantifying effect through descriptive statistical analysis...
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
An algebraic approach to the scattering equations
Energy Technology Data Exchange (ETDEWEB)
Huang, Rijun; Rao, Junjie [Zhejiang Institute of Modern Physics, Zhejiang University,Hangzhou, 310027 (China); Feng, Bo [Zhejiang Institute of Modern Physics, Zhejiang University,Hangzhou, 310027 (China); Center of Mathematical Science, Zhejiang University,Hangzhou, 310027 (China); He, Yang-Hui [School of Physics, NanKai University,Tianjin, 300071 (China); Department of Mathematics, City University,London, EC1V 0HB (United Kingdom); Merton College, University of Oxford,Oxford, OX14JD (United Kingdom)
2015-12-10
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
An algebraic approach to the scattering equations
International Nuclear Information System (INIS)
Huang, Rijun; Rao, Junjie; Feng, Bo; He, Yang-Hui
2015-01-01
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
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
Small angle neutron scattering
Directory of Open Access Journals (Sweden)
Cousin Fabrice
2015-01-01
Full Text Available Small Angle Neutron Scattering (SANS is a technique that enables to probe the 3-D structure of materials on a typical size range lying from ∼ 1 nm up to ∼ a few 100 nm, the obtained information being statistically averaged on a sample whose volume is ∼ 1 cm3. This very rich technique enables to make a full structural characterization of a given object of nanometric dimensions (radius of gyration, shape, volume or mass, fractal dimension, specific area… through the determination of the form factor as well as the determination of the way objects are organized within in a continuous media, and therefore to describe interactions between them, through the determination of the structure factor. The specific properties of neutrons (possibility of tuning the scattering intensity by using the isotopic substitution, sensitivity to magnetism, negligible absorption, low energy of the incident neutrons make it particularly interesting in the fields of soft matter, biophysics, magnetic materials and metallurgy. In particular, the contrast variation methods allow to extract some informations that cannot be obtained by any other experimental techniques. This course is divided in two parts. The first one is devoted to the description of the principle of SANS: basics (formalism, coherent scattering/incoherent scattering, notion of elementary scatterer, form factor analysis (I(q→0, Guinier regime, intermediate regime, Porod regime, polydisperse system, structure factor analysis (2nd Virial coefficient, integral equations, characterization of aggregates, and contrast variation methods (how to create contrast in an homogeneous system, matching in ternary systems, extrapolation to zero concentration, Zero Averaged Contrast. It is illustrated by some representative examples. The second one describes the experimental aspects of SANS to guide user in its future experiments: description of SANS spectrometer, resolution of the spectrometer, optimization of
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
Pion nucleus scattering lengths
International Nuclear Information System (INIS)
Huang, W.T.; Levinson, C.A.; Banerjee, M.K.
1971-09-01
Soft pion theory and the Fubini-Furlan mass dispersion relations have been used to analyze the pion nucleon scattering lengths and obtain a value for the sigma commutator term. With this value and using the same principles, scattering lengths have been predicted for nuclei with mass number ranging from 6 to 23. Agreement with experiment is very good. For those who believe in the Gell-Mann-Levy sigma model, the evaluation of the commutator yields the value 0.26(m/sub σ//m/sub π/) 2 for the sigma nucleon coupling constant. The large dispersive corrections for the isosymmetric case implies that the basic idea behind many of the soft pion calculations, namely, slow variation of matrix elements from the soft pion limit to the physical pion mass, is not correct. 11 refs., 1 fig., 3 tabs
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
Explicit Covariance Matrix for Particle Measurement Precision
Karimäki, Veikko
1997-01-01
We derive explicit and precise formulae for 3 by 3 error matrix of the particle transverse momentum, direction and impact parameter. The error matrix elements are expressed as functions of up to fourth order statistical moments of the measured coordinates. The formulae are valid for any curvature and track length in case of negligible multiple scattering.
The black hole S-Matrix from quantum mechanics
Betzios, Panagiotis; Gaddam, Nava; Papadoulaki, Olga
2016-01-01
We revisit the old black hole S-Matrix construction and its new partial wave expansion of 't Hooft. Inspired by old ideas from non-critical string theory \\& $c=1$ Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model\\textemdash of waves scattering off
Bodewig, E
1959-01-01
Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well
Significance of collective motions in biopolymers and neutron scattering
Energy Technology Data Exchange (ETDEWEB)
Go, Nobuhiro [Kyoto Univ. (Japan)
1996-05-01
Importance of collective variable description of conformational dynamics of biopolymers and the vital role that neutron inelastic scattering phenomena would play in its experimental determination are discussed. (author)
Medium energy hadron scattering from nuclei
International Nuclear Information System (INIS)
Ginocchio, J.N.; Wenes, G.
1986-01-01
The Glauber approximation for medium energy scattering of hadronic projectiles from nuclei is combined with the interacting boson model of nuclei to produce a transition matrix for elastic and inelastic scattering in algebraic form which includes coupling to all the intermediate states. We present closed form analytic expresions for the transition matrix elements for the three dynamical symmetries of the interacting boson model; that is for, a spherical quadrupole vibrator, a γ unstable rotor, and both prolate and oblate axially symmetric rotors. We give examples of application of this formalism to proton scattering from 154 Sm and 154 Gd. 27 refs., 5 figs., 1 tab
The scattering properties of anisotropic dielectric spheres on electromagnetic waves
International Nuclear Information System (INIS)
Chen Hui; Zhang Weiyi; Wang Zhenlin; Ming Naiben
2004-01-01
The scattering coefficients of spheres with dielectric anisotropy are calculated analytically in this paper using the perturbation method. It is found that the different modes of vector spherical harmonics and polarizations are coupled together in the scattering coefficients (c-matrix) in contrast to the isotropic case where all modes are decoupled from each other. The generalized c-matrix is then incorporated into our codes for a vector wave multiple scattering program; the preliminary results on face centred cubic structure show that dielectric anisotropy reduces the symmetry of the scattering c-matrix and removes the degeneracy in photonic band structures composed of isotropic dielectric spheres
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
Energy Technology Data Exchange (ETDEWEB)
Friedrich, Harald [Technische Univ. Muenchen, Garching (Germany). Physik-Department
2016-07-01
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 kept as low as at all possible and deeper questions related to the mathematical foundations of scattering theory are passed by. It should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. The book is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.
t matrix of metallic wire structures
International Nuclear Information System (INIS)
Zhan, T. R.; Chui, S. T.
2014-01-01
To study the electromagnetic resonance and scattering properties of complex structures of which metallic wire structures are constituents within multiple scattering theory, the t matrix of individual structures is needed. We have recently developed a rigorous and numerically efficient equivalent circuit theory in which retardation effects are taken into account for metallic wire structures. Here, we show how the t matrix can be calculated analytically within this theory. We illustrate our method with the example of split ring resonators. The density of states and cross sections for scattering and absorption are calculated, which are shown to be remarkably enhanced at resonant frequencies. The t matrix serves as the basic building block to evaluate the interaction of wire structures within the framework of multiple scattering theory. This will open the door to efficient design and optimization of assembly of wire structures
Conformal bootstrap, universality and gravitational scattering
Directory of Open Access Journals (Sweden)
Steven Jackson
2015-12-01
Full Text Available We use the conformal bootstrap equations to study the non-perturbative gravitational scattering between infalling and outgoing particles in the vicinity of a black hole horizon in AdS. We focus on irrational 2D CFTs with large c and only Virasoro symmetry. The scattering process is described by the matrix element of two light operators (particles between two heavy states (BTZ black holes. We find that the operator algebra in this regime is (i universal and identical to that of Liouville CFT, and (ii takes the form of an exchange algebra, specified by an R-matrix that exactly matches the scattering amplitude of 2+1 gravity. The R-matrix is given by a quantum 6j-symbol and the scattering phase by the volume of a hyperbolic tetrahedron. We comment on the relevance of our results to scrambling and the holographic reconstruction of the bulk physics near black hole horizons.
Scattering theory and automorphic functions
International Nuclear Information System (INIS)
Lachaud, G.
1982-01-01
After a consideration of the Fourier expansion of an automorphic function corresponding to the group SL(2,R) and a description of the Eisenstein series the author describes the application of these results to the quantum mechanical scattering theory using the group SO(2,R). (HSI)
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
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.
Heavy ion elastic scattering of code : OPTHI
International Nuclear Information System (INIS)
Ismail, M.; Divatia, A.S.
1982-01-01
A computer code, OPTHI has been designed to calculate nuclear optical model elastic cross sections for the scattering of heavy ions. The program has been designed to be utilitarian rather than capable of giving an exact description of elastic scattering. Input format is described and the program listing is given. (M.G.B.)
Towards a nonpotential scattering theory
International Nuclear Information System (INIS)
Mignani, R.
1985-01-01
We present a formal approach to nonpotential scattering theory (i.e. scattering under unrestricted nonlocal non-Hamiltonian forces), based on the generalization of the concept of scattering matrix (and related topics) to the Lie-isotopic and Lie-admissible case. In the time-dependent formalism, the main taks is the determination of the evolution operator, from which the S matrix is found as a double infinite limit. The study of time-development operators is carried out in detail in the isotopic case, and involves the isotopic generalizations of Moller wave operators, in- and out-states, and temporal (retarded and advanced) propagators. We give also expansion techniques for the S matrix, which extend to the Lie-isotopic formulation the Feynman-Dyson perturbation series, the Magnus expansion, and the Wei-Norman theorem. In the time-independent approach, we solve the isotopic Schroedinger eigenvalue equation by exploiting the properties of isotopic Green operators, Lippmann-Schwinger equations, and incoming and outgoing states, which turn out to be suitable generalizations of the conventional ones. The changes in cross sections due to nonpotential forces are explicitly worked out in some simple cases. A purely algebraic approach to nonpotential scattering, essentially based on the properties of the isowave operators, is presented. The Lie-admissible formulation of the main results is briefly outlined
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.
EISPACK, Subroutines for Eigenvalues, Eigenvectors, Matrix Operations
International Nuclear Information System (INIS)
Garbow, Burton S.; Cline, A.K.; Meyering, J.
1993-01-01
1 - Description of problem or function: EISPACK3 is a collection of 75 FORTRAN subroutines, both single- and double-precision, that compute the eigenvalues and eigenvectors of nine classes of matrices. The package can determine the Eigen-system of complex general, complex Hermitian, real general, real symmetric, real symmetric band, real symmetric tridiagonal, special real tridiagonal, generalized real, and generalized real symmetric matrices. In addition, there are two routines which use the singular value decomposition to solve certain least squares problem. The individual subroutines are - Identification/Description: BAKVEC: Back transform vectors of matrix formed by FIGI; BALANC: Balance a real general matrix; BALBAK: Back transform vectors of matrix formed by BALANC; BANDR: Reduce sym. band matrix to sym. tridiag. matrix; BANDV: Find some vectors of sym. band matrix; BISECT: Find some values of sym. tridiag. matrix; BQR: Find some values of sym. band matrix; CBABK2: Back transform vectors of matrix formed by CBAL; CBAL: Balance a complex general matrix; CDIV: Perform division of two complex quantities; CG: Driver subroutine for a complex general matrix; CH: Driver subroutine for a complex Hermitian matrix; CINVIT: Find some vectors of complex Hess. matrix; COMBAK: Back transform vectors of matrix formed by COMHES; COMHES: Reduce complex matrix to complex Hess. (elementary); COMLR: Find all values of complex Hess. matrix (LR); COMLR2: Find all values/vectors of cmplx Hess. matrix (LR); CCMQR: Find all values of complex Hessenberg matrix (QR); COMQR2: Find all values/vectors of cmplx Hess. matrix (QR); CORTB: Back transform vectors of matrix formed by CORTH; CORTH: Reduce complex matrix to complex Hess. (unitary); CSROOT: Find square root of complex quantity; ELMBAK: Back transform vectors of matrix formed by ELMHES; ELMHES: Reduce real matrix to real Hess. (elementary); ELTRAN: Accumulate transformations from ELMHES (for HQR2); EPSLON: Estimate unit roundoff
Nick, Todd G
2007-01-01
Statistics is defined by the Medical Subject Headings (MeSH) thesaurus as the science and art of collecting, summarizing, and analyzing data that are subject to random variation. The two broad categories of summarizing and analyzing data are referred to as descriptive and inferential statistics. This chapter considers the science and art of summarizing data where descriptive statistics and graphics are used to display data. In this chapter, we discuss the fundamentals of descriptive statistics, including describing qualitative and quantitative variables. For describing quantitative variables, measures of location and spread, for example the standard deviation, are presented along with graphical presentations. We also discuss distributions of statistics, for example the variance, as well as the use of transformations. The concepts in this chapter are useful for uncovering patterns within the data and for effectively presenting the results of a project.
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
Scattering of photons from atomic electrons
International Nuclear Information System (INIS)
Pratt, R.H.; Zhou, B.; Bergstrom, P.M. Jr.; Pisk, K.; Suric, T.
1990-01-01
Validity of simpler approaches for elastic and inelastic photon scattering by atoms and ions is assessed by comparison with second-order S-matrix predictions. A simple scheme for elastic scattering based on angle-independent anomalous scattering factors has been found to give useful predictions near and below photoeffect thresholds. In inelastic scattering, major deviations are found from A 2 -based calculations. Extension of free-atom and free-ion cross sections to the dense plasma regime is discussed. 20 refs., 6 figs
Quantum mechanics in matrix form
Ludyk, Günter
2018-01-01
This book gives an introduction to quantum mechanics with the matrix method. Heisenberg's matrix mechanics is described in detail. The fundamental equations are derived by algebraic methods using matrix calculus. Only a brief description of Schrödinger's wave mechanics is given (in most books exclusively treated), to show their equivalence to Heisenberg's matrix method. In the first part the historical development of Quantum theory by Planck, Bohr and Sommerfeld is sketched, followed by the ideas and methods of Heisenberg, Born and Jordan. Then Pauli's spin and exclusion principles are treated. Pauli's exclusion principle leads to the structure of atoms. Finally, Dirac´s relativistic quantum mechanics is shortly presented. Matrices and matrix equations are today easy to handle when implementing numerical algorithms using standard software as MAPLE and Mathematica.
International Nuclear Information System (INIS)
Craps, Ben; Evnin, Oleg; Nguyen, Kévin
2017-01-01
Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.
Craps, Ben; Evnin, Oleg; Nguyen, Kévin
2017-02-01
Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.
Energy Technology Data Exchange (ETDEWEB)
Craps, Ben [Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium); Evnin, Oleg [Department of Physics, Faculty of Science, Chulalongkorn University, Thanon Phayathai, Pathumwan, Bangkok 10330 (Thailand); Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium); Nguyen, Kévin [Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium)
2017-02-08
Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.
The description of compton lines in energy-dispersive x-ray Fluorescence
International Nuclear Information System (INIS)
Van Gysel, Mon; Van Espen, P.J.M.
2001-01-01
Energy-Dispersive X-Ray Fluorescence (ED-XRF) is a non-destructive technique for the element analysis in a concentration range ppm - % making use of X rays up to 100 keV. Generally, two photon matter interactions occur, respectively absorption and scattering. The absorption of incident photons gives raise to characteristic lines. Scattering gives an incoherent and a coherent line. A Gaussian peak model is adequate to describe the characteristic and coherent scattered lines. Incoherent lines appear as non-Gaussian, broadened peaks. The profile of a Compton peak is complex. It depends on the geometry and the composition of the sample. Especially, when analyzing a low Z matrix; dominant scattering and multiple scattering may cause large interferences. The absence of an appropriate fitting model makes the Compton profile seen as a limiting factor in the evaluation of spectra. An accurate description of incoherent lines should improve quantitative analysis. Therefore, a suitable fitting model, making use of the expertise of non-linear least squares procedures and Monte-Carlo calculations was systematically investigated. The proposed model, containing a modified Gaussian, is tested on experimental data recorded with a HPGe detector
Burnett, K.; Cooper, J.
1980-01-01
The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.
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
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
Asymptotic angular dependences of exclusive hadron large-angle scattering
International Nuclear Information System (INIS)
Goloskokov, S.V.; Kudinov, A.V.; Kuleshov, S.P.
1979-01-01
Asymptotic approach to the description of the large-angle scattering amplitudes of the meson-nucleon and nucleon-nucleon scattering is studied. The paper is based on the Mandelstam representation and quark counting rules. The crossing summetry, SU-3 symmetry and spin effects are taken into account. Formulae obtained are used for the description of the differential cross sections of πsup(+-)p, pp and pn scattering. The predictions about ksup(+-)p and p anti p scattering are made. It is shown that formulae provide quantitative description of experimental data for the considered reactions
Multichannel quantum defect and reduced R-matrix
International Nuclear Information System (INIS)
Hategan, C.; Ionescu, R.A.; Cutoiu, D.; Gugiu, M.
2002-01-01
The collision of an electron with the atomic electronic core or the scattering of a nucleon on the atomic nucleus, usually, result into multiparticle excitations producing a resonance of a compound system, followed by its decay in reaction channels. Both in the electron-atom collisions and in nucleon-nucleus reactions, these multichannel resonances are described by poles of all R-Matrix elements. The resonances originating in single particle states, either in electron-atom collision or in nucleon-nucleus scattering, are approached in quite different descriptions. For example, the single-particle resonance in nuclear scattering is described, in R-Matrix Theory, by a perturbative method due to Bloch. The original single-nucleon state overlaps the actual states of the nucleus, resulting into a micro-giant description of the single particle resonance. The spectroscopic aspects of the single particle state, mixed with actual nuclear states, are subject of nucleon (or single particle) Strength Function. The electron, involving single particle Rydberg state in an atomic collision, 'avoids' its wave function mixing with that of inner multielectron core, because it is spatially far-away located from that core. This process is usually described by the Multichannel Quantum Defect Theory (MQDT). In the electron-atom scattering rather the effect of inner multielectron core on Rydberg electrons is studied by means of a global parameter, historically called 'Quantum Defect'. Both these types of resonances have in common the preserving of the single-particle wave function in a complex system with multiparticle excitations. In this work one approaches description of single-particle (electron or nucleon) resonance in a multichannel system. The single particle multichannel resonances are not longer described by a R-Matrix pole (specific for resonances originating in multiparticle excitations) but rather by a natural method for incorporating a single particle state in R-Matrix Theory
Scattering of atomic and molecular ions from single crystal surfaces of Cu, Ag and Fe
International Nuclear Information System (INIS)
Zoest, J.M. van.
1986-01-01
This thesis deals with analysis of crystal surfaces of Cu, Ag and Fe with Low Energy Ion scattering Spectroscopy (LEIS). Different atomic and molecular ions with fixed energies below 7 keV are scattered by a metal single crystal (with adsorbates). The energy and direction of the scattered particles are analysed for different selected charge states. In that way information can be obtained concerning the composition and atomic and electronic structure of the single crystal surface. Energy spectra contain information on the composition of the surface, while structural atomic information is obtained by direction measurements (photograms). In Ch.1 a description is given of the experimental equipment, in Ch.2 a characterization of the LEIS method. Ch.3 deals with the neutralization of keV-ions in surface scattering. Two different ways of data interpretation are presented. First a model is treated in which the observed directional dependence of neutralization action of the first atom layer of the surface is presented by a laterally varying thickness of the neutralizing layer. Secondly it is shown that the data can be reproduced by a more realistic, physical model based on atomic transition matrix elements. In Ch.4 the low energy hydrogen scattering is described. The study of the dissociation of H 2 + at an Ag surface r0230ted in a model based on electronic dissociation, initialized by electron capture into a repulsive (molecular) state. In Ch.5 finally the method is applied to the investigation of the surface structure of oxidized Fe. (Auth.)
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
Fatigue and damage tolerance scatter models
Raikher, Veniamin L.
1994-09-01
Effective Total Fatigue Life and Crack Growth Scatter Models are proposed. The first of them is based on the power form of the Wohler curve, fatigue scatter dependence on mean life value, cycle stress ratio influence on fatigue scatter, and validated description of the mean stress influence on the mean fatigue life. The second uses in addition are fracture mechanics approach, assumption of initial damage existence, and Paris equation. Simple formulas are derived for configurations of models. A preliminary identification of the parameters of the models is fulfilled on the basis of experimental data. Some new and important results for fatigue and crack growth scatter characteristics are obtained.
Zhan, Xingzhi
2002-01-01
The main purpose of this monograph is to report on recent developments in the field of matrix inequalities, with emphasis on useful techniques and ingenious ideas. Among other results this book contains the affirmative solutions of eight conjectures. Many theorems unify or sharpen previous inequalities. The author's aim is to streamline the ideas in the literature. The book can be read by research workers, graduate students and advanced undergraduates.
Theory of deep inelastic lepton-hadron scattering
International Nuclear Information System (INIS)
Geyer, B.; Robaschik, D.; Wieczorek, E.
