Quantum-Mechanical Scattering Problem in Lobachevsky Space at Low Energies

Abstract

Based on the use of the asymptotics for the wave function of a scattered particle in a Lobachevsky space in a form close to the asymptotics in flat space, general formulas for the theory of quantum mechanical scattering in this space are derived. This approach makes it possible to represent the basic formulas of the theory of scattering in the Lobachevsky space in the form that coincides with the corresponding expressions in three-dimensional Euclidean space. We offer quantities (length of scattering, effective scattering radius), that are used in describing scattering at short-range potentials and are convenient as phenomenological parameters in describing nuclear interactions at low energies. Numerical estimates of these quantities and cross sections at low energies, that are characteristic of nuclear physics, are given.