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Phase shifts for single-channel elastic electron-atom scattering are derived from time-dependent density functional theory. The H$^-$ ion is placed in a spherical box, its discrete spectrum found, and phase shifts deduced. Exact-exchange…
An algorithm$^{\ref{Fig1}}$ has been developed with the purpose of obtaining inverse potentials, where the Riccati-type non-linear differential equation, also called phase equation, has been kept in tandem with the Variational Monte Carlo…
This paper is about the scattering theory for one-dimensional matrix Schr\"odinger operators with a matrix potential having a finite first moment. The transmission coefficients are analytically continued and extended to the band edges. An…
We study a low-energy effective field theory (EFT) describing the NN system in which all exchanged particles are integrated out. We show that fitting the residue of the 3S1 amplitude at the deuteron pole, rather than the 3S1 effective…
We present a linear coordinate transform to expand the solution of scattering and emission problems into a basis of forward and backward directional vector harmonics. The transform provides intuitive algebraic and geometric interpretations…
Semiconductor heterostructures with prescribed energy dependence of the transmittance can be designed by combining: {\em a)} Pad\'e approximant reconstruction of the S-matrix; {\em b)} inverse scattering theory for Schro\"dinger's equation;…
Nonperturbative effective field theory calculations for NN scattering seem to break down at rather low momenta. By examining several toy models, we clarify how effective field theory expansions can in general be used to properly separate…
In this work, the transition matrix elements for inelastic electron--electron scattering are investigated. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in…
We present a multichannel model for elastic interactions, comprised of an arbitrary number of coupled finite square-well potentials, and derive semi-analytic solutions for its scattering behavior. Despite the model's simplicity, it is…
Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of $T$-matrices are unraveled using rigorous solutions and an inverse form of algebraic Lippmann-schwinger equation. The intrinsic…
In what follows we first set the context for inverse scattering in nuclear physics with a brief account of inverse problems in general. We then turn to inverse scattering which involves the S-matrix, which connects the interaction potential…
Due to an accidentally large $s$-wave scattering length, in a relatively wide range of energy, neutrons are approximately described by the nonrelativistic conformal field theory of unitarity fermions, perturbed by one relevant and an…
We study the direct and inverse scattering problem for the one-dimensional Schr\"odinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed…
We study one of multidimensional inverse scattering problems for quantum systems in a constant electric field, by utilization of the Enss-Weder time-dependent method. The main purpose of this paper is to propose some methods of sharpening…
Inclusive electron scattering off 4He is calculated exactly with a complete treatment of the final state interaction within a simple semirealistic potential model. We discuss results for both the longitudinal and the transverse response…
Within the framework of potential scattering theory we derive an analytical two-potential formula for the on-shell partial wave scattering amplitude. This formula embodies a large number of possible applications, including long range…
The Laplace transform approach with convolution theorem is used to find the scattering phase shifts of a Mie-type potential. The normalized scattering wave functions are also studied. The bound state spectrum and the corresponding…
The renormalization of the $T$-matrix for $NN$ scattering with a contact potential is reexamined in a nonperturbative regime through rigorous nonperturbative solutions. Based on the underlying theory point of view, it is shown that the UV…
We prove that the inverse scattering problem for the Schr\"odinger operator with the separable potential can be reduced to the solving of a certain singular integral equation. We establish the uniqueness of the potential corresponding to…
We study the stationary scattering theory for the matrix Schr\"odinger equation on the half line, with the most general boundary condition at the origin, and with integrable selfadjoint matrix potentials. We prove the limiting absorption…