1979-01-01
The description of deep inelastic lepton-nucleon scattering in the lowest order of the electromagnetic and weak coupling constants leads to a study of virtual Compton amplitudes and their absorptive parts. Some aspects of quantum chromodynamics are discussed. Deep inelastic scattering enables a central quantity of quantum field theory, namely the light cone behaviour of the current commutator. The moments of structure functions are used for the description of deep inelastic scattering. (author)
Electron scattering off palladium isotopes
International Nuclear Information System (INIS)
Laan, J.B. van der.
1986-01-01
The low-lying states of the even Pd isotopes are characterized by vibrator-like properties. In this thesis the results of an electron scattering experiment on the Pd isotopes, designed to study the description of such nuclei in the Anharmonic Vibrator Model (AVM) and the Interacting Boson Approximation (IBA), are presented and discussed. Data have been taken at the high-resolution electron scattering facility of NIKHEF-K and covered a momentum-transfer range of 0.4 to 2.5 fm -1 . (Auth.)
Q-space analysis of scattering by particles: A review
International Nuclear Information System (INIS)
Sorensen, Christopher M.
2013-01-01
This review describes and demonstrates the Q-space analysis of light scattering by particles. This analysis involves plotting the scattered intensity versus the scattering wave vector q=(4π/λ)sin(θ/2) on a double log plot. The analysis uncovers power law descriptions of the scattering with length scale dependent crossovers between the power laws. It also systematically describes the magnitude of the scattering and the interference ripple structure that often underlies the power laws. It applies to scattering from dielectric spheres of arbitrary size and refractive index (Mie scattering), fractal aggregates and irregularly shaped particles such as dusts. The benefits of Q-space analysis are that it provides a simple and comprehensive description of scattering in terms of power laws with quantifiable exponents; it can be used to differentiate scattering by particles of different shapes, and it yields a physical understanding of scattering based on diffraction. -- Highlights: ► Angular scattering functions for spheres show power laws versus the wave vector q. ► The power laws uncover patterns involving length scales and functionalities. ► Similar power laws appear in scattering from aggregates and irregular particles. ► Power laws provide a comprehensive and quantitative description of scattering
A diffuse neutron scattering study of clustering kinetics in Cu-Ni alloys
International Nuclear Information System (INIS)
Vrijen, J.; Radelaar, S.; Schwahn, D.
1977-01-01
Diffuse scattering of thermal neutrons was used to investigate the kinetics of clustering in Cu-Ni alloys. In order to optimize the experimental conditions the isotopes 65 Cu and 62 Ni were alloyed. The time evolution of the diffuse scattered intensity at 400 0 C has been measured for eight Cu-Ni alloys, varying in composition between 30 and 80 at. pour cent Ni. The relaxation of the so called null matrix, containing 56.5 at. pour cent Ni has also been investigated at 320, 340, 425 and 450 0 C. Using Cook's model from all these measurements information has been deduced about diffusion at low temperatures and about thermodynamic properties of the Cu-Ni system. It turns out that Cook's model is not sufficiently detailed for an accurate description of the initial stages of these relaxations
Quantum scattering theory of a single-photon Fock state in three-dimensional spaces.
Liu, Jingfeng; Zhou, Ming; Yu, Zongfu
2016-09-15
A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.
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
MDL, Collineations and the Fundamental Matrix
Maybank , Steve; Sturm , Peter
1999-01-01
International audience; Scene geometry can be inferred from point correspondences between two images. The inference process includes the selection of a model. Four models are considered: background (or null), collineation, affine fundamental matrix and fundamental matrix. It is shown how Minimum Description Length (MDL) can be used to compare the different models. The main result is that there is little reason for preferring the fundamental matrix model over the collineation model, even when ...
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.
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)
A wave propagation matrix method in semiclassical theory
International Nuclear Information System (INIS)
Lee, S.Y.; Takigawa, N.
1977-05-01
A wave propagation matrix method is used to derive the semiclassical formulae of the multiturning point problem. A phase shift matrix and a barrier transformation matrix are introduced to describe the processes of a particle travelling through a potential well and crossing a potential barrier respectively. The wave propagation matrix is given by the products of phase shift matrices and barrier transformation matrices. The method to study scattering by surface transparent potentials and the Bloch wave in solids is then applied
Structure of high excited nuclear states and elastic scattering
International Nuclear Information System (INIS)
Zhivopistsev, F.A.; Rzhevskij, E.S.
1979-01-01
An approach to a unified description of nuclear reactions and nuclear structure based on the formalism of the quantum Green functions and on the ideas of the theory of finite Fermi systems has been formulated. New structural vertices are introduced, which are responsible for nucleon collectivization in an atomic nucleus and for the excitation of many-phonon, quasideuteron, quasitriton and other configurations. The vertices define both the processes of particle scattering by atomic nuclei (T matrix and optical potentials) and the nuclear structure (secular equations and wave functions). The vertices are determined from the equations with effective many-particle forces Fsub(nm)sup(c). In their turn the Fsub(nm)sup(c) forces are either determined from a comparison of theory and experiment, or calculated from the equations with more fundamental nucleon-nucleon forces in a nucleus. The effective forces Fsub(nm)sup(c) are more universal than the constants of the theory of finite Fermi-systems, which extends the boundaries of applicability of the particle-hole formalism in the description of nuclear processes. In this approach the traditional methods of description of the nuclear structure, based on particular models of hamiltonian and wave functions, acquire a natural interpretation
Variation of entanglement entropy in scattering process
Energy Technology Data Exchange (ETDEWEB)
Seki, Shigenori, E-mail: sigenori@hanyang.ac.kr [Research Institute for Natural Science, Hanyang University, Seoul 133-791 (Korea, Republic of); Park, I.Y., E-mail: inyongpark05@gmail.com [Department of Applied Mathematics, Philander Smith College, Little Rock, AR 72223 (United States); Sin, Sang-Jin, E-mail: sjsin@hanyang.ac.kr [Department of Physics, Hanyang University, Seoul 133-791 (Korea, Republic of)
2015-04-09
In a scattering process, the final state is determined by an initial state and an S-matrix. We focus on two-particle scattering processes and consider the entanglement between these particles. For two types initial states, i.e., an unentangled state and an entangled one, we calculate perturbatively the change of entanglement entropy from the initial state to the final one. Then we show a few examples in a field theory and in quantum mechanics.
Energy Technology Data Exchange (ETDEWEB)
Pratt, R.H., E-mail: rpratt@pitt.ed [Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 (United States); LaJohn, L.A., E-mail: lal18@pitt.ed [Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 (United States); Florescu, V., E-mail: flor@barutu.fizica.unibuc.r [Centre for Advanced Quantum Physics, University of Bucharest, MG-11 Bucharest-Magurele, 077125 Magurele (Romania); Suric, T., E-mail: suric@irb.h [R. Boskovic Institute, Bijenicka 54, 10000 Zagreb (Croatia); Chatterjee, B.K., E-mail: barun_k_chatterjee@yahoo.co [Department of Physics, Bose Institute, Kolkata 700009 (India); Roy, S.C., E-mail: suprakash.roy@gmail.co [Department of Physics, Bose Institute, Kolkata 700009 (India)
2010-02-15
We review the standard theory of Compton scattering from bound electrons, and we describe recent findings that require modification of the usual understanding, noting the nature of consequences for experiment. The subject began with Compton and scattering from free electrons. Experiment actually involved bound electrons, and this was accommodated with the use of impulse approximation (IA), which described inelastic scattering from bound electrons in terms of scattering from free electrons. This was good for the Compton peak but failed for soft final photons. The standard theory was formalized by Eisenberger and Platzman (EP) [1970. Phys. Rev. A 2, 415], whose work also suggested why impulse approximation was better than one would expect, for doubly differential cross sections (DDCS), but not for triply differential cross sections (TDCS). A relativistic version of IA (RIA) was worked out by Ribberfors [1975. Phys. Rev. B 12, 2067]. And Suric et al. [1991. Phys. Rev. Lett. 67, 189] and Bergstrom et al. [1993. Phys. Rev. A 48, 1134] developed a full relativistic second order S-matrix treatment, not making impulse approximation, but within independent particle approximation (IPA). Newer developments in the theory of Compton scattering include: (1) Demonstration that the EP estimates of the validity of IA are incorrect, although the qualitative conclusion remains unchanged; IA is not to be understood as the first term in a standard series expansion. (2) The greater validity of IA for DDCS than for the TDCS, which when integrated give DDCS, is related to the existence of a sum rule, only valid for DDCS. (3) The so-called 'asymmetry' of a Compton profile is primarily to be understood as simply the shift of the peak position in the profile; symmetric and anti-symmetric deviations from a shifted Compton profile are very small, except for high Z inner shells where further p{sup -}>.A{sup -}> effects come into play. (4) Most relativistic effects, except at low
International Nuclear Information System (INIS)
Pratt, R.H.; LaJohn, L.A.; Florescu, V.; Suric, T.; Chatterjee, B.K.; Roy, S.C.
2010-01-01
We review the standard theory of Compton scattering from bound electrons, and we describe recent findings that require modification of the usual understanding, noting the nature of consequences for experiment. The subject began with Compton and scattering from free electrons. Experiment actually involved bound electrons, and this was accommodated with the use of impulse approximation (IA), which described inelastic scattering from bound electrons in terms of scattering from free electrons. This was good for the Compton peak but failed for soft final photons. The standard theory was formalized by Eisenberger and Platzman (EP) [1970. Phys. Rev. A 2, 415], whose work also suggested why impulse approximation was better than one would expect, for doubly differential cross sections (DDCS), but not for triply differential cross sections (TDCS). A relativistic version of IA (RIA) was worked out by Ribberfors [1975. Phys. Rev. B 12, 2067]. And Suric et al. [1991. Phys. Rev. Lett. 67, 189] and Bergstrom et al. [1993. Phys. Rev. A 48, 1134] developed a full relativistic second order S-matrix treatment, not making impulse approximation, but within independent particle approximation (IPA). Newer developments in the theory of Compton scattering include: (1) Demonstration that the EP estimates of the validity of IA are incorrect, although the qualitative conclusion remains unchanged; IA is not to be understood as the first term in a standard series expansion. (2) The greater validity of IA for DDCS than for the TDCS, which when integrated give DDCS, is related to the existence of a sum rule, only valid for DDCS. (3) The so-called 'asymmetry' of a Compton profile is primarily to be understood as simply the shift of the peak position in the profile; symmetric and anti-symmetric deviations from a shifted Compton profile are very small, except for high Z inner shells where further p → .A → effects come into play. (4) Most relativistic effects, except at low energies, are to be
Fluorescent and Raman scattering by molecules embedded in small particles: Final report
International Nuclear Information System (INIS)
Chew, H.; McNulty, P.J.
1987-02-01
The model takes into account the physical properties and the morphology of the particles, as well as the locations of the scatter(s). Brief descriptions of various applications of the model are presented. Brief descriptions of experimental studies of scattering by finite dielectric and cylindrical microstructures in plastic track detector plane surfaces are given
Bhatia, Rajendra
1997-01-01
A good part of matrix theory is functional analytic in spirit. This statement can be turned around. There are many problems in operator theory, where most of the complexities and subtleties are present in the finite-dimensional case. My purpose in writing this book is to present a systematic treatment of methods that are useful in the study of such problems. This book is intended for use as a text for upper division and gradu ate courses. Courses based on parts of the material have been given by me at the Indian Statistical Institute and at the University of Toronto (in collaboration with Chandler Davis). The book should also be useful as a reference for research workers in linear algebra, operator theory, mathe matical physics and numerical analysis. A possible subtitle of this book could be Matrix Inequalities. A reader who works through the book should expect to become proficient in the art of deriving such inequalities. Other authors have compared this art to that of cutting diamonds. One first has to...
Spectroscopy, scattering, and KK molecules
Energy Technology Data Exchange (ETDEWEB)
Weinstein, J. [Univ. of Mississippi, University, MS (United States)
1994-04-01
The author presents a pedagogical description of a new theoretical technique, based on the multichannel Schroedinger equation, for simultaneously applying the quark model to both meson spectroscopy and meson-meson scattering. This is an extension of an earlier analysis which led to the prediction that the f{sub o}(975) and a{sub o}(980) scalar mesons are K{bar K} molecular states.
Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.
2016-07-01
Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.
Towards Google matrix of brain
Energy Technology Data Exchange (ETDEWEB)
Shepelyansky, D.L., E-mail: dima@irsamc.ups-tlse.f [Laboratoire de Physique Theorique (IRSAMC), Universite de Toulouse, UPS, F-31062 Toulouse (France); LPT - IRSAMC, CNRS, F-31062 Toulouse (France); Zhirov, O.V. [Budker Institute of Nuclear Physics, 630090 Novosibirsk (Russian Federation)
2010-07-12
We apply the approach of the Google matrix, used in computer science and World Wide Web, to description of properties of neuronal networks. The Google matrix G is constructed on the basis of neuronal network of a brain model discussed in PNAS 105 (2008) 3593. We show that the spectrum of eigenvalues of G has a gapless structure with long living relaxation modes. The PageRank of the network becomes delocalized for certain values of the Google damping factor {alpha}. The properties of other eigenstates are also analyzed. We discuss further parallels and similarities between the World Wide Web and neuronal networks.
Towards Google matrix of brain
International Nuclear Information System (INIS)
Shepelyansky, D.L.; Zhirov, O.V.
2010-01-01
We apply the approach of the Google matrix, used in computer science and World Wide Web, to description of properties of neuronal networks. The Google matrix G is constructed on the basis of neuronal network of a brain model discussed in PNAS 105 (2008) 3593. We show that the spectrum of eigenvalues of G has a gapless structure with long living relaxation modes. The PageRank of the network becomes delocalized for certain values of the Google damping factor α. The properties of other eigenstates are also analyzed. We discuss further parallels and similarities between the World Wide Web and neuronal networks.
Double hard scattering without double counting
Energy Technology Data Exchange (ETDEWEB)
Diehl, Markus [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gaunt, Jonathan R. [VU Univ. Amsterdam (Netherlands). NIKHEF Theory Group; Schoenwald, Kay [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2017-02-15
Double parton scattering in proton-proton collisions includes kinematic regions in which two partons inside a proton originate from the perturbative splitting of a single parton. This leads to a double counting problem between single and double hard scattering. We present a solution to this problem, which allows for the definition of double parton distributions as operator matrix elements in a proton, and which can be used at higher orders in perturbation theory. We show how the evaluation of double hard scattering in this framework can provide a rough estimate for the size of the higher-order contributions to single hard scattering that are affected by double counting. In a numeric study, we identify situations in which these higher-order contributions must be explicitly calculated and included if one wants to attain an accuracy at which double hard scattering becomes relevant, and other situations where such contributions may be neglected.
Raman scattering of light off a superconductor
International Nuclear Information System (INIS)
Cuden, C.B.
1976-01-01
Raman scattering off a superconducting surface is formulated using Kubo's nonlinear response theory in a form suitable for systematic diagrammatic expansion. The effects of the sample surface are correctly taken into account. It is shown that in the presence of vacuum polarization processes, the contribution to the scattering efficiency from the density-density correlation function considered in the literature, is reduced. The relevant four-vertex parts, describing inelastic scattering of light by electronic excitations via intermediate interband states in a superconductor, are calculated. Frequency and temperature dependence of the relative scattering efficiency for the large momentum transfer (Pippard limit), and constant transition matrix elements, are obtained. The estimated magnitude of the total scattering efficiency is of the order of 10 -11
Double hard scattering without double counting
International Nuclear Information System (INIS)
Diehl, Markus; Gaunt, Jonathan R.
2017-02-01
Double parton scattering in proton-proton collisions includes kinematic regions in which two partons inside a proton originate from the perturbative splitting of a single parton. This leads to a double counting problem between single and double hard scattering. We present a solution to this problem, which allows for the definition of double parton distributions as operator matrix elements in a proton, and which can be used at higher orders in perturbation theory. We show how the evaluation of double hard scattering in this framework can provide a rough estimate for the size of the higher-order contributions to single hard scattering that are affected by double counting. In a numeric study, we identify situations in which these higher-order contributions must be explicitly calculated and included if one wants to attain an accuracy at which double hard scattering becomes relevant, and other situations where such contributions may be neglected.
Mueller matrix polarimetry for the characterization of complex ...
Indian Academy of Sciences (India)
Scattering; polarization; Mueller matrix; wave propagation in random media; ... Initial biomedical applications of this novel general method for polarimetry analysis in random media are also presented. ... Pramana – Journal of Physics | News.
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)
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
Magnetic scattering of neutrons by atoms
International Nuclear Information System (INIS)
Stassis, C.; Deckman, H.W.
1976-01-01
The magnetic scattering of neutrons by an atom or ion possessing both a spin and orbital magnetic moment is examined. For an atom in the 1sup(n) electronic configuration the magnetic scattering amplitude is determined by matrix elements of even-order electric and odd-order magnetic multipoles, whose order of multipolarity k is less than or equal to 21 + 1. The calculation of the matrix elements of these multipoles is separated into evaluating radial matrix elements and matrix elements of the Racah tensors Wsup(0,k) and Wsup(1,k') where k is an even integar less than or equal to 21. The calculation of the matrix elements of these tensors is considerably simplified by selection rules based on the groups Sp(41 + 2), R(21 + 1), R(3) and in the case of f-electrons, the special group G 2 . It is shown that, in the case of elastic scattering by an atom or an ion whose state is a single Russell-Saunders state, the magnetic scattering amplitude can be written in the conventional form p(q)qsub(m).sigma. General expressions for the amplitude p(q) as well as the elastic magnetic form factor are obtained. The evaluation of the coherent magnetic scattering amplitude by an atom in a magnetic field is discussed, and the small-q approximation to the elastic magnetic scattering is considered. The formation is illustrated for the important case of d- and f-electrons. The generalization of the formalism to the case of mixed atomic configurations is examined in some detail. (author)
Time-reversal of electromagnetic scattering for small scatterer classification
International Nuclear Information System (INIS)
Smith, J Torquil; Berryman, James G
2012-01-01
Time-reversal operators, or the alternatively labelled, but equivalent, multistatic response matrix methods, are used to show how to determine the number of scatterers present in an electromagnetic scattering scenario that might be typical of UneXploded Ordinance (UXO) detection, classification and removal applications. Because the nature of the target UXO application differs from that of many other common inversion problems, emphasis is placed here on classification and enumeration rather than on detailed imaging. The main technical issues necessarily revolve around showing that it is possible to find a sufficient number of constraints via multiple measurements (i.e. using several distinct views at the target site) to solve the enumeration problem. The main results show that five measurements with antenna pairs are generally adequate to solve the classification and enumeration problems. However, these results also demonstrate a need for decreasing noise levels in the multistatic matrix as the number n of scatterers increases for the intended practical applications of the method. (paper)
Basic matrix algebra and transistor circuits
Zelinger, G
1963-01-01
Basic Matrix Algebra and Transistor Circuits deals with mastering the techniques of matrix algebra for application in transistors. This book attempts to unify fundamental subjects, such as matrix algebra, four-terminal network theory, transistor equivalent circuits, and pertinent design matters. Part I of this book focuses on basic matrix algebra of four-terminal networks, with descriptions of the different systems of matrices. This part also discusses both simple and complex network configurations and their associated transmission. This discussion is followed by the alternative methods of de
Convergence of the multiple scattering expansion in XAFS and XANES
International Nuclear Information System (INIS)
Rehr, J.J.
1992-01-01
The convergence of the multiple-scattering expansion of XAFS and XANES by explicit path-bypath calculations. The approach is based on the fast scattering matrix formalism of Rehr and Albers, together with an automated path finder and filters that exclude negligible paths. High-order scattering terms are found to be essential, especially at low energies. Several factors including the magnitude of curved wave scattering amplitudes, inelastic losses and multiple-scattering Debye-Waller factors control convergence of the expansion. The convergence is illustrated explicitly for the case of diatomic molecules
Hard scattering and gauge/string duality
International Nuclear Information System (INIS)
Polchinski, Joseph; Strassler, Matthew J.
2002-01-01
We consider high-energy fixed-angle scattering of glueballs in confining gauge theories that have supergravity duals. Although the effective description is in terms of the scattering of strings, we find that the amplitudes are hard (power law). This is a consequence of the warped geometry of the dual theory, which has the effect that in an inertial frame the string process is never in the soft regime. At small angle we find hard and Regge behaviors in different kinematic regions
pp elastic scattering at LHC energies
Energy Technology Data Exchange (ETDEWEB)
Kohara, A.K.; Ferreira, E.; Kodama, T. [Universidade Federal do Rio de Janeiro, Instituto de Fisica, C.P. 68528, Rio de Janeiro, RJ (Brazil)
2014-11-15
Using a unified analytic representation for the elastic scattering amplitudes of pp scattering valid for all energies above 20 GeV, the behavior of observables in the LHC collisions in the range √(s) = 2.76-14 TeV is discussed. After the precise description of dσ/dt at 7 TeV, we discuss the energy dependence of the amplitudes and expect that the proposed analytical forms give equally good predictions for the future experiments. (orig.)
pp elastic scattering at LHC energies
International Nuclear Information System (INIS)
Kohara, A.K.; Ferreira, E.; Kodama, T.
