Related papers: Solving the two-center nuclear shell-model problem…
We analyze one particle, two-center quantum problems which admit separation of variables in prolate spheroidal coordinates, a natural restriction satisfied by the H$_2^+$ molecular ion. The symmetry operator is constructed explicitly. We…
The one-dimensional harmonic oscillator in a box problem is used to introduce the concept of a mixed-mode shell-model scheme. The method combines low-lying ``pure mode'' states of a system to achieve a better description in situations where…
A second-order supersymmetric transformation is presented, for the two-channel Schr\"odinger equation with equal thresholds. It adds a Breit-Wigner term to the mixing parameter, without modifying the eigenphase shifts, and modifies the…
We formulate and implement a microscopic framework to derive an optical potential from the solution to an effective Hamiltonian and use it to calculate neutron scattering cross sections for the deformed nuclei $^{24}$Mg, $^{48}$Cr and…
The advent of nucleon-nucleon potentials derived from chiral perturbation theory, as well as the so-called V-low-k approach to the renormalization of the strong short-range repulsion contained in the potentials, have brought renewed…
Bound-state solutions of the singular harmonic oscillator and singular Coulomb potentials in arbitrary dimensions are generated in a simple way from the solutions of the one-dimensional generalized Morse potential. The nonsingular harmonic…
The coupled-channel theory is a natural way of treating nonelastic channels, in particular those arising from collective excitations characterized by nuclear deformations. A proper treatment of such excitations is often essential to the…
The present paper is comprised of two parts. First, we give a brief survey of the theoretical framework for microscopic nuclear structure calculations starting from a free nucleon-nucleon potential. Then, we present some selected results of…
An important ingredient for applications of nuclear physics to e.g. astrophysics or nuclear energy are the cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often not possible, indirect methods like…
The supersymmetrical approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
The microscopic nucleus-nucleus optical potential is constructed basing on two patterns for real and imaginary parts, each calculated in the framework of microscopic models and multiplied by two normalizing factors, the free parameters,…
This is the second article in a series where we succeed in enlarging the class of solvable problems in one and three dimensions. We do that by working in a complete square integrable basis that carries a tridiagonal matrix representation of…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
The goal of this paper is to calculate bound, resonant and scattering states in the coupled-channel formalism without relying on the boundary conditions at large distances. The coupled-channel solution is expanded in eigenchannel bases i.e.…
An important ingredient for applications of nuclear physics to e.g. astrophysics or nuclear energy are the cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often not possible, indirect methods like…
A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates {\em nonuniform} and optimal spatial discretization.…
In contrast to the well-known solution of the two-body problem through the use of the concept of reduced mass, a solution is proposed involving separation of potentials. It is shown that each of the two point bodies moves in its own…
Using the ideas of supersymmetry and shape invariance we show that the eigenvalues and eigenfunctions of a wide class of noncentral potentials can be obtained in a closed form by the operator method. This generalization considerably extends…
We construct a tridiagonal matrix representation for the three dimensions Dirac-Coulomb Hamiltonian that provides for a simple and straightforward relativistic extension of the complex scaling method. Besides the Coulomb interaction,…