Strong-Coupling Limit in Potential Theory. II

The analytic properties of the Jost function in the coupling constant g, derived in an earlier article for a restricted class of potentials, are rederived generally for potentials V(r), for which |V(r)| can be bounded by a monotonically decreasing potential V̄(r), such that ${\mathrm{\int dr|V̄(r)|}}^{\frac{1}{2}}\mathrm{<\infty .}$ In particular, potentials with nonlinear exponential tails are studied as a function of the energy and coupling constant. Earlier results of Sartori on the energy dependence of the Jost function, derived only for special cases of such potentials in the Born approximation, are demonstrated to be true generally for large classes of such potentials.