2014-01-01
Using a unified analytic representation for the elastic scattering amplitudes of pp scattering valid for all energies above 20 GeV, the behavior of observables in the LHC collisions in the range √(s) = 2.76-14 TeV is discussed. After the precise description of dσ/dt at 7 TeV, we discuss the energy dependence of the amplitudes and expect that the proposed analytical forms give equally good predictions for the future experiments. (orig.)
Scattering on p-adic and on adelic symmetric spaces
International Nuclear Information System (INIS)
Freund, P.G.O.; Chicago Univ., IL
1991-01-01
Explicit S-matrices are constructed for scattering on p-adic hyperbolic planes. Combining these with the known S-matrix on the real hyperbolic plane, an adelic S-matrix is obtained. It has poles at the nontrivial zeros of the Riemann zeta-function, and is closely related to scattering on the modular domain of the real hyperbolic plane. Generalizations of this work and their possible arithmetic relevance are outlined. (orig.)
Plane-wave scattering from half-wave dipole arrays
DEFF Research Database (Denmark)
Jensen, Niels E.
1970-01-01
A matrix equation for determination of plane-wave scattering from arrays of thin short-circuited dipoles of lengths about half a wavelength is derived. Numerical and experimental results are presented for linear, circular, and concentric circular arrays.......A matrix equation for determination of plane-wave scattering from arrays of thin short-circuited dipoles of lengths about half a wavelength is derived. Numerical and experimental results are presented for linear, circular, and concentric circular arrays....
Study of elastic scattering between heavy ions. Reaction channel influence
International Nuclear Information System (INIS)
Doubre, Hubert.
1978-01-01
The role of absorption on the behavior of heavy ion angular distributions and excitaton functions has been investigated on light and medium mass systems. Comparison between 20 Ne+ 12 C and 16 O+ 16 O systems which lead to the same compound nucleus, shows that it originates from the direct channels strongly coupled to the entrance channel. Structures in the excitation functions occur for almost all the light systems and it is shown that the damping observed for heavier systems such as 40 Ca+ 40 Ca, essentially results on the predominance of Coulomb effects which hide the nuclear structure effects. Thus no valuable information on the details of S-matrix can be extracted for such an heavy system. A coherent description of the elastic scattering, based on a splitting of the scattering amplitude into two components, the modulus of each component varying smoothly as a function of energy and angle. The interference between these sub-amplitudes give rise to interference effects in angular distributions and excitation functions. The study of the main reaction channels of the 40 Ca+ 40 Ca system - i.e. deep inelastic reactions and fusion - also shows that the closed-shell nature of the interacting nuclei does not play any role in these processes due to the excitation processes in the first stage of the reactions which destroy the specific structure of the nuclei [fr
International Nuclear Information System (INIS)
Ahn, Changrim; Nepomechie, Rafael I.; Suzuki, Junji
2008-01-01
Beisert et al. have identified an integrable SU(2,2) quantum spin chain which gives the one-loop anomalous dimensions of certain operators in large N c QCD. We derive a set of nonlinear integral equations (NLIEs) for this model, and compute the scattering matrix of the various (in particular, magnon) excitations
Bidirectional optical scattering facility
Federal Laboratory Consortium — Goniometric optical scatter instrument (GOSI)The bidirectional reflectance distribution function (BRDF) quantifies the angular distribution of light scattered from a...
S matrix theory of the massive Thirring model
International Nuclear Information System (INIS)
Berg, B.
1980-01-01
The S matrix theory of the massive Thirring model, describing the exact quantum scattering of solitons and their boundstates, is reviewed. Treated are: Factorization equations and their solution, boundstates, generalized Jost functions and Levinson's theorem, scattering of boundstates, 'virtual' and anomalous thresholds. (orig.) 891 HSI/orig. 892 MKO
International Nuclear Information System (INIS)
Craps, Ben; Sethi, Savdeep; Verlinde, Erik
2005-01-01
The light-like linear dilaton background represents a particularly simple time-dependent 1/2 BPS solution of critical type-IIA superstring theory in ten dimensions. Its lift to M-theory, as well as its Einstein frame metric, are singular in the sense that the geometry is geodesically incomplete and the Riemann tensor diverges along a light-like subspace of codimension one. We study this background as a model for a big bang type singularity in string theory/M-theory. We construct the dual Matrix theory description in terms of a (1+1)-d supersymmetric Yang-Mills theory on a time-dependent world-sheet given by the Milne orbifold of (1+1)-d Minkowski space. Our model provides a framework in which the physics of the singularity appears to be under control
Energy Technology Data Exchange (ETDEWEB)
Craps, Ben [Instituut voor Theoretische Fysica, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Sethi, Savdeep [Enrico Fermi Institute, University of Chicago, Chicago, IL 60637 (United States); Verlinde, Erik [Instituut voor Theoretische Fysica, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)
2005-10-15
The light-like linear dilaton background represents a particularly simple time-dependent 1/2 BPS solution of critical type-IIA superstring theory in ten dimensions. Its lift to M-theory, as well as its Einstein frame metric, are singular in the sense that the geometry is geodesically incomplete and the Riemann tensor diverges along a light-like subspace of codimension one. We study this background as a model for a big bang type singularity in string theory/M-theory. We construct the dual Matrix theory description in terms of a (1+1)-d supersymmetric Yang-Mills theory on a time-dependent world-sheet given by the Milne orbifold of (1+1)-d Minkowski space. Our model provides a framework in which the physics of the singularity appears to be under control.
High energy asymptotics of the scattering amplitude for the ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Keywords. Scattering matrix; asymptotic expansion; high energy; diagonal singula- ..... (see subsection 2 of § 3) with functions of the generator of dilations. A = 1. 2 d ..... ness in quantum scattering theory, Ann. Inst. Henri Poincaré, Phys. Théor.
Lectures on matrix field theory
Ydri, Badis
2017-01-01
These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students – with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications – these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.
Absorption in multiple scattering systems of coated spheres: design applications
International Nuclear Information System (INIS)
Stout, Brian; Andraud, Christine; Stout, Sophie; Lafait, Jacques
2003-01-01
We illustrate the utility of some recently derived transfer matrix methods for electromagnetic scattering calculations in systems composed of coated spherical scatterers. Any of the spherical coatings, cores, or host media may be composed of absorbing materials. Our formulae permit the calculation of local absorption in either orientation fixed or orientation averaged situations. We introduce methods for estimating the macroscopic transport properties of such media, and show how our scattering calculations can permit 'design' optimization of macroscopic properties
Directory of Open Access Journals (Sweden)
Nataša Lah
2016-01-01
Full Text Available Taking into account the fact that, throughout history, certain artworks have been considered as “worth of watching” (according to the Greek etymon ἀξιοϑέατος / aksioteatos, preservation, or theorizing, while others were not, one is led to investigate the various types of evaluative descriptions. Those artworks that are more valuable than others, or simply valuable in themselves on the basis of rather specific features, have always represented the paradigmatic model for the evaluator, thus revealing the identitary nature of value as different from one epoch to another. Our aim has been to discern, with regard to this starting point, the way in which the process of evaluating artworks fits the general matrix of the universal theory of value, with its clearly distinguished levels of evaluation, beginning with value descriptions, continuing through the features of evaluation or abstract qualities of values extracted from these descriptions, and ending with value norms or systems of accepted generalizations in evaluation. Value standpoints in such an evaluation matrix represent dispositions or preferences in procedures, which reflect the norms or signifying concepts of the time. Corresponding procedures, or applications of the hierarchicized signification of artworks, are manifested in all known forms of artwork assessment: attribution, institutionalization, and setting of priorities in terms of exhibition, conservation, acquisition, restoration, and so on. Research in the history of European art-historical ideas has corroborated the hypothesis that, prior to the late 18th century, clear normative patterns were applied when it came to the evaluation of artworks. However, with the emergence of early Romanticism, this could no longer be done in the traditional way. Before the period in question, visual art was created (regardless of some stylistic discrepancies between individual authors and classified according to well-defined thematic
Scattering amplitudes in gauge theories
Henn, Johannes M
2014-01-01
At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum ...
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
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)
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)
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)
International Nuclear Information System (INIS)
Heggarty, J.W.
1999-06-01
For almost thirty years, sequential R-matrix computation has been used by atomic physics research groups, from around the world, to model collision phenomena involving the scattering of electrons or positrons with atomic or molecular targets. As considerable progress has been made in the understanding of fundamental scattering processes, new data, obtained from more complex calculations, is of current interest to experimentalists. Performing such calculations, however, places considerable demands on the computational resources to be provided by the target machine, in terms of both processor speed and memory requirement. Indeed, in some instances the computational requirements are so great that the proposed R-matrix calculations are intractable, even when utilising contemporary classic supercomputers. Historically, increases in the computational requirements of R-matrix computation were accommodated by porting the problem codes to a more powerful classic supercomputer. Although this approach has been successful in the past, it is no longer considered to be a satisfactory solution due to the limitations of current (and future) Von Neumann machines. As a consequence, there has been considerable interest in the high performance multicomputers, that have emerged over the last decade which appear to offer the computational resources required by contemporary R-matrix research. Unfortunately, developing codes for these machines is not as simple a task as it was to develop codes for successive classic supercomputers. The difficulty arises from the considerable differences in the computing models that exist between the two types of machine and results in the programming of multicomputers to be widely acknowledged as a difficult, time consuming and error-prone task. Nevertheless, unless parallel R-matrix computation is realised, important theoretical and experimental atomic physics research will continue to be hindered. This thesis describes work that was undertaken in
QUEUEING DISCIPLINES BASED ON PRIORITY MATRIX
Directory of Open Access Journals (Sweden)
Taufik I. Aliev
2014-11-01
Full Text Available The paper deals with queueing disciplines for demands of general type in queueing systems with multivendor load. A priority matrix is proposed to be used for the purpose of mathematical description of such disciplines, which represents the priority type (preemptive priority, not preemptive priority or no priority between any two demands classes. Having an intuitive and simple way of priority assignment, such description gives mathematical dependencies of system operation characteristics on its parameters. Requirements for priority matrix construction are formulated and the notion of canonical priority matrix is given. It is shown that not every matrix, constructed in accordance with such requirements, is correct. The notion of incorrect priority matrix is illustrated by an example, and it is shown that such matrixes do not ensure any unambiguousness and determinacy in design of algorithm, which realizes corresponding queueing discipline. Rules governing construction of correct matrixes are given for canonical priority matrixes. Residence time for demands of different classes in system, which is the sum of waiting time and service time, is considered as one of the most important characteristics. By introducing extra event method Laplace transforms for these characteristics are obtained, and mathematical dependencies are derived on their basis for calculation of two first moments for corresponding characteristics of demands queueing
Quantum theory of scattering of atoms and diatomic molecules by solid surfaces
International Nuclear Information System (INIS)
Liu, W.S.
1973-01-01
The unitary treatment, based on standard t-matrix theory, of the quantum theory of scattering of atoms by solid surfaces, is extended to the scattering of particles having internal degrees of freedom by perfect harmonic crystalline surfaces. The diagonal matrix element of the interaction potential which enters into the quantum scattering theory is obtained to represent the potential for the specular beam. From the two-potential formula, the scattering intensities for the diffracted beams and the inelastic beams with or without internal transitions of the particles are obtained by solving the equation for the t-matrix elements. (author)
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)
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)
Light scattering in glass-ceramics
International Nuclear Information System (INIS)
Hendy, S.C.
2002-01-01
Full text: Glass-ceramic materials with microstructures comprised of dispersed nanocrystallites in a residual glass matrix show promise for many new technological applications. In particular, transparent glass-ceramics offer low thermal expansion and stability, in addition to the prospect of novel non-linear optical properties that can arise from the nanocrystallites. Good transparency requires low optical scattering and low atomic absorption. Light scattering in the glass-ceramic arises primarily from the glass-crystallite interface. The attenuation due to scattering (turbidity) will depend upon the difference in refractive index of the two phases and the size and distribution of nanocrystallites in the glass. Here we consider models of glass-ceramic structure formation and look at scattering in these model structures to increase our understanding of the transparency of glass-ceramics
Markov chain solution of photon multiple scattering through turbid slabs.
Lin, Ying; Northrop, William F; Li, Xuesong
2016-11-14
This work introduces a Markov Chain solution to model photon multiple scattering through turbid slabs via anisotropic scattering process, i.e., Mie scattering. Results show that the proposed Markov Chain model agree with commonly used Monte Carlo simulation for various mediums such as medium with non-uniform phase functions and absorbing medium. The proposed Markov Chain solution method successfully converts the complex multiple scattering problem with practical phase functions into a matrix form and solves transmitted/reflected photon angular distributions by matrix multiplications. Such characteristics would potentially allow practical inversions by matrix manipulation or stochastic algorithms where widely applied stochastic methods such as Monte Carlo simulations usually fail, and thus enable practical diagnostics reconstructions such as medical diagnosis, spray analysis, and atmosphere sciences.
Electron scattering and nuclear structure
International Nuclear Information System (INIS)
Frois, B.
1987-01-01
The search for the appropriate degrees of freedom to describe nuclei is the central focus of nuclear physics today. Therefore the authors explore in this review their current understanding of nuclear structure as defined by electromagnetic data. The precision of the electromagnetic probe allows us to define accurately the limits of present theoretical descriptions. The authors review here a broad range of subjects that have been addressed by recent experiments, from the study of meson exchange currents and single-particle distributions to collective excitations in heavy nuclei. However, they do not discuss elastic magnetic scattering, inelastic excitation of discrete states, or single-nucleon knockout reactions since these reactions were recently reviewed. The principal aim of this review is to offer a fresh perspective on nuclear structure, based on the new generation of electron scattering data presented here and in the above-mentioned articles
Munoz, O.; Volten, H.; Hovenier, J.W.; Veihelmann, B.; Zande, W.J. van der; Waters, L.; Rose, W.I.
2004-01-01
[1] We present measurements of the whole scattering matrix as a function of the scattering angle at a wavelength of 632.8 nm in the scattering angle range 3degrees - 174degrees of randomly oriented particles taken from seven samples of volcanic ashes corresponding to four different volcanic
Muñoz, O.; Volten, H.; Hovenier, J.W.; Veihelmann, B.; van der Zande, W.J.; Waters, L.B.F.M.; Rose, W.I.
2004-01-01
We present measurements of the whole scattering matrix as a function of the scattering angle at a wavelength of 632.8 nm in the scattering angle range 3°-174° of randomly oriented particles taken from seven samples of volcanic ashes corresponding to four different volcanic eruptions: the 18 May 1980
The Whiteness of Things and Light Scattering
Gratton, L. M.; Lopez-Arias, T.; Calza, G.; Oss, S.
2009-01-01
We discuss some simple experiments dealing with intriguing properties of light and its interaction with matter. In particular, we show how to emphasize that light reflection, refraction and scattering can provide a proper, physical description of human perception of the "colour" white. These experiments can be used in the classroom with an enquiry…
Elastic and inelastic electron and muon scattering
International Nuclear Information System (INIS)
Hand, L.N.
1977-01-01
The current status of experiments in the field of elastic and inelastic electron and muon scattering is discussed. The talk is divided into discussions of the single arm inclusive experiments at SLAC and Fermilab; the multiparticle inclusive experiments at SLAC, Fermilab und Cornell, and a description of selected results from exclusive channel measurements on electroproduced final states. (orig.) [de
Diffraction scattering and the parton model in QCD
International Nuclear Information System (INIS)
White, A.
1985-01-01
Arguments are presented that the validity of the parton model for hadron scattering in QCD is directly related to the occurrence of the Critical Pomeron description of diffraction scattering. An attractive route suggested for Electroweak and Grand Unification is also briefly described
Recent advances in Multi-Channel Algebraic Scattering
International Nuclear Information System (INIS)
Karataglidis, S.; Fraser, P. R.; Amos, K.; Canton, L.; Pisent, G.; Svenne, J. P.; Knijff, D. van der
2011-01-01
For coupled-channel descriptions of low-energy nucleon-induced interactions involving nuclei with particle-unstable exited states, it is necessary to include the widths of the target states. How those widths may affect the elastic scattering cross sections is examined within the framework of the Multi-Channel Algebraic Scattering (MCAS) method.
Multiple scattering and attenuation corrections in Deep Inelastic Neutron Scattering experiments
International Nuclear Information System (INIS)
Dawidowski, J; Blostein, J J; Granada, J R
2006-01-01
Multiple scattering and attenuation corrections in Deep Inelastic Neutron Scattering experiments are analyzed. The theoretical basis of the method is stated, and a Monte Carlo procedure to perform the calculation is presented. The results are compared with experimental data. The importance of the accuracy in the description of the experimental parameters is tested, and the implications of the present results on the data analysis procedures is examined
International Nuclear Information System (INIS)
Hemmady, Sameer; Zheng, Xing; Hart, James; Antonsen, Thomas M. Jr.; Ott, Edward; Anlage, Steven M.
2006-01-01
Statistical fluctuations in the eigenvalues of the scattering, impedance, and admittance matrices of two-port wave-chaotic systems are studied experimentally using a chaotic microwave cavity. These fluctuations are universal in that their properties are dependent only upon the degree of loss in the cavity. We remove the direct processes introduced by the nonideally coupled driving ports through a matrix normalization process that involves the radiation-impedance matrix of the two driving ports. We find good agreement between the experimentally obtained marginal probability density functions (PDFs) of the eigenvalues of the normalized impedance, admittance, and scattering matrix and those from random matrix theory (RMT). We also experimentally study the evolution of the joint PDF of the eigenphases of the normalized scattering matrix as a function of loss. Experimental agreement with the theory by Brouwer and Beenakker for the joint PDF of the magnitude of the eigenvalues of the normalized scattering matrix is also shown
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
Coulomb interaction in multiple scattering theory
International Nuclear Information System (INIS)
Ray, L.; Hoffmann, G.W.; Thaler, R.M.
1980-01-01
The treatment of the Coulomb interaction in the multiple scattering theories of Kerman-McManus-Thaler and Watson is examined in detail. By neglecting virtual Coulomb excitations, the lowest order Coulomb term in the Watson optical potential is shown to be a convolution of the point Coulomb interaction with the distributed nuclear charge, while the equivalent Kerman-McManus-Thaler Coulomb potential is obtained from an averaged, single-particle Coulombic T matrix. The Kerman-McManus-Thaler Coulomb potential is expressed as the Watson Coulomb term plus additional Coulomb-nuclear and Coulomb-Coulomb cross terms, and the omission of the extra terms in usual Kerman-McManus-Thaler applications leads to negative infinite total reaction cross section predictions and incorrect pure Coulomb scattering limits. Approximations are presented which eliminate these anomalies. Using the two-potential formula, the full projectile-nucleus T matrix is separated into two terms, one resulting from the distributed nuclear charge and the other being a Coulomb distorted nuclear T matrix. It is shown that the error resulting from the omission of the Kerman-McManus-Thaler Coulomb terms is effectively removed when the pure Coulomb T matrix in Kerman-McManus-Thaler is replaced by the analogous quantity in the Watson approach. Using the various approximations, theoretical angular distributions are obtained for 800 MeV p+ 208 Pb elastic scattering and compared with experimental data
Coherence effects in radiative scattering
International Nuclear Information System (INIS)
Knoll, J.; Lenk, R.
1993-03-01
The bremsstrahl-production of photons in dense matter is reinvestigated using the example of an exactly solvable quantum mechanical model in one space dimension. Coherence phenomena between successive radiative scatterings among the constituents lead to a modification of the production cross section in the medium relative to the incoherent quasi-free prescription used in kinetic models. Analytic expressions for the correction factor have been derived comparing the quantum rates with the corresponding incoherent quasi-free rates. The result has implications for the kinetic description of all kinds of radiative processes in nucleus-nucleus collisions, both on the level of hadron and parton dynamics. (orig.)
Modal Ring Method for the Scattering of Electromagnetic Waves
Baumeister, Kenneth J.; Kreider, Kevin L.
1993-01-01
The modal ring method for electromagnetic scattering from perfectly electric conducting (PEC) symmetrical bodies is presented. The scattering body is represented by a line of finite elements (triangular) on its outer surface. The infinite computational region surrounding the body is represented analytically by an eigenfunction expansion. The modal ring method effectively reduces the two dimensional scattering problem to a one-dimensional problem similar to the method of moments. The modal element method is capable of handling very high frequency scattering because it has a highly banded solution matrix.
