Perturbation theory for the one-dimensional Schrödinger 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 complete study of the problem of scattering by a superposition of the Coulomb potential and the potential $V(x)$ which decrease faster than the centrifugal potential. As a zero approximation of the theory for regular and irregular solutions to this problem, for normalization factors, scattering phase and amplitude, use is made of the corresponding functions calculated for the potential $V(x)$ cut off at a certain point $x=b$. All subsequent approximations are determined analytically by the iteration method. Perturbation theory is applied to investigate the asymptotics of the partial waves of scattering phases and amplitudes in the low-energy limit and in the limit of large angular momenta.