Related papers: J-matrix method of scattering for potentials with …
We present an exact procedure that allows one to calculate the scattering lenth for any potential expressed as an algebraic sum of inverse powers of the interatomic distance. We apply it to (12, $s$) Lennard-Jones potentials, with different…
We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally…
In this work we study the scattering and transfer matrices for electric fields defined with respect to an angular spectrum of plane waves. For these matrices, we derive the constraints that are enforced by conservation of energy,…
We discuss the regularization of attractive singular potentials $-\alpha _{s}/r^{s}$, $s\geq 2$ by infinitesimal imaginary addition to interaction constant $\alpha_{s}=\alpha_{s}\pm i0$. Such a procedure enables unique definition of…
Accurate and fast modeling of electric fields in layered structures have a great scientific and practical value. Prevalent method for that is transfer-matrix method. However, transfer matrix method is limited to infinite plane wave…
The transition operator T for the scattering of a particle from N potentials V_j can be expanded into a series featuring the transition operators t_j associated with the individual potentials. For V_j(x) both absolutely and square…
We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…
We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…
Problem for a cubic string having the shape of a step is studied. It is proved that here we have two scattering problems: the direct one and its dual. The direct problem describes scattering of the waves coming from ``$+\infty$'', and its…
Predicting the optical response of macroscopic arrangements of individual scatterers is a computational challenge, as the problem involves length scales across multiple orders of magnitude. We present a full-wave optical method to highly…
The present study presents a comprehensive theoretical investigation of atom and asymmetric top molecule inelastic scattering based on the R-matrix formalism. The proposed methodology establishes a rigorous framework for treating inelastic…
Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at…
Quantum scattering at zero energy is studied with stochastic methods. A path integral representation for the scattering cross section is developed. It is demonstrated that Monte Carlo simulation can be used to compare effective potentials…
This paper is concerned with the electromagnetic inverse scattering problem that aims to determine the location and shape of anisotropic scatterers from far field data (at a fixed frequency). We study the orthogonality sampling method which…
The formalism to describe the scattering of a weakly bound projectile nucleus by a heavy target is investigated, using the Uncorrelated Scattering Approximation. The main assumption involved is to neglect the correlation between the…
The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional…
A new method of path averaging for waves propagating in a random dilute system of identical scatterers is developed. The scattering matrix of such a system is calculated. The method systematically takes into account repeating scatterings on…
This is the fourth article in a series where we succeed in enlarging the class of exactly solvable quantum systems. We do that by working in a complete set of square integrable basis that carries a tridiagonal matrix representation for the…
We establish modified scattering for solutions of the cubic NLS on the line with a repulsive inverse square potential and small localized data. The method is based on a comparison between the free and distorted Galilei vector fields and a…
We present a fully microscopic three-cluster nuclear model for light nuclei on the basis of a J-Matrix approach. We apply the Modified J-Matrix method on $^{6}He$ and $^{6}Be$ for both scattering and reaction problems, analyse the Modified…