Gaussian basis functions for highly oscillatory scattering wavefunctions
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.
CERN. Geneva
2016-01-01
In this talk I will describe recent work aiming to reinvigorate the 50 year old S-matrix program, which aims to constrain scattering of massive particles non-perturbatively. I will begin by considering quantum fields in anti-de Sitter space and show that one can extract information about the S-matrix by considering correlators in conformally invariant theories. The latter can be studied with "bootstrap" techniques, which allow us to constrain the S-matrix. In particular, in 1+1D one obtains bounds which are saturated by known integrable models. I will also show that it is also possible to directly constrain the S-matrix, without using the CFT crutch, by using crossing symmetry and unitarity. This alternative method is simpler and gives results in agreement with the previous approach. Both techniques are generalizable to higher dimensions.
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
Modeling small angle scattering data using FISH
International Nuclear Information System (INIS)
Elliott, T.; Buckely, C.E.
2002-01-01
Full text: Small angle neutron scattering (SANS) and small angle x-ray scattering (SAXS) are important techniques for the characterisation of samples on the nanometer scale. From the scattered intensity pattern information about the sample such as particle size distribution, concentration and particle interaction can be determined. Since the experimental data is in reciprocal space and information is needed about real space, modeling of the scattering data to obtain parameters is extremely important and several paradigms are available. The use of computer programs to analyze the data is imperative for a robust description of the sample to be obtained. This presentation gives an overview of the SAS process and describes the data-modeling program FISH, written by R. Heenan 1983-2000. The results of using FISH to obtain the particle size distribution of bubbles in the aluminum hydrogen system and other systems of interest are described. Copyright (2002) Australian X-ray Analytical Association Inc
Holmes, Jesse Curtis
established that depends on uncertainties in the physics models and methodology employed to produce the DOS. Through Monte Carlo sampling of perturbations from the reference phonon spectrum, an S(alpha, beta) covariance matrix may be generated. In this work, density functional theory and lattice dynamics in the harmonic approximation are used to calculate the phonon DOS for hexagonal crystalline graphite. This form of graphite is used as an example material for the purpose of demonstrating procedures for analyzing, calculating and processing thermal neutron inelastic scattering uncertainty information. Several sources of uncertainty in thermal neutron inelastic scattering calculations are examined, including sources which cannot be directly characterized through a description of the phonon DOS uncertainty, and their impacts are evaluated. Covariances for hexagonal crystalline graphite S(alpha, beta) data are quantified by coupling the standard methodology of LEAPR with a Monte Carlo sampling process. The mechanics of efficiently representing and processing this covariance information is also examined. Finally, with appropriate sensitivity information, it is shown that an S(alpha, beta) covariance matrix can be propagated to generate covariance data for integrated cross sections, secondary energy distributions, and coupled energy-angle distributions. This approach enables a complete description of thermal neutron inelastic scattering cross section uncertainties which may be employed to improve the simulation of nuclear systems.
Inelastic proton scattering at medium energy
International Nuclear Information System (INIS)
Love, W.G.
1980-01-01
Some of the most essential characteristics of the nucleon-nucleon interaction for probing nuclear structure at bombarding energies between 100 and 800 MeV are considered. With a local representation of the on-shell N-N t-matrix, data for a variety of specific transitions at IUCF and LAMPF energies are discussed with an emphasis on the nuclear structure information sampled by proton scattering. The importance of incorporating constraints on nuclear structure imposed by electron scattering is stressed. Some rather unique aspects of the (p,n) reaction at intermediate energies are discussed in terms of its energy dependence and nuclear structure sum rules. 11 figures
Relativistic scattering theory of charged spinless particles
International Nuclear Information System (INIS)
Alt, E.O.; Hannemann, M.
1986-01-01
In the context of relativistic quantum mechanics the scattering is discussed of two and three charged spinless particles. The corresponding transition operators are shown to satisfy four-dimensional Lippmann-Schwinger and eight-dimensional Faddeev-type equations, respectively. A simplified model of two particles with Coulomb interaction can be solved exactly. Calculations have been made of (i) the partial wave S-matrix from which the bound state spectrum has been extracted; the latter agrees with a fourth-order result of Schwinger; (ii) the full scattering amplitude which in the weak-field limit coincides with the expression derived by Fried et al. from eikonalized QED. (author)
Zhao, Yan; Stratt, Richard M.
2018-05-01
Surprisingly long-ranged intermolecular correlations begin to appear in isotropic (orientationally disordered) phases of liquid crystal forming molecules when the temperature or density starts to close in on the boundary with the nematic (ordered) phase. Indeed, the presence of slowly relaxing, strongly orientationally correlated, sets of molecules under putatively disordered conditions ("pseudo-nematic domains") has been apparent for some time from light-scattering and optical-Kerr experiments. Still, a fully microscopic characterization of these domains has been lacking. We illustrate in this paper how pseudo-nematic domains can be studied in even relatively small computer simulations by looking for order-parameter tensor fluctuations much larger than one would expect from random matrix theory. To develop this idea, we show that random matrix theory offers an exact description of how the probability distribution for liquid-crystal order parameter tensors converges to its macroscopic-system limit. We then illustrate how domain properties can be inferred from finite-size-induced deviations from these random matrix predictions. A straightforward generalization of time-independent random matrix theory also allows us to prove that the analogous random matrix predictions for the time dependence of the order-parameter tensor are similarly exact in the macroscopic limit, and that relaxation behavior of the domains can be seen in the breakdown of the finite-size scaling required by that random-matrix theory.
Measurement of Rank and Other Properties of Direct and Scattered Signals
Directory of Open Access Journals (Sweden)
Svante Björklund
2016-01-01
Full Text Available We have designed an experiment for low-cost indoor measurements of rank and other properties of direct and scattered signals with radar interference suppression in mind. The signal rank is important also in many other applications, for example, DOA (Direction of Arrival estimation, estimation of the number of and location of transmitters in electronic warfare, and increasing the capacity in wireless communications. In real radar applications, such measurements can be very expensive, for example, involving airborne radars with array antennas. We have performed the measurements in an anechoic chamber with several transmitters, a receiving array antenna, and a moving reflector. Our experiment takes several aspects into account: transmitted signals with different correlation, decorrelation of the signals during the acquisition interval, covariance matrix estimation, noise eigenvalue spread, calibration, near-field compensation, scattering in a rough surface, and good control of the influencing factors. With our measurements we have observed rank, DOA spectrum, and eigenpatterns of direct and scattered signals. The agreement of our measured properties with theoretic and simulated results in the literature shows that our experiment is realistic and sound. The detailed description of our experiment could serve as help for conducting other well-controlled experiments.
Multiple scattering of polarized light: comparison of Maxwell theory and radiative transfer theory.
Voit, Florian; Hohmann, Ansgar; Schäfer, Jan; Kienle, Alwin
2012-04-01
For many research areas in biomedical optics, information about scattering of polarized light in turbid media is of increasing importance. Scattering simulations within this field are mainly performed on the basis of radiative transfer theory. In this study a polarization sensitive Monte Carlo solution of radiative transfer theory is compared to exact Maxwell solutions for all elements of the scattering Müller matrix. Different scatterer volume concentrations are modeled as a multitude of monodisperse nonabsorbing spheres randomly positioned in a cubic simulation volume which is irradiated with monochromatic incident light. For all Müller matrix elements effects due to dependent scattering and multiple scattering are analysed. The results are in overall good agreement between the two methods with deviations related to dependent scattering being prominent for high volume concentrations and high scattering angles.
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...
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
Boundary description of Planckian scattering in curved spacetimes
Arcioni, G.; Haro, S. de; O'Loughlin, M.
2001-01-01
We show that for an eikonal limit of gravity in a space-time of any dimension with a non-vanishing cosmological constant, the Einstein - Hilbert action reduces to a boundary action. This boundary action describes the interaction of shock-waves up to the point ofevolution at which the forward
Description of two-proton radioactivity by the methods of the quantum theory of ternary fission
International Nuclear Information System (INIS)
Kadmenskij, S.G.
2005-01-01
Two-proton decay of spherical nuclei has been investigated on the base of the formalism of quantum mechanical theory of ternary fission. The suggested method of construction of partial two-proton-decay-width amplitudes and of asymptotics of the decaying nucleus wave functions allows to solve a problem of two-proton radioactivity description without the traditionally used in R-matrix approaches laborious sewing procedure for internal and external parent nucleus wave functions in three-body scheme. In the frame of diagonal approximation, the wave-function structure for Cooper pair of two emitted protons in parent nucleus was analyzed as well as the behavior of the wave function describing potential scattering of two-proton-decay products with taking into account decay channel coupling and properties of interaction potentials between these products [ru
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.
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
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
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)
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.
Efficiency criterion for teleportation via channel matrix, measurement matrix and collapsed matrix
Directory of Open Access Journals (Sweden)
Xin-Wei Zha
Full Text Available In this paper, three kinds of coefficient matrixes (channel matrix, measurement matrix, collapsed matrix associated with the pure state for teleportation are presented, the general relation among channel matrix, measurement matrix and collapsed matrix is obtained. In addition, a criterion for judging whether a state can be teleported successfully is given, depending on the relation between the number of parameter of an unknown state and the rank of the collapsed matrix. Keywords: Channel matrix, Measurement matrix, Collapsed matrix, Teleportation
Containment Code Validation Matrix
International Nuclear Information System (INIS)
Chin, Yu-Shan; Mathew, P.M.; Glowa, Glenn; Dickson, Ray; Liang, Zhe; Leitch, Brian; Barber, Duncan; Vasic, Aleks; Bentaib, Ahmed; Journeau, Christophe; Malet, Jeanne; Studer, Etienne; Meynet, Nicolas; Piluso, Pascal; Gelain, Thomas; Michielsen, Nathalie; Peillon, Samuel; Porcheron, Emmanuel; Albiol, Thierry; Clement, Bernard; Sonnenkalb, Martin; Klein-Hessling, Walter; Arndt, Siegfried; Weber, Gunter; Yanez, Jorge; Kotchourko, Alexei; Kuznetsov, Mike; Sangiorgi, Marco; Fontanet, Joan; Herranz, Luis; Garcia De La Rua, Carmen; Santiago, Aleza Enciso; Andreani, Michele; Paladino, Domenico; Dreier, Joerg; Lee, Richard; Amri, Abdallah
2014-01-01
The Committee on the Safety of Nuclear Installations (CSNI) formed the CCVM (Containment Code Validation Matrix) task group in 2002. The objective of this group was to define a basic set of available experiments for code validation, covering the range of containment (ex-vessel) phenomena expected in the course of light and heavy water reactor design basis accidents and beyond design basis accidents/severe accidents. It was to consider phenomena relevant to pressurised heavy water reactor (PHWR), pressurised water reactor (PWR) and boiling water reactor (BWR) designs of Western origin as well as of Eastern European VVER types. This work would complement the two existing CSNI validation matrices for thermal hydraulic code validation (NEA/CSNI/R(1993)14) and In-vessel core degradation (NEA/CSNI/R(2001)21). The report initially provides a brief overview of the main features of a PWR, BWR, CANDU and VVER reactors. It also provides an overview of the ex-vessel corium retention (core catcher). It then provides a general overview of the accident progression for light water and heavy water reactors. The main focus is to capture most of the phenomena and safety systems employed in these reactor types and to highlight the differences. This CCVM contains a description of 127 phenomena, broken down into 6 categories: - Containment Thermal-hydraulics Phenomena; - Hydrogen Behaviour (Combustion, Mitigation and Generation) Phenomena; - Aerosol and Fission Product Behaviour Phenomena; - Iodine Chemistry Phenomena; - Core Melt Distribution and Behaviour in Containment Phenomena; - Systems Phenomena. A synopsis is provided for each phenomenon, including a description, references for further information, significance for DBA and SA/BDBA and a list of experiments that may be used for code validation. The report identified 213 experiments, broken down into the same six categories (as done for the phenomena). An experiment synopsis is provided for each test. Along with a test description
5D Black Holes and Matrix Strings
Dijkgraaf, R; Verlinde, Herman L
1997-01-01
We derive the world-volume theory, the (non)-extremal entropy and background geometry of black holes and black strings constructed out of the NS IIA fivebrane within the framework of matrix theory. The CFT description of strings propagating in the black hole geometry arises as an effective field theory.
Extended biorthogonal matrix polynomials
Directory of Open Access Journals (Sweden)
Ayman Shehata
2017-01-01
Full Text Available The pair of biorthogonal matrix polynomials for commutative matrices were first introduced by Varma and Tasdelen in [22]. The main aim of this paper is to extend the properties of the pair of biorthogonal matrix polynomials of Varma and Tasdelen and certain generating matrix functions, finite series, some matrix recurrence relations, several important properties of matrix differential recurrence relations, biorthogonality relations and matrix differential equation for the pair of biorthogonal matrix polynomials J(A,B n (x, k and K(A,B n (x, k are discussed. For the matrix polynomials J(A,B n (x, k, various families of bilinear and bilateral generating matrix functions are constructed in the sequel.
DEFF Research Database (Denmark)
Birkedal, Dan; Shah, Jagdeep; Shchegrov, Andrei V.
2000-01-01
Resonant Rayleigh scattering from quantum well excitons is investigated using ultrafast spectral interferometry. We isolate the coherent Rayleigh scattering from incoherent luminescence in a single speckle. Averaging the resonant Rayleigh intensity over several speckles allows us to identify...... features in support of quantum corrections to the classical description of the underlying scattering process....
Matrix completion by deep matrix factorization.
Fan, Jicong; Cheng, Jieyu
2018-02-01
Conventional methods of matrix completion are linear methods that are not effective in handling data of nonlinear structures. Recently a few researchers attempted to incorporate nonlinear techniques into matrix completion but there still exists considerable limitations. In this paper, a novel method called deep matrix factorization (DMF) is proposed for nonlinear matrix completion. Different from conventional matrix completion methods that are based on linear latent variable models, DMF is on the basis of a nonlinear latent variable model. DMF is formulated as a deep-structure neural network, in which the inputs are the low-dimensional unknown latent variables and the outputs are the partially observed variables. In DMF, the inputs and the parameters of the multilayer neural network are simultaneously optimized to minimize the reconstruction errors for the observed entries. Then the missing entries can be readily recovered by propagating the latent variables to the output layer. DMF is compared with state-of-the-art methods of linear and nonlinear matrix completion in the tasks of toy matrix completion, image inpainting and collaborative filtering. The experimental results verify that DMF is able to provide higher matrix completion accuracy than existing methods do and DMF is applicable to large matrices. Copyright © 2017 Elsevier Ltd. All rights reserved.
Description of nuclear properties
International Nuclear Information System (INIS)
Faessler, A.
1991-01-01
The lectures want to give a survey about new developments in the description of nuclei. In a first chapter we try to derive nuclear properties from the basis theory of quantum chromodynamics. This is not rigorously possible. There are still many cracks in the bridge between QCD and nuclear structure. The basic ingredient for nuclear structure calculations is the nucleon-nucleon interaction. We shall discuss the nucleon-nucleon interaction in a quark model. In a further chapter we discuss the way to come from a bare nucleon-nucleon interaction in free space to an effective nucleon-nucleon interaction in a limited model space for nuclear structure calculations. Such nuclear structure calculations can be done as shell model calculations. But they are due to the large number of configurations limited to light nuclei. We discuss possibilities (MONSTER and VAMPIR) to enlarge the model space for medium heavy and heavy nuclei. As the example of the low lying isovector 1 + states we discuss collective models (Bohr - Mottelson Model, interacting Boson Model) with proton and neutron degrees of freedom. The same states can also be described microscopically with the Quasi-Particle Random Phase Approximation (QRPA). We discuss the removal of spurious states in RPA. We also discuss the calculation of form factors and compare with inelastic electron scattering data. Finally we apply QRPA to the double-beta decay. Grand unified models predict, that the neutrino is identical with his antiparticle, that it has a finite mass and a weak right-handed interaction. If these properties are found the standard model of the strong and the electro-weak interaction can not be correct. Presently we can only derive from lower limits of the half lives of neutrinoless double-beta decays upper limits of the neutrino mass and of the right-handedness of the weak interaction and lower limits of the mass of the right handed heavy vector boson, if a specific grand unified model is given. (author)
International Nuclear Information System (INIS)
Jayaswal, B.; Mazumder, S.
1998-09-01
Small-angle scattering data from strong scattering systems, e.g. porous materials, cannot be analysed invoking single scattering approximation as specimen needed to replicate the bulk matrix in essential properties are too thick to validate the approximation. The presence of multiple scattering is indicated by invalidity of the functional invariance property of the observed scattering profile with variation of sample thickness and/or wave length of the probing radiation. This article delineates how non accounting of multiple scattering affects the results of analysis and then how to correct the data for its effect. It deals with an algorithm to extract single scattering profile from small-angle scattering data affected by multiple scattering. The algorithm can process the scattering data and deduce single scattering profile in absolute scale. A software package, SIMSAS, is introduced for executing this inversion step. This package is useful both to simulate and to analyse multiple small-angle scattering data. (author)
Similarities and differences between antipp and pp scattering at TeV energies and beyond
International Nuclear Information System (INIS)
Gauron, P.; Nicolescu, B.
1986-12-01
The significant difference between the pp and antipp elastic dσ/dt discovered at the CERN ISR, and the behaviour of the antipp dσ/dt at the CERN collider, which have profound implications for the asymptotic behaviour of hadron scattering amplitudes, are explained in terms of a model theory based upon general S-matrix principles and a dynamical assumption of ''maximal strength'' for the strong interactions. Our model theory provides an excellent description of the pp and antipp data in the huge range 10 ≤ √s ≤ 630 GeV for /t/ ≤2.5 (GeV) 2 . Several striking consequences of the theory will be testable at Tevatron energies and beyond
Description of quantum states using in free space optic communication
Kučera, Petr
2017-11-01
In the article we concentrate our attention on the quantum description of states which are prepared by light sources. The main goal of the article is the determination of density matrix of background radiation source. It is shown that these matrix elements satisfy Geometric distribution in the number state representation.
Binding of matrix metalloproteinase inhibitors to extracellular matrix: 3D-QSAR analysis.
Zhang, Yufen; Lukacova, Viera; Bartus, Vladimir; Nie, Xiaoping; Sun, Guorong; Manivannan, Ethirajan; Ghorpade, Sandeep R; Jin, Xiaomin; Manyem, Shankar; Sibi, Mukund P; Cook, Gregory R; Balaz, Stefan
2008-10-01
Binding to the extracellular matrix, one of the most abundant human protein complexes, significantly affects drug disposition. Specifically, the interactions with extracellular matrix determine the free concentrations of small molecules acting in tissues, including signaling peptides, inhibitors of tissue remodeling enzymes such as matrix metalloproteinases, and other drug candidates. The nature of extracellular matrix binding was elucidated for 63 matrix metalloproteinase inhibitors, for which the association constants to an extracellular matrix mimic were reported here. The data did not correlate with lipophilicity as a common determinant of structure-nonspecific, orientation-averaged binding. A hypothetical structure of the binding site of the solidified extracellular matrix surrogate was analyzed using the Comparative Molecular Field Analysis, which needed to be applied in our multi-mode variant. This fact indicates that the compounds bind to extracellular matrix in multiple modes, which cannot be considered as completely orientation-averaged and exhibit structural dependence. The novel comparative molecular field analysis models, exhibiting satisfactory descriptive and predictive abilities, are suitable for prediction of the extracellular matrix binding for the untested chemicals, which are within applicability domains. The results contribute to a better prediction of the pharmacokinetic parameters such as the distribution volume and the tissue-blood partition coefficients, in addition to a more imminent benefit for the development of more effective matrix metalloproteinase inhibitors.
