Asymptotic forms of radial wavefunctions and Jost functions for cutoff potentials

Abstract

Rigorous asymptotic forms for the radial wavefunctions and the Jost functions are obtained for a broad class of cutoff potentials as the momentum k tends to infinity in the complex k plane. The asymptotic positions of the zeros of the Jost functions (S matrix poles) are also determined. It is found that the solutions of fl(−k) =0 for which ‖k‖ is very large, form a finite sequence of families of the form kN(m) ≈ αmN−iβm log N with N≈N0≫ 1 and m=1 to max with max a finite integer greater than or equal to one which is determined by the potential parameters.