Sa. Rakityansky et al., A METHOD FOR CALCULATING THE JOST FUNCTION FOR ANALYTIC POTENTIALS, Nuovo cimento della Societa italiana di fisica. B, Relativity, classical and statistical physics, 111(3), 1996, pp. 363-378
A combination of the variable-constant and complex coordinate rotation
methods is used to solve the two-body Schrodinger equation. The latte
r is replaced by a system of linear first-order differential equations
, which enables one to perform direct calculation of the Jest function
for all complex momenta of physical interest, including the spectral
points corresponding to bound and resonance states. Explicit forms of
the equations, appropriate for central short-range and Coulomb-tailed
potentials, are given. Within the proposed method, the scattering, bou
nd, virtual, and resonance state problems can be treated in a unified
way. The effectiveness of the method is demonstrated by a numerical ex
ample.