Zuffada, Cinzia; Crisp, David
1997-01-01
Reliable descriptions of the optical properties of clouds and aerosols are essential for studies of radiative transfer in planetary atmospheres. The scattering algorithms provide accurate estimates of these properties for spherical particles with a wide range of sizes and refractive indices, but these methods are not valid for non-spherical particles (e.g., ice crystals, mineral dust, and smoke). Even though a host of methods exist for deriving the optical properties of nonspherical particles that are very small or very large compared with the wavelength, only a few methods are valid in the resonance regime, where the particle dimensions are comparable with the wavelength. Most such methods are not ideal for particles with sharp edges or large axial ratios. We explore the utility of an integral equation approach for deriving the single-scattering optical properties of axisymmetric particles with large axial ratios. The accuracy of this technique is shown for spheres of increasing size parameters and an ensemble of randomly oriented prolate spheroids of size parameter equal to 10.079368. In this last case our results are compared with published results obtained with the T-matrix approach. Next we derive cross sections, single-scattering albedos, and phase functions for cylinders, disks, and spheroids of ice with dimensions extending from the Rayleigh to the geometric optics regime. Compared with those for a standard surface integral equation method, the storage requirement and the computer time needed by this method are reduced, thus making it attractive for generating databases to be used in multiple-scattering calculations. Our results show that water ice disks and cylinders are more strongly absorbing than equivalent volume spheres at most infrared wavelengths. The geometry of these particles also affects the angular dependence of the scattering. Disks and columns with maximum linear dimensions larger than the wavelength scatter much more radiation in the forward
International Nuclear Information System (INIS)
Rehfeld, Niklas; Alber, Markus
2007-01-01
Scatter correction techniques in iterative positron emission tomography (PET) reconstruction increasingly utilize Monte Carlo (MC) simulations which are very well suited to model scatter in the inhomogeneous patient. Due to memory constraints the results of these simulations are not stored in the system matrix, but added or subtracted as a constant term or recalculated in the projector at each iteration. This implies that scatter is not considered in the back-projector. The presented scheme provides a method to store the simulated Monte Carlo scatter in a compressed scatter system matrix. The compression is based on parametrization and B-spline approximation and allows the formation of the scatter matrix based on low statistics simulations. The compression as well as the retrieval of the matrix elements are parallelizable. It is shown that the proposed compression scheme provides sufficient compression so that the storage in memory of a scatter system matrix for a 3D scanner is feasible. Scatter matrices of two different 2D scanner geometries were compressed and used for reconstruction as a proof of concept. Compression ratios of 0.1% could be achieved and scatter induced artifacts in the images were successfully reduced by using the compressed matrices in the reconstruction algorithm
On the scattering over the GKP vacuum
International Nuclear Information System (INIS)
Fioravanti, Davide; Piscaglia, Simone; Rossi, Marco
2014-01-01
By converting the asymptotic Bethe Ansatz (ABA) of N=4 SYM into non-linear integral equations, we find 2D scattering amplitudes of excitations on top of the GKP vacuum. We prove that this is a suitable and powerful set-up for the understanding and computation of the whole S-matrix. We show that all the amplitudes depend on the fundamental scalar–scalar one
Neutron scattering from a substitutional mass defect
International Nuclear Information System (INIS)
Williams, R.D.; Lovesey, S.W.
1985-06-01
The dynamic structure factor is calculated for a low concentration of light mass scatterers substituted in a cubic crystal matrix. A new numerical method for the exact calculation is demonstrated. A local density of states for the low momentum transfer limit, and the shifts and widths of the oscillator peaks in the high momentum transfer limit are derived. The limitations of an approximation which decouples the defect from the lattice is discussed. (author)
Neutron Scattering in Biology Techniques and Applications
Fitter, Jörg; Katsaras, John
2006-01-01
The advent of new neutron facilities and the improvement of existing sources and instruments world wide supply the biological community with many new opportunities in the areas of structural biology and biological physics. The present volume offers a clear description of the various neutron-scattering techniques currently being used to answer biologically relevant questions. Their utility is illustrated through examples by some of the leading researchers in the field of neutron scattering. This volume will be a reference for researchers and a step-by-step guide for young scientists entering the field and the advanced graduate student.
Fast-neutron scattering from elemental cadmium
International Nuclear Information System (INIS)
Smith, A.B.; Guenther, P.T.
1982-07-01
Neutron differential-elastic-scattering cross sections of elemental cadmium are measured from approx. = 1.5 to 4.0 MeV at incident-neutron energy intervals of 50 to 200 keV and at 10 to 20 scattering angles distributed between approx. = 20 and 160 degrees. Concurrently, lumped-level neutron inelastic-excitation cross sections are measured. The experimental results are used to deduce parameters of an optical-statistical model that is descriptive of the observables and are compared with corresponding quantities given in ENDF/B-V
Scattering equations, supergravity integrands, and pure spinors
Energy Technology Data Exchange (ETDEWEB)
Adamo, Tim; Casali, Eduardo [Department of Applied Mathematics & Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2015-05-25
The tree-level S-matrix of type II supergravity can be computed in scattering equation form by correlators in a worldsheet theory analogous to a chiral, infinite tension limit of the pure spinor formalism. By defining a non-minimal version of this theory, we give a prescription for computing correlators on higher genus worldsheets which manifest space-time supersymmetry. These correlators are conjectured to provide the loop integrands of supergravity scattering amplitudes, supported on the scattering equations. We give non-trivial evidence in support of this conjecture at genus one and two with four external states. Throughout, we find a close correspondence with the pure spinor formalism of superstring theory, particularly regarding regulators and zero-mode counting.
Scattering equations, supergravity integrands, and pure spinors
International Nuclear Information System (INIS)
Adamo, Tim; Casali, Eduardo
2015-01-01
The tree-level S-matrix of type II supergravity can be computed in scattering equation form by correlators in a worldsheet theory analogous to a chiral, infinite tension limit of the pure spinor formalism. By defining a non-minimal version of this theory, we give a prescription for computing correlators on higher genus worldsheets which manifest space-time supersymmetry. These correlators are conjectured to provide the loop integrands of supergravity scattering amplitudes, supported on the scattering equations. We give non-trivial evidence in support of this conjecture at genus one and two with four external states. Throughout, we find a close correspondence with the pure spinor formalism of superstring theory, particularly regarding regulators and zero-mode counting.
DEFF Research Database (Denmark)
Petersen, Kaare Brandt; Pedersen, Michael Syskind
Matrix identities, relations and approximations. A desktop reference for quick overview of mathematics of matrices.......Matrix identities, relations and approximations. A desktop reference for quick overview of mathematics of matrices....
Stimulated light emission in a dielectrically disordered composite porous matrix
Gross, E.; Künzner, N.; Diener, J.; Fujii, Minoru; Timoshenko, V. Yu.; Kovalev, D.
2005-06-01
We report on a medium exhibiting extremely efficient light scattering properties: a liquid network formed in a porous matrix. Liquid fragments confined in the solid matrix result in a random fluctuation of the dielectric function and act as scattering objects for photons. The optical scattering efficiency is defined by the filling factor of the liquid in the pores and its dielectric constant. The spectral dependence of the scattering length of photons indicates that the phenomenon is governed by a Mie-type scattering mechanism. The degree of the dielectric disorder of the medium, i.e. the level of opacity is tunable by the ambient vapor pressure of the dielectric substance. In the strongest scattering regime the scattering length of photons is found to be in the micrometer range. By incorporation of dye molecules in the voids of the porous layer a system exhibiting optical gain is realized. In the multiple scattering regime the optical path of diffusively propagating photons is enhanced and light amplification through stimulated emission occurs: a strong intensity enhancement of the dye emission accompanied by significant spectral narrowing is observed above the excitation threshold for a layer being in the opalescence state.
Farooque, Mohammad; Yuh, Chao-Yi
1996-01-01
A carbonate fuel cell matrix comprising support particles and crack attenuator particles which are made platelet in shape to increase the resistance of the matrix to through cracking. Also disclosed is a matrix having porous crack attenuator particles and a matrix whose crack attenuator particles have a thermal coefficient of expansion which is significantly different from that of the support particles, and a method of making platelet-shaped crack attenuator particles.
Scattering of electrons in copper by a Frenkel pair defect
Energy Technology Data Exchange (ETDEWEB)
Lodder, A.; Rijsdijk, G.A.; Bukman, D.J.; Baratta, A.J.; Molenaar, J.
1988-06-01
The Korringa-Kohn-Rostoker (KKR) Green function extended-defect formalism, used to describe the scattering of Bloch electrons in a dilute alloy, is generalised to include an asymmetric defect centred on a lattice site. The revised theory is then used to investigate conduction electron scattering from Frenkel pairs in Cu. Such defects consist of two self-interstitial atoms centred on a vacant lattice site forming a dumb-bell oriented along the <100> axis. The generalised formalism allows one to calculate the cluster t matrix T for the Frenkel pair cluster including the surrounding displaced nearest neighbours. It was found that the interstitials at the vacant lattice site could still be treated within the muffin-tin potential as a central scatterer characterised by a t matrix which is non-diagonal in the angular momentum. Electron scattering rates and Dingle temperatures are calculated and discussed in view of preliminary experimental results.
Scattering of electrons in copper by a Frenkel pair defect
International Nuclear Information System (INIS)
Lodder, A.; Rijsdijk, G.A.; Bukman, D.J.; Baratta, A.J.; Molenaar, J.
1988-01-01
The Korringa-Kohn-Rostoker (KKR) Green function extended-defect formalism, used to describe the scattering of Bloch electrons in a dilute alloy, is generalised to include an asymmetric defect centred on a lattice site. The revised theory is then used to investigate conduction electron scattering from Frenkel pairs in Cu. Such defects consist of two self-interstitial atoms centred on a vacant lattice site forming a dumb-bell oriented along the axis. The generalised formalism allows one to calculate the cluster t matrix T for the Frenkel pair cluster including the surrounding displaced nearest neighbours. It was found that the interstitials at the vacant lattice site could still be treated within the muffin-tin potential as a central scatterer characterised by a t matrix which is non-diagonal in the angular momentum. Electron scattering rates and Dingle temperatures are calculated and discussed in view of preliminary experimental results. (author)
Matrix with Prescribed Eigenvectors
Ahmad, Faiz
2011-01-01
It is a routine matter for undergraduates to find eigenvalues and eigenvectors of a given matrix. But the converse problem of finding a matrix with prescribed eigenvalues and eigenvectors is rarely discussed in elementary texts on linear algebra. This problem is related to the "spectral" decomposition of a matrix and has important technical…
Indian Academy of Sciences (India)
Much of linear algebra is devoted to reducing a matrix (via similarity or unitary similarity) to another that has lots of zeros. The simplest such theorem is the Schur triangularization theorem. This says that every matrix is unitarily similar to an upper triangular matrix. Our aim here is to show that though it is very easy to prove it ...
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)
True many-particle scattering theory in oscillator representation
International Nuclear Information System (INIS)
Smirnov, Yu.F.; Shirokov, A.M.
1988-01-01
The scattering theory in oscillator representation in case of true multiparticle scattering (TMS) is generalized. All necessary expressions to construct a wave function of several particles system in a discrete or continuous spectra at TMS approximation are obtained. Essential advantage of the method suggested lies in the fact that the most difficult part: construction and diagonolization of the Hamiltonian cutted matrix is to be carried out only once, and then the wave function can be calculated at any designed energy. 23 refs
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.)
Relativistic description of directly interacting pions and nucleons
International Nuclear Information System (INIS)
Heller, L.
1976-01-01
The expected magnitudes of the leading relativistic effects on an off-energy-shell T matrix element are estimated using the Bakamjian--Thomas formulation of relativistic potential theory. For pion-nucleon scattering at medium energy, the two largest corrections are expected to result from the use of relativistic relative momenta rather than nonrelativistic values. The importance of additional terms depends upon the detailed behavior of the T matrix
Hatada, Keisuke; Ebert, Hubert
2018-01-01
This edited book, based on material presented at the EU Spec Training School on Multiple Scattering Codes and the following MSNano Conference, is divided into two distinct parts. The first part, subtitled “basic knowledge”, provides the basics of the multiple scattering description in spectroscopies, enabling readers to understand the physics behind the various multiple scattering codes available for modelling spectroscopies. The second part, “extended knowledge”, presents “state- of-the-art” short chapters on specific subjects associated with improving of the actual description of spectroscopies within the multiple scattering formalism, such as inelastic processes, or precise examples of modelling.
Hybrid transfer-matrix FDTD method for layered periodic structures.
Deinega, Alexei; Belousov, Sergei; Valuev, Ilya
2009-03-15
A hybrid transfer-matrix finite-difference time-domain (FDTD) method is proposed for modeling the optical properties of finite-width planar periodic structures. This method can also be applied for calculation of the photonic bands in infinite photonic crystals. We describe the procedure of evaluating the transfer-matrix elements by a special numerical FDTD simulation. The accuracy of the new method is tested by comparing computed transmission spectra of a 32-layered photonic crystal composed of spherical or ellipsoidal scatterers with the results of direct FDTD and layer-multiple-scattering calculations.
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)
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.)
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.
On the quantum inverse scattering problem
International Nuclear Information System (INIS)
Maillet, J.M.; Terras, V.
2000-01-01
A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an R-matrix) for a large class of lattice quantum integrable models is given. The principal requirement being the initial condition (R(0)=P, the permutation operator) for the quantum R-matrix solving the Yang-Baxter equation, it applies not only to most known integrable fundamental lattice models (such as Heisenberg spin chains) but also to lattice models with arbitrary number of impurities and to the so-called fused lattice models (including integrable higher spin generalizations of Heisenberg chains). Our method is then applied to several important examples like the sl n XXZ model, the XYZ spin-((1)/(2)) chain and also to the spin-s Heisenberg chains
Links, P.; Horsman, Peter; Kühnel, Karsten; Priddy, M.; Reijnhoudt, Linda; Merenmies, Mark
2013-01-01
The Guidelines follow the conceptual metadata model (deliverable 17.2). They include guidelines for description of collection-holding institutions, document collections, organisations, personalities, events, camps and ghettos. As much as possible the guidelines comply with the descriptive standards
Kaon-nucleon scattering in three-dimensional technique
International Nuclear Information System (INIS)
Salam, Agus; Fachruddin, Imam
2016-01-01
Kaon-nucleon (KN) scattering is formulated in the three-dimensional (3D) momentum space, in which the basis state is not expanded into partial waves. Based on this basis the Lippmann-Schwinger equation for the T-matrix is evaluated. We obtain as final equation for the T-matrix elements a set of two coupled integral equations in two variables, which are the momentum’s magnitude and the scattering angle. Calculations for the differential cross section and some spin observables are shown, for which we employ a hadrons exchange model with the second order contributions only.
Kaon-nucleon scattering in three-dimensional technique
Energy Technology Data Exchange (ETDEWEB)
Salam, Agus, E-mail: agus.salam@sci.ui.ac.id; Fachruddin, Imam [Departemen Fisika, FMIPA, Universitas Indonesia, Depok 16424 (Indonesia)
2016-03-11
Kaon-nucleon (KN) scattering is formulated in the three-dimensional (3D) momentum space, in which the basis state is not expanded into partial waves. Based on this basis the Lippmann-Schwinger equation for the T-matrix is evaluated. We obtain as final equation for the T-matrix elements a set of two coupled integral equations in two variables, which are the momentum’s magnitude and the scattering angle. Calculations for the differential cross section and some spin observables are shown, for which we employ a hadrons exchange model with the second order contributions only.
Positron scattering by atomic hydrogen at intermediate energies
International Nuclear Information System (INIS)
Higgins, K.; Burke, P.G.; Walters, H.R.J.
1990-01-01
Results of an accurate calculation based upon the intermediate energy R-matrix theory are reported for elastic scattering of positrons by atomic hydrogen. T-matrix elements for both low and intermediate energy scattering are evaluated for the S e , P o , D e and F o partial wave symmetries. The low-energy elastic phaseshifts are found to be in good agreement with previous accurate variational calculations. Using an optical potential approach to include the effect of the higher partial waves, elastic and total cross sections are presented for energies ranging from near threshold to 3.7 Rydbergs. (author)
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
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
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
Exponential time-dependent perturbation theory in rotationally inelastic scattering
International Nuclear Information System (INIS)
Cross, R.J.
1983-01-01
An exponential form of time-dependent perturbation theory (the Magnus approximation) is developed for rotationally inelastic scattering. A phase-shift matrix is calculated as an integral in time over the anisotropic part of the potential. The trajectory used for this integral is specified by the diagonal part of the potential matrix and the arithmetic average of the initial and final velocities and the average orbital angular momentum. The exponential of the phase-shift matrix gives the scattering matrix and the various cross sections. A special representation is used where the orbital angular momentum is either treated classically or may be frozen out to yield the orbital sudden approximation. Calculations on Ar+N 2 and Ar+TIF show that the theory generally gives very good agreement with accurate calculations, even where the orbital sudden approximation (coupled-states) results are seriously in error
Modeling cometary photopolarimetric characteristics with Sh-matrix method
Kolokolova, L.; Petrov, D.
2017-12-01
Cometary dust is dominated by particles of complex shape and structure, which are often considered as fractal aggregates. Rigorous modeling of light scattering by such particles, even using parallelized codes and NASA supercomputer resources, is very computer time and memory consuming. We are presenting a new approach to modeling cometary dust that is based on the Sh-matrix technique (e.g., Petrov et al., JQSRT, 112, 2012). This method is based on the T-matrix technique (e.g., Mishchenko et al., JQSRT, 55, 1996) and was developed after it had been found that the shape-dependent factors could be separated from the size- and refractive-index-dependent factors and presented as a shape matrix, or Sh-matrix. Size and refractive index dependences are incorporated through analytical operations on the Sh-matrix to produce the elements of T-matrix. Sh-matrix method keeps all advantages of the T-matrix method, including analytical averaging over particle orientation. Moreover, the surface integrals describing the Sh-matrix elements themselves can be solvable analytically for particles of any shape. This makes Sh-matrix approach an effective technique to simulate light scattering by particles of complex shape and surface structure. In this paper, we present cometary dust as an ensemble of Gaussian random particles. The shape of these particles is described by a log-normal distribution of their radius length and direction (Muinonen, EMP, 72, 1996). Changing one of the parameters of this distribution, the correlation angle, from 0 to 90 deg., we can model a variety of particles from spheres to particles of a random complex shape. We survey the angular and spectral dependencies of intensity and polarization resulted from light scattering by such particles, studying how they depend on the particle shape, size, and composition (including porous particles to simulate aggregates) to find the best fit to the cometary observations.
Quantum graphs: a simple model for chaotic scattering
International Nuclear Information System (INIS)
Kottos, Tsampikos; Smilansky, Uzy
2003-01-01
We connect quantum graphs with infinite leads, and turn them into scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay time and conductance distributions, Ericson fluctuations, and when considered statistically, the ensemble of scattering matrices reproduces quite well the predictions of the appropriately defined random matrix ensembles. The underlying classical dynamics can be defined, and it provides important parameters which are needed for the quantum theory. In particular, we derive exact expressions for the scattering matrix, and an exact trace formula for the density of resonances, in terms of classical orbits, analogous to the semiclassical theory of chaotic scattering. We use this in order to investigate the origin of the connection between random matrix theory and the underlying classical chaotic dynamics. Being an exact theory, and due to its relative simplicity, it offers new insights into this problem which is at the forefront of the research in chaotic scattering and related fields
SCAP-82, Single Scattering, Albedo Scattering, Point-Kernel Analysis in Complex Geometry
International Nuclear Information System (INIS)
Disney, R.K.; Vogtman, S.E.
1987-01-01
1 - Description of problem or function: SCAP solves for radiation transport in complex geometries using the single or albedo scatter point kernel method. The program is designed to calculate the neutron or gamma ray radiation level at detector points located within or outside a complex radiation scatter source geometry or a user specified discrete scattering volume. Geometry is describable by zones bounded by intersecting quadratic surfaces within an arbitrary maximum number of boundary surfaces per zone. Anisotropic point sources are describable as pointwise energy dependent distributions of polar angles on a meridian; isotropic point sources may also be specified. The attenuation function for gamma rays is an exponential function on the primary source leg and the scatter leg with a build- up factor approximation to account for multiple scatter on the scat- ter leg. The neutron attenuation function is an exponential function using neutron removal cross sections on the primary source leg and scatter leg. Line or volumetric sources can be represented as a distribution of isotropic point sources, with un-collided line-of-sight attenuation and buildup calculated between each source point and the detector point. 2 - Method of solution: A point kernel method using an anisotropic or isotropic point source representation is used, line-of-sight material attenuation and inverse square spatial attenuation between the source point and scatter points and the scatter points and detector point is employed. A direct summation of individual point source results is obtained. 3 - Restrictions on the complexity of the problem: - The SCAP program is written in complete flexible dimensioning so that no restrictions are imposed on the number of energy groups or geometric zones. The geometric zone description is restricted to zones defined by boundary surfaces defined by the general quadratic equation or one of its degenerate forms. The only restriction in the program is that the total
Low-energy electron scattering from CO. 2: Ab-initio study using the frame-transformation theory
Chandra, N.
1976-01-01
The Wigner-Eisenbud R matrix method has been combined with the frame transformation theory to study electron scattering from molecular systems. The R matrix, calculated at the boundary point of the molecular core radius, has been transformed to the space frame in order to continue the solution of the scattering equations in the outer region where rotational motion of the nuclei is taken into account. This procedure has been applied to a model calculation of thermal energy electron scattering from CO.
Lorentz violation, gravitoelectromagnetic field and Bhabha scattering
Santos, A. F.; Khanna, Faqir C.
