Related papers: Validity of Born Approximation for Nuclear Scatter…
We discuss three ways of obtaining the Born approximations for Coulomb scattering: The standard way, making use of a convergence factor ("screening"), Oppenheimer's way using cylindrical (instead of spherical) coordinates, and finally…
On the basis of the eikonal approximation of quantum scattering theory, the problem of fast charged particles scattering in a thin crystal when particles fall along one its plane of atoms and in a thin layer of amorphous matter is…
We formulate the Born approximation for finding resonance poles in the complex plane for potential scattering problems. Using the method, we study the distribution of resonance poles for several scattering potentials. In particular, we find…
We study explicit formulas for phaseless inverse scattering in the Born approximation at high energies for the Schr\"odinger equation with compactly supported potential in dimension d $\ge$ 2. We obtain error estimates for these formulas in…
Scattering by an isolated defect embedded in a dielectric medium of two dimensional periodicity is of interest in many sub-fields of electrodynamics. Present approaches to compute this scattering rely either on the Born approximation and…
Modelling the acoustic scattering response due to penetrable objects of arbitrary shapes, such as those of many marine organisms, can be computationally intensive, often requiring high-performance computing equipment when considering a…
Light scattering is one of the most important elementary processes in near-field optics. We build up the Born series for scattering by dielectric bodies with step boundaries. The Green function for a 2-dimensional homogeneous dielectric…
In this work we illustrate a number of properties of the Born approximation in the three-dimensional Calder\'on inverse conductivity problem by numerical experiments. The results are based on an explicit representation formula for the Born…
We study the numerical approximation of the inverse scattering problem in the two-dimensional homogeneous isotropic linear elasticity with an unknown linear load given by a square matrix. For both backscattering data and fixed-angle…
This work reports the conditions under which weak scattering assumptions can be applied in a beam loaded by multiple resonators supporting both longitudinal and flexural waves. The work derives the equations of motion of a one-dimensional…
We study the elastic scattering of atomic argon by electron in the presence of a bichromatic laser field in the second Born approximation. The target atom is approximated by a simple screening potential and the continuum states of the…
Solutions in the form of series expansion, as the Born approximation, are very useful for describing time-independent scattering of quantum particles. In this work, it is mathematically demonstred that such solutions, when applied to…
We study the validity of the Neumann or Born series approach in solving the Helmholtz equation and coefficient identification in related inverse scattering problems. Precisely, we derive a sufficient and necessary condition under which the…
The elastic neutron-${}^3\mathrm{H}$ scattering at intermediate energies is studied using rigorous integral equations solved in the momentum-space partial-wave basis. The four-particle transition operators are expanded into…
We formulate eikonal approximation to the calculation of high energy scattering amplitude in the frame where both colliding objects are very energetic. We express the eikonal scattering matrix in terms of the color charge densities of the…
Laser photons carrying non-zero orbital angular momentum are known and exploited during the last twenty years. Recently it has been demonstrated experimentally that such (twisted) electrons can be produced and even focused to a subnanometer…
We prove the existence of scattering solutions for multidimensional magnetic Schr\"odinger equation which belong to the weighted Sobolev space H^1_s (R^n)(n=2,3) with some s < -1/2. As a consequence of this we formulate the direct Born…
Sharp-momentum transition matrix elements for scattering from a short-range Gaussian potential are computed using a real-time path integral. The computation is based on a numerical implementation of a new interpretation of the path integral…
Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…
The resonant mode approximation of the scattering matrix is considered for calculating the optical properties of multilayered periodic structures within the formalism of the Fourier-modal method for two diffraction thresholds in close…