Bound state energies and scattering phase shifts in a short-range potential

Abstract

The semi-classical Wentzel–Kramers–Brillouin (WKB) approximation has been used to determine the bound state energies and scattering phase-shifts in a short range potential having a cut-off. The corresponding pure coulomb cases are found to follow as limiting cases when the screening parameter tends to zero. The mutual interrelationship between the bound state poles and the analyticity of the scattering amplitude has also been explored in the context of the WKB approximation.