2018-01-01
Lorentz symmetry is a fundamental symmetry in the Standard Model (SM) and in General Relativity (GR). This symmetry holds true for all models at low energies. However, at energies near the Planck scale, it is conjectured that there may be a very small violation of Lorentz symmetry. The Standard Model Extension (SME) is a quantum field theory that includes a systematic description of Lorentz symmetry violations in all sectors of particle physics and gravity. In this paper, SME is considered to study the physical process of Bhabha Scattering in the Gravitoelectromagnetism (GEM) theory. GEM is an important formalism that is valid in a suitable approximation of general relativity. A new nonminimal coupling term that violates Lorentz symmetry is used in this paper. Differential cross-section for gravitational Bhabha scattering is calculated. The Lorentz violation contributions to this GEM scattering cross-section are small and are similar in magnitude to the case of the electromagnetic field.
Scattering amplitudes in gauge theories
Energy Technology Data Exchange (ETDEWEB)
Henn, Johannes M. [Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Plefka, Jan C. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2014-03-01
First monographical text on this fundamental topic. Course-tested, pedagogical and self-contained exposition. Includes exercises and solutions. At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.
Scattering amplitudes in gauge theories
International Nuclear Information System (INIS)
Henn, Johannes M.; Plefka, Jan C.
2014-01-01
First monographical text on this fundamental topic. Course-tested, pedagogical and self-contained exposition. Includes exercises and solutions. At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.
Lectures on neutron scattering techniques: 1
International Nuclear Information System (INIS)
Carlile, C.J.
1988-08-01
The lecture on the production of neutrons was presented at a Summer School on neutron scattering, Rome, 1986. A description is given of the production of neutrons by natural radioactive sources, fission, and particle accelerator sources. Modern neutron sources with high intensities are discussed including the ISIS pulsed neutron source at the Rutherford Appleton Laboratory and the High Flux Reactor at the Institut Laue Langevin. (U.K.)
Elastic and inelastic photon scattering on the atomic nuclei
International Nuclear Information System (INIS)
Piskarev, I.M.
1982-01-01
Works on investigation of elastic and inelastic scattering of photons on heavy and intermediate nuclei are briefly reviewed. Theoretical problems of nuclear and electron Tompson, Releev and Delbrueck scatterings as well as nuclear resonance scattering are briefly discussed. It is shown that differential cross section of coherent elastic scattering is expressed by means of partial amplitudes of shown processes. Experimental investigations on elastic scattering in the region of threshold energies of photonucleon reactions are described. Problems of theoretical description of elastic scattering in different variants of collective models are considered. Discussed are works, investigating channels of inelastic photon scattering with excitation of nuclear Raman effect. It is noted that to describe channels of inelastic photon scattering it is necessary to use models, that correctly regard the microscopic structure of giant resonance levels to obtain information on the nature of these levels. Investigations of processes of photon elastic and inelastic scattering connected with fundamental characteristics of atomic nucleus, permit to obtain valuable spectroscopic information on high-lying levels of nucleus. Detail investigation of photon scattering in a wide range of energies is necessary [ru
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
Born amplitudes and seagull term in meson-soliton scattering
International Nuclear Information System (INIS)
Liang, Y.G.; Li, B.A.; Liu, K.F.; Su, R.K.
1990-01-01
The meson-soliton scattering for the φ 4 theory in 1+1 dimensions is calculated. We show that when the seagull term from the equal time commutator is included in addition to the Born amplitudes, the t-matrix from the reduction formula approach is identical to that of the potential scattering with small quantum fluctuations to leading order in weak coupling. The seagull term is equal to the Born term in the potential scattering. This confirms the speculation that the leading order Yukawa coupling is derivable from the classical soliton. (orig.)
Multichannel scattering of charge carriers on quantum well heterostructures
Galiev, V I; Polupanov, A F; Goldis, E M; Tansli, T L
2002-01-01
An efficient numerical analytical method has been developed for finding continuum spectrum states in quantum well systems with arbitrary potential profiles that are described by coupled Schroedinger equations. Scattering states and S matrix have been built for the case of multichannel scattering in one-dimensional systems with quantum wells and their symmetry properties are obtained and analyzed. The method is applied for studying hole scattering by strained GaInAs-InGaAsP quantum wells. Coefficients of the hole transmission and reflection as well as delay time are calculated as functions of the energy of the incident hole for various values of parameters of structures and values of the momentum
Elastic scattering of positronium: Application of the confined variational method
Zhang, Junyi
2012-08-01
We demonstrate for the first time that the phase shift in elastic positronium-atom scattering can be precisely determined by the confined variational method, in spite of the fact that the Hamiltonian includes an unphysical confining potential acting on the center of mass of the positron and one of the atomic electrons. As an example, we study the S-wave elastic scattering for the positronium-hydrogen scattering system, where the existing 4% discrepancy between the Kohn variational calculation and the R-matrix calculation is resolved. © Copyright EPLA, 2012.
Elastic scattering of positronium: Application of the confined variational method
Zhang, Junyi; Yan, Zong-Chao; Schwingenschlö gl, Udo
2012-01-01
We demonstrate for the first time that the phase shift in elastic positronium-atom scattering can be precisely determined by the confined variational method, in spite of the fact that the Hamiltonian includes an unphysical confining potential acting on the center of mass of the positron and one of the atomic electrons. As an example, we study the S-wave elastic scattering for the positronium-hydrogen scattering system, where the existing 4% discrepancy between the Kohn variational calculation and the R-matrix calculation is resolved. © Copyright EPLA, 2012.
Matrix diffusion user guide (release 2)
International Nuclear Information System (INIS)
Herbert, A.W.; Preece, T.E.
1989-04-01
This report presents an introduction to the use of the matrix diffusion option of the finite-element package NAMMU. The facilities available in the package are described; and the process of preparing the necessary input data is illustrated with an example. The matrix diffusion option of NAMMU models the transport of radionuclides in groundwater in a flow field governed by Darcy's Law. A detailed description of the mathematical model used for this option is given. The package uses the finite-element method. This allows the easy modelling of complex geological structures. (author)
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
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....
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
Concentric layered Hermite scatterers
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.
Coupling between scattering channels with SUSY transformations for equal thresholds
International Nuclear Information System (INIS)
Pupasov, Andrey M; Samsonov, Boris F; Sparenberg, Jean-Marc; Baye, Daniel
2009-01-01
Supersymmetric (SUSY) transformations of the multichannel Schroedinger equation with equal thresholds and arbitrary partial waves in all channels are studied. The structures of the transformation function and the superpotential are analysed. Relations between Jost and scattering matrices of superpartner potentials are obtained. In particular, we show that a special type of SUSY transformation allows us to introduce a coupling between scattering channels starting from a potential with an uncoupled scattering matrix. The possibility for this coupling to be trivial is discussed. We show that the transformation introduces bound and virtual states with a definite degeneracy at the factorization energy. A detailed study of the potential and scattering matrices is given for the 2 x 2 case. The possibility of inverting coupled-channel scattering data by such a SUSY transformation is demonstrated by several examples (s-s, s-p and s-d partial waves)
Correlation expansion: a powerful alternative multiple scattering calculation method
International Nuclear Information System (INIS)
Zhao Haifeng; Wu Ziyu; Sebilleau, Didier
2008-01-01
We introduce a powerful alternative expansion method to perform multiple scattering calculations. In contrast to standard MS series expansion, where the scattering contributions are grouped in terms of scattering order and may diverge in the low energy region, this expansion, called correlation expansion, partitions the scattering process into contributions from different small atom groups and converges at all energies. It converges faster than MS series expansion when the latter is convergent. Furthermore, it takes less memory than the full MS method so it can be used in the near edge region without any divergence problem, even for large clusters. The correlation expansion framework we derive here is very general and can serve to calculate all the elements of the scattering path operator matrix. Photoelectron diffraction calculations in a cluster containing 23 atoms are presented to test the method and compare it to full MS and standard MS series expansion
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)
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
Topics in elementary scattering theory
International Nuclear Information System (INIS)
Imrie, D.C.
1980-01-01
In these lectures a summary is given of some of the fundamental ideas and formalism used to describe and understand the interactions of elementary particles. A brief review of relativistic kinematics is followed by a discussion of Lorentz-invariant variables for describing two-body processes, phase space and plots, such as the Dalitz plot, which can be used to study some aspects of the dynamics of an interaction, relatively free from kinematic complications. A general description of scattering and decay is given and then, more specifically, some aspects of two-body interactions in the absence of spin are discussed. Finally, complications that arise when particle spin has to be taken into account are considered. (U.K.)
Extreme Scale FMM-Accelerated Boundary Integral Equation Solver for Wave Scattering
AbdulJabbar, Mustafa Abdulmajeed; Al Farhan, Mohammed; Al-Harthi, Noha A.; Chen, Rui; Yokota, Rio; Bagci, Hakan; Keyes, David E.
2018-01-01
scattering, which uses FMM as a matrix-vector multiplication inside the GMRES iterative method. Our FMM Helmholtz kernels treat nontrivial singular and near-field integration points. We implement highly optimized kernels for both shared and distributed memory
Inelastic magnetic electron scattering form factors of the 26 Mg nucleus
Indian Academy of Sciences (India)
Magnetic electron scattering (3) form factors with core polarization effects, ... to 3+ states of the 26Mg nucleus have been studied using shell model calculations. ... The wave functions of the radial single-particle matrix elements have been ...
A Pade-Aided Analysis of Nonperturbative NN Scattering in 1S0 Channel
International Nuclear Information System (INIS)
Yang Jifeng; Huang Jianhua
2007-01-01
We carried out a Pade approximant analysis on a compact factor of the T-matrix for NN scattering to explore the nonperturbative renormalization prescription in a universal manner. The utilities and virtues for this Pade analysis are discussed.
Parallelism in matrix computations
Gallopoulos, Efstratios; Sameh, Ahmed H
2016-01-01
This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of pa...
International Nuclear Information System (INIS)
Strobel, E.L.
1985-01-01
Given the many conflicting experimental results, examination is made of the neutrino mass matrix in order to determine possible masses and mixings. It is assumed that the Dirac mass matrix for the electron, muon, and tau neutrinos is similar in form to those of the quarks and charged leptons, and that the smallness of the observed neutrino masses results from the Gell-Mann-Ramond-Slansky mechanism. Analysis of masses and mixings for the neutrinos is performed using general structures for the Majorana mass matrix. It is shown that if certain tentative experimental results concerning the neutrino masses and mixing angles are confirmed, significant limitations may be placed on the Majorana mass matrix. The most satisfactory simple assumption concerning the Majorana mass matrix is that it is approximately proportional to the Dirac mass matrix. A very recent experimental neutrino mass result and its implications are discussed. Some general properties of matrices with structure similar to the Dirac mass matrices are discussed
Magnetic nanoparticles studied by small angle X-ray scattering
International Nuclear Information System (INIS)
Oliveira, Cristiano Luis Pinto; Antonel, Soledad; Negri, Martin
2011-01-01
because they exhibit magnetic (ferromagnetic) and electrical properties in the same material. Then, the nickel nanoparticles could be used for the development of electroelastic materials. In this case, the electrical conductivity of the material can be strongly dependent on the applied magnetic field, for example the case of nickel metal nanoparticles dispersed in a polymer, resulting in an anisotropic material with combined piezomagnetic and piezoelectric properties. In order to investigate the structural characteristics of cobalt-iron oxides and nickel nanoparticles, powder samples of those magnetic materials were studied by Small-Angle X-Ray Scattering. As will be shown, from the analysis and modeling of the scattering data, structural information could be obtained, enabling a detailed description of the structural properties of the studied samples which could be directly correlated to the magnetic properties. (author)
Magnetic nanoparticles studied by small angle X-ray scattering
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Cristiano Luis Pinto [Universidade de Sao Paulo (IF/USP), SP (Brazil). Inst. de Fisica. Grupo de Fluidos Complexos; Antonel, Soledad; Negri, Martin [Universidad de Buenos Aires (UBA) (Argentina). Facultad de Ciencias Exactas y Naturales. Dept. de Quimica Inorganica, Analitica y Quimica Fisica
2011-07-01
nanoparticles are very interesting because they exhibit magnetic (ferromagnetic) and electrical properties in the same material. Then, the nickel nanoparticles could be used for the development of electroelastic materials. In this case, the electrical conductivity of the material can be strongly dependent on the applied magnetic field, for example the case of nickel metal nanoparticles dispersed in a polymer, resulting in an anisotropic material with combined piezomagnetic and piezoelectric properties. In order to investigate the structural characteristics of cobalt-iron oxides and nickel nanoparticles, powder samples of those magnetic materials were studied by Small-Angle X-Ray Scattering. As will be shown, from the analysis and modeling of the scattering data, structural information could be obtained, enabling a detailed description of the structural properties of the studied samples which could be directly correlated to the magnetic properties. (author)
Translucent Radiosity: Efficiently Combining Diffuse Inter-Reflection and Subsurface Scattering.
Sheng, Yu; Shi, Yulong; Wang, Lili; Narasimhan, Srinivasa G
2014-07-01
It is hard to efficiently model the light transport in scenes with translucent objects for interactive applications. The inter-reflection between objects and their environments and the subsurface scattering through the materials intertwine to produce visual effects like color bleeding, light glows, and soft shading. Monte-Carlo based approaches have demonstrated impressive results but are computationally expensive, and faster approaches model either only inter-reflection or only subsurface scattering. In this paper, we present a simple analytic model that combines diffuse inter-reflection and isotropic subsurface scattering. Our approach extends the classical work in radiosity by including a subsurface scattering matrix that operates in conjunction with the traditional form factor matrix. This subsurface scattering matrix can be constructed using analytic, measurement-based or simulation-based models and can capture both homogeneous and heterogeneous translucencies. Using a fast iterative solution to radiosity, we demonstrate scene relighting and dynamically varying object translucencies at near interactive rates.
Inelastic Light Scattering Processes
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.
LIGHT SCATTERING BY FRACTAL DUST AGGREGATES. I. ANGULAR DEPENDENCE OF SCATTERING
Energy Technology Data Exchange (ETDEWEB)
Tazaki, Ryo [Department of Astronomy, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502 (Japan); Tanaka, Hidekazu [Astronomical Institute, Tohoku University, 6-3 Aramaki, Aoba-ku, Sendai 980-8578 (Japan); Okuzumi, Satoshi; Nomura, Hideko [Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan); Kataoka, Akimasa, E-mail: rtazaki@kusastro.kyoto-u.ac.jp [Institute for Theoretical Astrophysics, Heidelberg University, Albert-Ueberle-Strasse 2, D-69120 Heidelberg (Germany)
2016-06-01
In protoplanetary disks, micron-sized dust grains coagulate to form highly porous dust aggregates. Because the optical properties of these aggregates are not completely understood, it is important to investigate how porous dust aggregates scatter light. In this study, the light scattering properties of porous dust aggregates were calculated using a rigorous method, the T -matrix method, and the results were then compared with those obtained using the Rayleigh–Gans–Debye (RGD) theory and Mie theory with the effective medium approximation (EMT). The RGD theory is applicable to moderately large aggregates made of nearly transparent monomers. This study considered two types of porous dust aggregates—ballistic cluster–cluster agglomerates (BCCAs) and ballistic particle–cluster agglomerates. First, the angular dependence of the scattered intensity was shown to reflect the hierarchical structure of dust aggregates; the large-scale structure of the aggregates is responsible for the intensity at small scattering angles, and their small-scale structure determines the intensity at large scattering angles. Second, it was determined that the EMT underestimates the backward scattering intensity by multiple orders of magnitude, especially in BCCAs, because the EMT averages the structure within the size of the aggregates. It was concluded that the RGD theory is a very useful method for calculating the optical properties of BCCAs.
Propagation and scattering of light in fluctuating media
Kuz'min, V. L.; Romanov, V. P.; Zubkov, L. A.
1994-11-01
The monograph deals with the problems of the propagation and scattering of light in molecular media. The explicit statistical mechanical averaging procedure for the equations of electrodynamics is developed. It permits to transform the molecular level description into the macroscopic one for the electrodynamics of the fluctuating media. In the framework of such an approach, the problems of the molecular correlation contribution into the dielectric permeability, of the calculation of the reflection coefficients with an account of surface layers and of the multiple light scattering are considered. The developed theory is applied to the description of the critical opalescence, the coherent backscattering enhancement, the light scattering depolarization phenomena and the propagation and scattering of light in anisotropic media, including the case of liquid crystals.
Inclusive quasielastic and deep inelastic electron scattering at high energies
International Nuclear Information System (INIS)
Day, D.B.
1990-01-01
With high electron energies a kinematic regime can be reached where it will be possible to separate quasielastic and deep inelastic scattering. We present a short description of these processes which dominate the inclusive spectrum. Using the highest momentum transfer data available to guide our estimates, we give the kinematic requirements and the cross sections expected. These results indicate that inclusive scattering at high q has a yet unfilled potential. 18 refs., 13 figs
Scattering theory in quantum mechanics. Physical principles and mathematical methods
International Nuclear Information System (INIS)
Amrein, W.O.; Jauch, J.M.; Sinha, K.B.
1977-01-01
A contemporary approach is given to the classical topics of physics. The purpose is to explain the basic physical concepts of quantum scattering theory, to develop the necessary mathematical tools for their description, to display the interrelation between the three methods (the Schroedinger equation solutions, stationary scattering theory, and time dependence) to derive the properties of various quantities of physical interest with mathematically rigorous methods
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.
Analytical techniques for instrument design - Matrix methods
International Nuclear Information System (INIS)
Robinson, R.A.
1997-01-01
The authors take the traditional Cooper-Nathans approach, as has been applied for many years for steady-state triple-axis spectrometers, and consider its generalization to other inelastic scattering spectrometers. This involves a number of simple manipulations of exponentials of quadratic forms. In particular, they discuss a toolbox of matrix manipulations that can be performed on the 6-dimensional Cooper-Nathans matrix. They show how these tools can be combined to solve a number of important problems, within the narrow-band limit and the gaussian approximation. They will argue that a generalized program that can handle multiple different spectrometers could (and should) be written in parallel to the Monte-Carlo packages that are becoming available. They also discuss the complementarity between detailed Monte-Carlo calculations and the approach presented here. In particular, Monte-Carlo methods traditionally simulate the real experiment as performed in practice, given a model scattering law, while the Cooper-Nathans method asks the inverse question: given that a neutron turns up in a particular spectrometer configuration (e.g. angle and time of flight), what is the probability distribution of possible scattering events at the sample? The Monte-Carlo approach could be applied in the same spirit to this question
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
Quantum mechanical description of the two fluid model of liquid /sup 4/He solving the Bloch equation
International Nuclear Information System (INIS)
Fung, P.C.W.; Lam, C.C.
1986-01-01
The authors apply the U-matrix theory recently developed (Lam and Fung, Phys. Rev. A, vol.27, p.1760, 1983) to study certain physical properties of liquid /sup 4/He across a range of temperatures including the lambda -point. They propose a model for the chemical potential mu which is constant above T/sub lambda / but is a function of T below T/sub lambda /. They have discovered that the super-particles 'emerge' mathematically due to the uncommutability of the Hamiltonians at different temperatures, leading to a quantum mechanical description of the two-fluid model. Using the two-particle potential function deduced from scattering data, they have calculated numerically the approximate values of the number density for a range of temperatures starting from T/sub lambda /, taking the hard-core diameter Delta , 'effective chemical potential' mu ' as parameters
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...
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.)
Interior and exterior resonances in acoustic scattering. pt. 1 - spherical targets
International Nuclear Information System (INIS)
Gaunaurd, G.C.; Tanglis, E.; Uberall, H.; Brill, D.
1983-01-01
In acoustic scattering from elastic objects, resonance features appear in the returned echo at frequencies at which the object's eigenfrequencies are located, which are explained by the excitation of 'interior' creeping waves. Corresponding resonance terms may be split off from the total scattering amplitude, leaving behind an apparently nonresonant background amplitude. This is demonstrated here for scatterers of spherical geometry and in a companion paper also for scatterers of arbitrary geometry, by using the T-matrix approach. For the case of near-impenetrable spheres, it is subsequently shown that the background amplitude can be split further into specularly reflected contributions, plus highly attenuated resonance terms which are explained by the excitation of 'exterior' (Franz-type) creeping waves. The singularity structure of the scattering function is shown mathematically, by using the R-matrix approach of the nuclear-scattering theory, as that of a meromorphic function 'without' any additional 'entire function' (as had been postulated by the singularity expansion method)
First-order neutron-deuteron scattering in a three-dimensional approach
International Nuclear Information System (INIS)
Topolnicki, K.; Golak, J.; Skibinski, R.; Witala, H.; Bertulani, C.A.
