PERTURBATION-THEORY FOR THE ONE-DIMENSIONAL SCHRODINGER SCATTERING PROBLEM

A perturbation theory is constructed within the framework of a linear version of the variable-phase approach, with the aim of making a compl ete study of the problem of scattering by a superposition of the Coulo mb potential and the potential V(x) which decrease faster than the cen trifugal potential. As a zero approximation of the theory for regular and irregular solutions to this problem, for normalization factors, sc attering phase and amplitude, use is made of the corresponding functio ns calculated for the potential V(x) cut off at a certain point x = b. All subsequent approximations are determined analytically by the iter ation method. Perturbation theory is applied to investigate the asympt otics of the partial waves of scattering phases and amplitudes in the low-energy limit and in the limit of large angular momenta.