Vv. Pupyshev, PERTURBATION-THEORY FOR THE ONE-DIMENSIONAL SCHRODINGER SCATTERING PROBLEM, Theoretical and mathematical physics, 105(1), 1995, pp. 1210-1223
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.