2015-01-01
The description of the neutron-deuteron scattering process has been possible using the partial wave approach since the 1980s (Few-Body Syst. 3, 123 (1988); Phys. Rep. 274, 107 (1996); Acta Phys. Pol. B 28, 1677 (1997)). In recent years the so-called ''three-dimensional'' formalism was developed, where the calculations are performed with operators acting directly on the three-dimensional degrees of freedom of the nucleons. This approach avoids a tedious step of the classical calculations, the partial wave decomposition of operators, and in this paper is applied to the neutron-deuteron scattering process. The calculations presented here are a first step toward a new calculation scheme that would make it possible to easily produce precise predictions for a wide range of nuclear force models. This paper is a continuation of the work presented in Eur. Phys. J. A 43, 339 (2010) where the breakup channel was considered in detail. The theoretical formulation used in this paper is very closely related to the formalism introduced in Eur. Phys. J. A 43, 339 (2010) and Phys. Rev. C 68, 054003 (2003), however, we work directly with the matrix representation of operators in the joined isospin-spin space of the three-nucleon system and use only the driving term of the three-nucleon Faddeev equations. This greatly simplifies the numerical realization of the calculation and allows us to consider also the elastic channel of the reaction. (orig.)
Semimicroscopic analysis of 6Li+28Si elastic scattering at 76 to 318 MeV
Hassanain, M. A.; Anwar, M.; Behairy, Kassem O.
2018-04-01
Using the α-cluster structure of colliding nuclei, the elastic scattering of 6Li+28Si at energies from 76 to 318 MeV has been investigated by the use of the real folding cluster approach. The results of the cluster analysis are compared with those obtained by the CDM3Y6 effective density- and energy-dependent nucleon-nucleon (NN) interaction based upon G -matrix elements of the M3Y-Paris potential. A Woods-Saxon (WS) form was used for the imaginary potential. For all energies and derived potentials, the diffraction region was well reproduced, except at Elab=135 and 154 MeV at large angle. These results suggest that the addition of the surface (DWS) imaginary potential term to the volume imaginary potential is essential for a correct description of the refractive structure of the 6Li elastic scattering distribution at these energies. The energy dependence of the total reaction cross sections and that of the real and imaginary volume integrals is also discussed.
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Ibsen-Jensen, Rasmus; Podolskii, Vladimir V.
2013-01-01
For matrix games we study how small nonzero probability must be used in optimal strategies. We show that for image win–lose–draw games (i.e. image matrix games) nonzero probabilities smaller than image are never needed. We also construct an explicit image win–lose game such that the unique optimal...
DEFF Research Database (Denmark)
Schneider, Jesper Wiborg; Borlund, Pia
2007-01-01
The present two-part article introduces matrix comparison as a formal means for evaluation purposes in informetric studies such as cocitation analysis. In the first part, the motivation behind introducing matrix comparison to informetric studies, as well as two important issues influencing such c...
Saleem, M
2002-01-01
The Unitarity of the CKM matrix is examined in the light of the latest available accurate data. The analysis shows that a conclusive result cannot be derived at present. Only more precise data can determine whether the CKM matrix opens new vistas beyond the standard model or not.
General theory of intensity correlation on light scattering
International Nuclear Information System (INIS)
Villaeys, A.A.
1978-01-01
A general theory for spatio-temporal intensity correlations measurements for a scattered beam is developed. A completely quantum mechanical description for both excitation and detection set up is used. This description is essentially valid for weak incident light beams and single photon absorption processes. From a unified point of view both, stationary as well as, time resolved experiments are described. The interest for such experiments in the study of processes like resonance raman scattering and resonance fluorescence is emphasized. Also an observable coherent contribution associated to different final levels of the target-atoms or molecules is obtained a result which cannot be reached by intensity measurements
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 ....
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
Measuring isospin mixing in nuclei using π+- inelastic scattering
International Nuclear Information System (INIS)
Cottingame, W.B.; Braithwaite, W.J.; Morris, C.L.
1979-01-01
A new strongly isospin-mixed doublet has been found in 12 C near 19.5 MeV. in a comparison of π - and π + inelastic scattering at 180 MeV, The present techniques may be universally employable, at least in self-conjugate nuclei, in extracting isospin-mixing matrix elements
Statistical properties of chaotic scattering with one open channel
International Nuclear Information System (INIS)
Izrajlev, F.M.; Saher, D.; Sokolov, V.V.
1993-01-01
The correspondence between statistical properties of decaying states and fluctuations in resonance scattering is studied in a statistical model with one open channel. The model is described by an ensemble of random nonhermitian matrices. The dependence of the correlation length on the coupling parameter both for the S-matrix and the cross-section is studied numerically. 37 refs., 7 figs
Multi-scattering inversion for low model wavenumbers
Alkhalifah, Tariq Ali
2015-08-19
A successful full wavenumber inversion (FWI) implementation updates the low wavenumber model components first for proper wavefield propagation description, and slowly adds the high-wavenumber potentially scattering parts of the model. The low-wavenumber components can be extracted from the transmission parts of the recorded data given by direct arrivals or the transmission parts of the single and double-scattering wave-fields developed from a predicted scatter field. We develop a combined inversion of data modeled from the source and those corresponding to single and double scattering to update both the velocity model and the component of the velocity (perturbation) responsible for the single and double scattering. The combined inversion helps us access most of the potential model wavenumber information that may be embedded in the data. A scattering angle filter is used to divide the gradient of the combined inversion so initially the high wavenumber (low scattering angle) components of the gradient is directed to the perturbation model and the low wavenumber (high scattering angle) components to the velocity model. As our background velocity matures, the scattering angle divide is slowly lowered to allow for more of the higher wavenumbers to contribute the velocity model.
Energy Technology Data Exchange (ETDEWEB)
Xin, Zhou [Wisconsin Univ., Madison (USA). Dept. of Mathematics
1990-03-01
For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.).
A method to measure the antikaon-nucleon scattering length in lattice QCD
International Nuclear Information System (INIS)
Lage, Michael; Meissner, Ulf-G.; Rusetsky, Akaki
2009-01-01
We propose a method to determine the isoscalar K-bar N scattering length on the lattice. Our method represents the generalization of Luescher's approach in the presence of inelastic channels (complex scattering length). In addition, the proposed approach allows one to find the position of the S-matrix pole corresponding the Λ(1405) resonance.
International Nuclear Information System (INIS)
Zhou Xin
1990-01-01
For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.)
Compton scatter imaging: A tool for historical exploration
International Nuclear Information System (INIS)
Harding, G.; Harding, E.
2010-01-01
This review discusses the principles and technological realisation of a technique, termed Compton scatter imaging (CSI), which is based on spatially resolved detection of Compton scattered X-rays. The applicational focus of this review is to objects of historical interest. Following a historical survey of CSI, a description is given of the major characteristics of Compton X-ray scatter. In particular back-scattered X-rays allow massive objects to be imaged, which would otherwise be too absorbing for the conventional transmission X-ray technique. The ComScan (an acronym for Compton scatter scanner) is a commercially available backscatter imaging system, which is discussed here in some detail. ComScan images from some artefacts of historical interest, namely a fresco, an Egyptian mummy and a mediaeval clasp are presented and their use in historical analysis is indicated. The utility of scientific and technical advance for not only exploring history, but also restoring it, is briefly discussed.
Dielectric effects on Thomson scattering in a relativistic magnetized plasma
DEFF Research Database (Denmark)
Bindslev, H.
1991-01-01
The effects of the dielectric properties of a relativistic magnetized plasma on the scattering of electromagnetic radiation by fluctuations in electron density are investigated. The origin of the density fluctuations is not considered. Expressions for the scattering cross-section and the scattered...... power accepted by the receiving antenna are derived for a plasma with spatial dispersion. The resulting expressions allow thermal motion to be included in the description of the plasma and remain valid for frequencies of the probing radiation in the region of omega(p) and omega(ce), provided...... the absorption is small. Symmetry between variables relating to incident and scattered fields is demonstrated and shown to be in agreement with the reciprocity relation. Earlier results are confirmed in the cold plasma limit. Significant relativistic effects, of practical importance to the scattering...
Scattering theory of infrared divergent Pauli-Fierz Hamiltonians
Derezinski, J
2003-01-01
We consider in this paper the scattering theory of infrared divergent massless Pauli-Fierz Hamiltonians. We show that the CCR representations obtained from the asymptotic field contain so-called {\\em coherent sectors} describing an infinite number of asymptotically free bosons. We formulate some conjectures leading to mathematically well defined notion of {\\em inclusive and non-inclusive scattering cross-sections} for Pauli-Fierz Hamiltonians. Finally we give a general description of the scattering theory of QFT models in the presence of coherent sectors for the asymptotic CCR representations.
Experimental light scattering by small particles in Amsterdam and Granada
Directory of Open Access Journals (Sweden)
Volten H.
2010-06-01
Full Text Available We report on two light scattering instruments located in Amsterdam and Granada, respectively. These instruments enable measuring scattering matrices as functions of the scattering angle of collections of randomly orieneted irregular particles. In the past decades, the experimental setup located in Amsterdam, The Netherlands, has produced a significant amount of experimental data. Unfortunately, this setup was officially closed a couple of years ago. We also present a modernized descendant of the Dutch experimental setup recently constructed at the Instituto de Astrofísica de Andalucía (IAA in Granada, Spain. We give a brief description of the instruments, and present some representative results.
Resonant inelastic scattering by use of geometrical optics.
Schulte, Jörg; Schweiger, Gustav
2003-02-01
We investigate the inelastic scattering on spherical particles that contain one concentric inclusion in the case of input and output resonances, using a geometrical optics method. The excitation of resonances is included in geometrical optics by use of the concept of tunneled rays. To get a quantitative description of optical tunneling on spherical surfaces, we derive appropriate Fresnel-type reflection and transmission coefficients for the tunneled rays. We calculate the inelastic scattering cross section in the case of input and output resonances and investigate the influence of the distribution of the active material in the particle as well as the influence of the inclusion on inelastic scattering.
International Nuclear Information System (INIS)
Markowski, Adam S.; Mannan, M. Sam
2008-01-01
A risk matrix is a mechanism to characterize and rank process risks that are typically identified through one or more multifunctional reviews (e.g., process hazard analysis, audits, or incident investigation). This paper describes a procedure for developing a fuzzy risk matrix that may be used for emerging fuzzy logic applications in different safety analyses (e.g., LOPA). The fuzzification of frequency and severity of the consequences of the incident scenario are described which are basic inputs for fuzzy risk matrix. Subsequently using different design of risk matrix, fuzzy rules are established enabling the development of fuzzy risk matrices. Three types of fuzzy risk matrix have been developed (low-cost, standard, and high-cost), and using a distillation column case study, the effect of the design on final defuzzified risk index is demonstrated
International Nuclear Information System (INIS)
Baron, Jorge H.; Rivera, S.S.
2000-01-01
The so-called vulnerability matrix is used in the evaluation part of the probabilistic safety assessment for a nuclear power plant, during the containment event trees calculations. This matrix is established from what is knows as Numerical Categories for Engineering Judgement. This matrix is usually established with numerical values obtained with traditional arithmetic using the set theory. The representation of this matrix with fuzzy numbers is much more adequate, due to the fact that the Numerical Categories for Engineering Judgement are better represented with linguistic variables, such as 'highly probable', 'probable', 'impossible', etc. In the present paper a methodology to obtain a Fuzzy Vulnerability Matrix is presented, starting from the recommendations on the Numerical Categories for Engineering Judgement. (author)
International Nuclear Information System (INIS)
Sun, Wenbo; Videen, Gorden; Fu, Qiang; Hu, Yongxiang
2013-01-01
As fundamental parameters for polarized-radiative-transfer calculations, the single-scattering phase matrix of irregularly shaped aerosol particles must be accurately modeled. In this study, a scattered-field finite-difference time-domain (FDTD) model and a scattered-field pseudo-spectral time-domain (PSTD) model are developed for light scattering by arbitrarily shaped dielectric aerosols. The convolutional perfectly matched layer (CPML) absorbing boundary condition (ABC) is used to truncate the computational domain. It is found that the PSTD method is generally more accurate than the FDTD in calculation of the single-scattering properties given similar spatial cell sizes. Since the PSTD can use a coarser grid for large particles, it can lower the memory requirement in the calculation. However, the Fourier transformations in the PSTD need significantly more CPU time than simple subtractions in the FDTD, and the fast Fourier transform requires a power of 2 elements in calculations, thus using the PSTD could not significantly reduce the CPU time required in the numerical modeling. Furthermore, because the scattered-field FDTD/PSTD equations include incident-wave source terms, the FDTD/PSTD model allows for the inclusion of an arbitrarily incident wave source, including a plane parallel wave or a Gaussian beam like those emitted by lasers usually used in laboratory particle characterizations, etc. The scattered-field FDTD and PSTD light-scattering models can be used to calculate single-scattering properties of arbitrarily shaped aerosol particles over broad size and wavelength ranges. -- Highlights: • Scattered-field FDTD and PSTD models are developed for light scattering by aerosols. • Convolutional perfectly matched layer absorbing boundary condition is used. • PSTD is generally more accurate than FDTD in calculating single-scattering properties. • Using same spatial resolution, PSTD requires much larger CPU time than FDTD
International Nuclear Information System (INIS)
Nikolaev, N.N.; Zakharov, B.G.
1994-01-01
We develop the novel description of diffractive deep inelastic scattering based on the technique of lightcone wave functions of multiparton Fock states of the photon. The technique takes advantage of the exact diagonalization of the diffractive S-matrix in the dipole-cross section representation. In this paper we derive properties of the diffractive dissociation of virtual photons in the triple-pomeron regime. We demonstrate that the photon-pomeron interactions can be described by the partonic structure function, which satisfies the conventional GLDAP evolution equations. We identify the valence and sea (anti) quark and the valence gluon structure functions of the pomeron. We show how the gluon structure of the pomeron can be described by the constituent gluon wave function. We derive the leading unitarization correction to the rising structure functions at small x and conclude that the unitarized structure function satisfies the linear GLDAP evolution equations. This result holds even when the multipomeron exchanges are included. (orig.)
ACORNS, Covariance and Correlation Matrix Diagonalization
International Nuclear Information System (INIS)
Szondi, E.J.
1990-01-01
1 - Description of program or function: The program allows the user to verify the different types of covariance/correlation matrices used in the activation neutron spectrometry. 2 - Method of solution: The program performs the diagonalization of the input covariance/relative covariance/correlation matrices. The Eigen values are then analyzed to determine the rank of the matrices. If the Eigen vectors of the pertinent correlation matrix have also been calculated, the program can perform a complete factor analysis (generation of the factor matrix and its rotation in Kaiser's 'varimax' sense to select the origin of the correlations). 3 - Restrictions on the complexity of the problem: Matrix size is limited to 60 on PDP and to 100 on IBM PC/AT
Migration of scattered teleseismic body waves
Bostock, M. G.; Rondenay, S.
1999-06-01
The retrieval of near-receiver mantle structure from scattered waves associated with teleseismic P and S and recorded on three-component, linear seismic arrays is considered in the context of inverse scattering theory. A Ray + Born formulation is proposed which admits linearization of the forward problem and economy in the computation of the elastic wave Green's function. The high-frequency approximation further simplifies the problem by enabling (1) the use of an earth-flattened, 1-D reference model, (2) a reduction in computations to 2-D through the assumption of 2.5-D experimental geometry, and (3) band-diagonalization of the Hessian matrix in the inverse formulation. The final expressions are in a form reminiscent of the classical diffraction stack of seismic migration. Implementation of this procedure demands an accurate estimate of the scattered wave contribution to the impulse response, and thus requires the removal of both the reference wavefield and the source time signature from the raw record sections. An approximate separation of direct and scattered waves is achieved through application of the inverse free-surface transfer operator to individual station records and a Karhunen-Loeve transform to the resulting record sections. This procedure takes the full displacement field to a wave vector space wherein the first principal component of the incident wave-type section is identified with the direct wave and is used as an estimate of the source time function. The scattered displacement field is reconstituted from the remaining principal components using the forward free-surface transfer operator, and may be reduced to a scattering impulse response upon deconvolution of the source estimate. An example employing pseudo-spectral synthetic seismograms demonstrates an application of the methodology.
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.
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)
Applied electromagnetic scattering theory
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...
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)
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
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
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
Calculating Rayleigh scattering amplitudes from 100 eV to 10 MeV
International Nuclear Information System (INIS)
Parker, J.C.; Reynaud, G.W.; Botto, D.J.; Pratt, R.H.
1979-01-01
An attempt is made to explain how to calculate the contribution to elastic photon-atom scattering due to Rayleigh scattering (the scattering off bound electrons) in the photon energy range 100 eV less than or equal to W less than or equal to 10 MeV. All intermediate calculations are described, including the calculation of the potential, bound state wave functions, matrix elements, and final cross sections. 12 references
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
Moschovakis, YN
1987-01-01
Now available in paperback, this monograph is a self-contained exposition of the main results and methods of descriptive set theory. It develops all the necessary background material from logic and recursion theory, and treats both classical descriptive set theory and the effective theory developed by logicians.
CSIR Research Space (South Africa)
Klarman, S
2013-05-01
Full Text Available We introduce Description Logics of Context (DLCs) - an extension of Description Logics (DLs) for context-based reasoning. Our approach descends from J. McCarthy's tradition of treating contexts as formal objects over which one can quantify...
Physics 3204. Course Description.
Newfoundland and Labrador Dept. of Education.
A description of the physics 3204 course in Newfoundland and Labrador is provided. The description includes: (1) statement of purpose, including general objectives of science education; (2) a list of six course objectives; (3) course content for units on sound, light, optical instruments, electrostatics, current electricity, Michael Faraday and…
Evaluating the scattered radiation intensity in CBCT
Gonçalves, O. D.; Boldt, S.; Nadaes, M.; Devito, K. L.
2018-03-01
In this work we calculate the ratio between scattered and transmitted photons (STRR) by a water cylinder reaching a detector matrix element (DME) in a flat array of detectors, similar to the used in cone beam tomography (CBCT), as a function of the field of view (FOV) and the irradiated volume of the scanned object. We perform the calculation by obtaining an equation to determine the scattered and transmitted radiation and building a computer code in order to calculate the contribution of all voxels of the sample. We compare calculated results with the shades of gray in a central slice of a tomography obtained from a cylindrical glass container filled with distilled water. The tomography was performed with an I-CAT tomograph (Imaging Science International), from the Department of Dental Clinic - Oral Radiology, Universidade Federal de Juiz de Fora. The shade of gray (voxel gray value - VGV) was obtained using the software provided with the I-CAT. The experimental results show a general behavior compatible with theoretical previsions attesting the validity of the method used to calculate the scattering contributions from simple scattering theories in cone beam tomography. The results also attest to the impossibility of obtaining Hounsfield values from a CBCT.
Analytical techniques for instrument design - matrix methods
International Nuclear Information System (INIS)
Robinson, R.A.
1997-01-01
We take the traditional Cooper-Nathans approach, as has been applied for many years for steady-state triple-axis spectrometers, and consider its generalisation to other inelastic scattering spectrometers. This involves a number of simple manipulations of exponentials of quadratic forms. In particular, we discuss a toolbox of matrix manipulations that can be performed on the 6- dimensional Cooper-Nathans matrix: diagonalisation (Moller-Nielsen method), coordinate changes e.g. from (Δk I ,Δk F to ΔE, ΔQ ampersand 2 dummy variables), integration of one or more variables (e.g. over such dummy variables), integration subject to linear constraints (e.g. Bragg's Law for analysers), inversion to give the variance-covariance matrix, and so on. We show how these tools can be combined to solve a number of important problems, within the narrow-band limit and the gaussian approximation. We will argue that a generalised program that can handle multiple different spectrometers could (and should) be written in parallel to the Monte-Carlo packages that are becoming available. We will also discuss the complementarity between detailed Monte-Carlo calculations and the approach presented here. In particular, Monte-Carlo methods traditionally simulate the real experiment as performed in practice, given a model scattering law, while the Cooper-Nathans method asks the inverse question: given that a neutron turns up in a particular spectrometer configuration (e.g. angle and time of flight), what is the probability distribution of possible scattering events at the sample? The Monte-Carlo approach could be applied in the same spirit to this question
Separable expansion for realistic multichannel scattering problems
International Nuclear Information System (INIS)
Canton, L.; Cattapan, G.; Pisent, G.
1987-01-01
A new approach to the multichannel scattering problem with realistic local or nonlocal interactions is developed. By employing the negative-energy solutions of uncoupled Sturmian eigenvalue problems referring to simple auxiliary potentials, the coupling interactions appearing to the original multichannel problem are approximated by finite-rank potentials. By resorting to integral-equation tecniques the coupled-channel equations are then reduced to linear algebraic equations which can be straightforwardly solved. Compact algebraic expressions for the relevant scattering matrix elements are thus obtained. The convergence of the method is tasted in the single-channel case with realistic optical potentials. Excellent agreement is obtained with a few terms in the separable expansion for both real and absorptive interactions
Scattering of elastic waves by thin inclusions
International Nuclear Information System (INIS)
Simons, D.A.
1980-01-01
A solution is derived for the elastic waves scattered by a thin inclusion. The solution is asymptotically valid as inclusion thickness tends to zero with the other dimensions and the frequency fixed. The method entails first approximating the total field in the inclusion in terms of the incident wave by enforcing the appropriate continuity conditions on traction and displacement across the interface, then using these displacements and strains in the volume integral that gives the scattered field. Expressions are derived for the far-field angular distributions of P and S waves due to an incident plane P wave, and plots are given for normalized differential cross sections of an oblate spheroidal tungsten carbide inclusion in a titanium matrix
Scattering theory some old and new problems
Yafaev, Dmitri R
2000-01-01
Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.
Classical wave experiments on chaotic scattering
International Nuclear Information System (INIS)
Kuhl, U; Stoeckmann, H-J; Weaver, R
2005-01-01
We review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves. Inasmuch as these experiments use antennas or transducers to couple waves into or out of the systems, scattering theory has to be applied for a quantitative interpretation of the measurements. Most experiments concentrate on tests of predictions from random matrix theory and the random plane wave approximation. In all studied examples a quantitative agreement between experiment and theory is achieved. To this end it is necessary, however, to take absorption and imperfect coupling into account, concepts that were ignored in most previous theoretical investigations. Classical phase space signatures of scattering are being examined in a small number of experiments
Duality and multi-gluon scattering
International Nuclear Information System (INIS)
Mangano, M.; Parke, S.; Xu Zhan
1988-01-01
For the six-gluon scattering process we give explicit and simple expressions for the amplitude and its square. To achieve this we use an analogy with string theories to identify a unique procedure for writing the multi-gluon scattering amplitudes in terms of a sum of gauge invariant dual sub-amplitudes multiplied by an appropriate color (Chan-Paton) factor. The sub-amplitudes defined in this way are invariant under cyclic permutations, satisfy powerful identities which relate different non-cyclic permutations and factorize in the soft gluon limit, the two-gluon collinear limit and on multi-gluon poles. Also, to leading order in the number of colors these sub-amplitudes sum incoherently in the square of the full matrix element. The results contained here are important for Monte Carlo studies of multi-jet processes at hadron colliders as well as for understanding the general structure of QCD. (orig.)
The black hole S-Matrix from quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Betzios, Panagiotis; Gaddam, Nava; Papadoulaki, Olga [Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena,Utrecht University, Princetonplein 5, Utrecht, 3508 TD The (Netherlands)
2016-11-22
We revisit the old black hole S-Matrix construction and its new partial wave expansion of ’t Hooft. Inspired by old ideas from non-critical string theory & c=1 Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model — of waves scattering off inverted harmonic oscillator potentials — that exactly reproduces the unitary black hole S-Matrix for all spherical harmonics; each partial wave corresponds to an inverted harmonic oscillator with ground state energy that is shifted relative to the s-wave oscillator. Identifying a connection to 2d string theory allows us to show that there is an exponential degeneracy in how a given total initial energy may be distributed among many partial waves of the 4d black hole.
The black hole S-Matrix from quantum mechanics
International Nuclear Information System (INIS)
Betzios, Panagiotis; Gaddam, Nava; Papadoulaki, Olga
2016-01-01
We revisit the old black hole S-Matrix construction and its new partial wave expansion of ’t Hooft. Inspired by old ideas from non-critical string theory & c=1 Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model — of waves scattering off inverted harmonic oscillator potentials — that exactly reproduces the unitary black hole S-Matrix for all spherical harmonics; each partial wave corresponds to an inverted harmonic oscillator with ground state energy that is shifted relative to the s-wave oscillator. Identifying a connection to 2d string theory allows us to show that there is an exponential degeneracy in how a given total initial energy may be distributed among many partial waves of the 4d black hole.
Renormalized multiple-scattering theory of photoelectron diffraction
International Nuclear Information System (INIS)
Biagini, M.
1993-01-01
The current multiple-scattering cluster techniques for the calculation of x-ray photoelectron and Auger-electron diffraction patterns consume much computer time in the intermediate-energy range (200--1000 eV); in fact, because of the large value of the electron mean free path and of the large forward-scattering amplitude at such energies, the electron samples a relatively large portion of the crystal, so that the number of paths to be considered becomes dramatically high. An alternative method is developed in the present paper: instead of calculating the individual contribution from each single path, the scattering matrix of each plane parallel to the surface is calculated with a renormalization process that calculates every scattering event in the plane up to infinite order. Similarly the scattering between two planes is calculated up to infinite order, and the double-plane scattering matrix is introduced. The process may then be applied to the calculation of a larger set of atomic layers. The advantage of the method is that a relatively small number of internuclear vectors have been used to obtain convergence in the calculation
Ultrasound scatter in heterogeneous 3D microstructures: Parameters affecting multiple scattering
Engle, B. J.; Roberts, R. A.; Grandin, R. J.
2018-04-01
This paper reports on a computational study of ultrasound propagation in heterogeneous metal microstructures. Random spatial fluctuations in elastic properties over a range of length scales relative to ultrasound wavelength can give rise to scatter-induced attenuation, backscatter noise, and phase front aberration. It is of interest to quantify the dependence of these phenomena on the microstructure parameters, for the purpose of quantifying deleterious consequences on flaw detectability, and for the purpose of material characterization. Valuable tools for estimation of microstructure parameters (e.g. grain size) through analysis of ultrasound backscatter have been developed based on approximate weak-scattering models. While useful, it is understood that these tools display inherent inaccuracy when multiple scattering phenomena significantly contribute to the measurement. It is the goal of this work to supplement weak scattering model predictions with corrections derived through application of an exact computational scattering model to explicitly prescribed microstructures. The scattering problem is formulated as a volume integral equation (VIE) displaying a convolutional Green-function-derived kernel. The VIE is solved iteratively employing FFT-based con-volution. Realizations of random microstructures are specified on the micron scale using statistical property descriptions (e.g. grain size and orientation distributions), which are then spatially filtered to provide rigorously equivalent scattering media on a length scale relevant to ultrasound propagation. Scattering responses from ensembles of media representations are averaged to obtain mean and variance of quantities such as attenuation and backscatter noise levels, as a function of microstructure descriptors. The computational approach will be summarized, and examples of application will be presented.
International Nuclear Information System (INIS)
Krenciglowa, E.M.; Kung, C.L.; Kuo, T.T.S.; Osnes, E.; and Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794)
1976-01-01
Different definitions of the reaction matrix G appropriate to the calculation of nuclear structure are reviewed and discussed. Qualitative physical arguments are presented in support of a two-step calculation of the G-matrix for finite nuclei. In the first step the high-energy excitations are included using orthogonalized plane-wave intermediate states, and in the second step the low-energy excitations are added in, using harmonic oscillator intermediate states. Accurate calculations of G-matrix elements for nuclear structure calculations in the Aapprox. =18 region are performed following this procedure and treating the Pauli exclusion operator Q 2 /sub p/ by the method of Tsai and Kuo. The treatment of Q 2 /sub p/, the effect of the intermediate-state spectrum and the energy dependence of the reaction matrix are investigated in detail. The present matrix elements are compared with various matrix elements given in the literature. In particular, close agreement is obtained with the matrix elements calculated by Kuo and Brown using approximate methods
Application of wavelets to singular integral scattering equations
International Nuclear Information System (INIS)
Kessler, B.M.; Payne, G.L.; Polyzou, W.N.
2004-01-01
The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The scaling properties of wavelets are used to derive an efficient method for evaluating the singular integrals. The accuracy and efficiency of the wavelet transforms are demonstrated by solving the two-body T-matrix equation without partial wave projection. The resulting matrix equation which is characteristic of multiparticle integral scattering equations is found to provide an efficient method for obtaining accurate approximate solutions to the integral equation. These results indicate that wavelet transforms may provide a useful tool for studying few-body systems
Neutron scattering facilities at China Institute of Atomic Energy. Present and future situations
International Nuclear Information System (INIS)
Ye, C.T.; Gou, C.; Yang, T.H.
2001-01-01
The 15 MW Heavy Water Research Reactor (HWRR) at CIAE in Beijing is the only neutron source available for neutron scattering experiments in China at present. So far totally 5 neutron scattering spectrometers are installed at 4 beam tubes. A 60 MW new research reactor, China Advanced Research Reactor (CARR), now is being built at CIAE to meet the increasing demand of neutron scattering research in China. A brief description of HWRR, the presently existing neutron scattering equipments at HWRP, CARR, and the neutron scattering facilities to be installed at CARR are presented. (J.P.N.)
Single-particle Glauber matrix elements
International Nuclear Information System (INIS)
Oset, E.; Strottman, D.
1983-01-01
The single-particle matrix elements of the Glauber profile function are tabulated for harmonic oscillator single-particle wave functions. The tables are presented in such a manner as to be applicable if the hadron--nucleon elementary scattering amplitude is specified by either a partial wave expansion or a Gaussian in momentum transfer squared. The table is complete through the 1 g/sub 9/2/ orbital and contains entries for the 3s/sub 1/2/ orbital for use if realistic wave functions are expanded in terms of harmonic oscillator functions
Low-energy electron scattering by C, N, and O atoms
Energy Technology Data Exchange (ETDEWEB)
Nesbet, R K [International Business Machines Corp., San Jose, Calif. (USA). Research Lab.
1977-07-01
Recent theoretical studies of low-energy electron scattering by C, N, and O atoms are reviewed and results are compared with available experimental data. A critical comparison is made of the two principal methods used in this work-polarized pseudostate expansion with R-matrix computations or direct integration, and Bethe-Goldstone expansion with matrix variational computations. 31 references.
Matrix Metalloproteinase Enzyme Family
Directory of Open Access Journals (Sweden)
Ozlem Goruroglu Ozturk
2013-04-01
Full Text Available Matrix metalloproteinases play an important role in many biological processes such as embriogenesis, tissue remodeling, wound healing, and angiogenesis, and in some pathological conditions such as atherosclerosis, arthritis and cancer. Currently, 24 genes have been identified in humans that encode different groups of matrix metalloproteinase enzymes. This review discuss the members of the matrix metalloproteinase family and their substrate specificity, structure, function and the regulation of their enzyme activity by tissue inhibitors. [Archives Medical Review Journal 2013; 22(2.000: 209-220
Matrix groups for undergraduates
Tapp, Kristopher
2005-01-01
Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori.
Eves, Howard
1980-01-01
The usefulness of matrix theory as a tool in disciplines ranging from quantum mechanics to psychometrics is widely recognized, and courses in matrix theory are increasingly a standard part of the undergraduate curriculum.This outstanding text offers an unusual introduction to matrix theory at the undergraduate level. Unlike most texts dealing with the topic, which tend to remain on an abstract level, Dr. Eves' book employs a concrete elementary approach, avoiding abstraction until the final chapter. This practical method renders the text especially accessible to students of physics, engineeri
Notes on branes in matrix theory
International Nuclear Information System (INIS)
Keski-Vakkuri, E.; Kraus, P.
1998-01-01
We study the effective actions of various brane configurations in matrix theory. Starting from the 0+1-dimensional quantum mechanics, we replace coordinate matrices by covariant derivatives in the large N limit, thereby obtaining effective field theories on the brane world-volumes. Even for non-compact branes, these effective theories are of Yang-Mills type, with constant background magnetic fields. In the case of a D2-brane, we show explicitly how the effective action equals the large magnetic field limit of the Born-Infeld action, and thus derive from matrix theory the action used by Polchinski and Pouliot to compute M-momentum transfer between membranes. We also consider the effect of compactifying transverse directions. Finally, we analyze a scattering process involving a recently proposed background representing a classically stable D6+D0 brane configuration. We compute the potential between this configuration and a D0-brane, and show that the result agrees with supergravity. (orig.)
Electromagnetic wave scattering by many small particles
International Nuclear Information System (INIS)
Ramm, A.G.
2007-01-01
Scattering of electromagnetic waves by many small particles of arbitrary shapes is reduced rigorously to solving linear algebraic system of equations bypassing the usual usage of integral equations. The matrix elements of this linear algebraic system have physical meaning. They are expressed in terms of the electric and magnetic polarizability tensors. Analytical formulas are given for calculation of these tensors with any desired accuracy for homogeneous bodies of arbitrary shapes. An idea to create a 'smart' material by embedding many small particles in a given region is formulated
Systematics of meson-Skyrmion scattering
International Nuclear Information System (INIS)
Mattis, M.P.
1986-02-01
The S-matrix characterizing the scattering of pions from nucleons is calculated in the context of skyrmion models of the nucleon. These are models in which the nucleon is considered a soliton in the field of pions. The spectrum of nucleon and delta resonances in the Skyrme model is calculated and found to be in overall good agreement with Nature. Model-independent sum rules between amplitudes in the same partial wave are derived and examined. An extension of the formalism to the case of three light flavors is presented. 31 refs., 26 figs., 6 tabs
Systematics of meson-Skyrmion scattering
Energy Technology Data Exchange (ETDEWEB)
Mattis, M.P.
1986-02-01
The S-matrix characterizing the scattering of pions from nucleons is calculated in the context of skyrmion models of the nucleon. These are models in which the nucleon is considered a soliton in the field of pions. The spectrum of nucleon and delta resonances in the Skyrme model is calculated and found to be in overall good agreement with Nature. Model-independent sum rules between amplitudes in the same partial wave are derived and examined. An extension of the formalism to the case of three light flavors is presented. 31 refs., 26 figs., 6 tabs.
High energy gravitational scattering: a numerical study
Marchesini, Giuseppe
2008-01-01
The S-matrix in gravitational high energy scattering is computed from the region of large impact parameters b down to the regime where classical gravitational collapse is expected to occur. By solving the equation of an effective action introduced by Amati, Ciafaloni and Veneziano we find that the perturbative expansion around the leading eikonal result diverges at a critical value signalling the onset of a new regime. We then discuss the main features of our explicitly unitary S-matrix down to the Schwarzschild's radius R=2G s^(1/2), where it diverges at a critical value b ~ 2.22 R of the impact parameter. The nature of the singularity is studied with particular attention to the scaling behaviour of various observables at the transition. The numerical approach is validated by reproducing the known exact solution in the axially symmetric case to high accuracy.
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
Predicting the optical observables for nucleon scattering on even-even actinides
Martyanov, D. S.; Soukhovitskiĩ, E. Sh.; Capote, R.; Quesada, J. M.; Chiba, S.
2017-09-01
The previously derived Lane consistent dispersive coupled-channel optical model for nucleon scattering on 232Th and 238U nuclei is extended to describe scattering on even-even actinides with Z = 90-98. A soft-rotator-model (SRM) description of the low-lying nuclear structure is used, where the SRM Hamiltonian parameters are adjusted to the observed collective levels of the target nucleus. SRM nuclear wave functions (mixed in K quantum number) have been used to calculate the coupling matrix elements of the generalized optical model. The “effective” deformations that define inter-band couplings are derived from the SRM Hamiltonian parameters. Conservation of nuclear volume is enforced by introducing a dynamic monopolar term to the deformed potential, leading to additional couplings between rotational bands. The fitted static deformation parameters are in very good agreement with those derived by Wang and collaborators using the Weizsäcker-Skyrme global mass model (WS4), allowing use of the latter to predict cross sections for nuclei without experimental data. A good description of the scarce “optical” experimental database is achieved. SRM couplings and volume conservation allow a precise calculation of the compound-nucleus formation cross sections, which is significantly different from that calculated with rigid-rotor potentials coupling the ground-state rotational band. The derived parameters can be used to describe both neutron- and proton-induced reactions. Supported by International Atomic Energy Agency, through the IAEA Research Contract 19263, by the Spanish Ministry of Economy and Competitivity under Contracts FPA2014-53290-C2-2-P and FPA2016-77689-C2-1-R.
Current stage of understanding and description of hadronic elastic diffraction
Energy Technology Data Exchange (ETDEWEB)
Godizov, A. A. [Institute for High Energy Physics, 142281 Protvino (Russian Federation)
2013-04-15
Current situation with phenomenological description of high-energy nucleon-nucleon diffractive elastic scattering is reviewed. Comparison of various model predictions with the recent D0 and TOTEM data on the nucleon-nucleon differential cross-sections is presented.
Neutron-neutron quasifree scattering in nd breakup at 10 MeV
Malone, R. C.; Crowe, B.; Crowell, A. S.; Cumberbatch, L. C.; Esterline, J. H.; Fallin, B. A.; Friesen, F. Q. L.; Han, Z.; Howell, C. R.; Markoff, D.; Ticehurst, D.; Tornow, W.; Witała, H.
2016-03-01
The neutron-deuteron (nd) breakup reaction provides a rich environment for testing theoretical models of the neutron-neutron (nn) interaction. Current theoretical predictions based on rigorous ab-initio calculations agree well with most experimental data for this system, but there remain a few notable discrepancies. The cross section for nn quasifree (QFS) scattering is one such anomaly. Two recent experiments reported cross sections for this particular nd breakup configuration that exceed theoretical calculations by almost 20% at incident neutron energies of 26 and 25 MeV [1, 2]. The theoretical values can be brought into agreement with these results by increasing the strength of the 1S0 nn potential matrix element by roughly 10%. However, this modification of the nn effective range parameter and/or the 1S0 scattering length causes substantial charge-symmetry breaking in the nucleon-nucleon force and suggests the possibility of a weakly bound di-neutron state [3]. We are conducting new measurements of the cross section for nn QFS in nd breakup. The measurements are performed at incident neutron beam energies below 20 MeV. The neutron beam is produced via the 2H(d, n)3He reaction. The target is a deuterated plastic cylinder. Our measurements utilize time-of-flight techniques with a pulsed neutron beam and detection of the two emitted neutrons in coincidence. A description of our initial measurements at 10 MeV for a single scattering angle will be presented along with preliminary results. Also, plans for measurements at other energies with broad angular coverage will be discussed.
PREFACE: Atom-surface scattering Atom-surface scattering
Miret-Artés, Salvador
2010-08-01
; all of them were ready for use! We cannot imagine him without his two old-fashioned Mercedes, also in his collection. He also has technical skills in construction and music and always has time for jogging. I would finally say that he is an even-tempered person. In brief, mens sana in corpore sano 1 . Dick is a theorist bound to experimental work, extremely intuitive and very dedicated. In his long stays outside Clemson, he always visited places where experiments were being carried out. He has been, and still is, of great help to experimental PhD students, postdocs or senior scientists in providing valuable advice and suggestions towards new measurements. Plausible interpretations of their results developing theoretical models or always searching for good agreement with experiment are two constants in his daily scientific work. Experimental work is present in most of his 150 papers. One of the main theoretical challenges in this field was to develop a formalism where the plethora of experimental results reported in the literature were accommodated. His transition matrix formalism was also seminal in the field of atom-surface scattering. Elastic and inelastic (single and double phonon) contributions were determined as well as the multiphonon background. This work was preceded by a theory for diffuse inelastic scattering and a posterior contribution for multiphonon scattering, both with V Celli. In a similar vein, a theory of molecule-surface scattering was also derived and, more recently, a theory for direct scattering, trapping and desorption. Very interesting extensions to scattering with molten metal and liquid surfaces have also been carried out. Along with collaborators he has studied energy accommodation and sticking coefficients, providing a better understanding of their meaning. G Armand and Dick proposed the well-known corrugated Morse potential as an interaction potential model providing reliable results of diffraction patterns and selective adsorption
Critical State of Sand Matrix Soils
Marto, Aminaton; Tan, Choy Soon; Makhtar, Ahmad Mahir; Kung Leong, Tiong
2014-01-01
The Critical State Soil Mechanic (CSSM) is a globally recognised framework while the critical states for sand and clay are both well established. Nevertheless, the development of the critical state of sand matrix soils is lacking. This paper discusses the development of critical state lines and corresponding critical state parameters for the investigated material, sand matrix soils using sand-kaolin mixtures. The output of this paper can be used as an interpretation framework for the research on liquefaction susceptibility of sand matrix soils in the future. The strain controlled triaxial test apparatus was used to provide the monotonic loading onto the reconstituted soil specimens. All tested soils were subjected to isotropic consolidation and sheared under undrained condition until critical state was ascertain. Based on the results of 32 test specimens, the critical state lines for eight different sand matrix soils were developed together with the corresponding values of critical state parameters, M, λ, and Γ. The range of the value of M, λ, and Γ is 0.803–0.998, 0.144–0.248, and 1.727–2.279, respectively. These values are comparable to the critical state parameters of river sand and kaolin clay. However, the relationship between fines percentages and these critical state parameters is too scattered to be correlated. PMID:24757417