Extension of Fuda’s off-shell analysis to screened Coulomb potentials for arbitrary l and limiting relations

Abstract

The Ecker–Weizel approximation technique is applied to the Schrödinger equation for a class of screened Coulomb potentials (Yukawa, Exponential cosine screened Coulomb and Hulthén) for any arbitrary angular momentum l. We find that the centrifugal term can be combined with the central screening potential to generate an effective Eckart potential with energy dependent strength parameters for which the s-wave Schrödinger equation is exactly solvable. Using this effective s-wave potential in the formalism of Fuda and Whiting for off-shell analysis, we obtain a closed expression for the off-shell Jost solution fS,l (k,q,r) in which k is the on-shell momentum, q is the off-shell momentum and the subscript S means screening. It turns out that for nonzero angular momentum, usual Jost function fS,l (k,q) can not be defined for finite screening parameter λ. However, we find that the Jost solution, as well as the Jost function defined in the limit λ → 0, show discontinuities at the on-shell point q=k, similar to the observation made by van Haeringen [Phys. Rev. A 18, 56 (1978)] for the s-wave Hulthén potential. For the l=0 case, we obtain explicit expressions for the off-shell and on-shell Jost solutions and Jost functions which possess the limiting behaviors discussed by van Haeringen for the Hulthén potential only. Our results not only extend previous works to higher partial waves, but at the same time indicate that certain limiting properties of the Jost solutions and the Jost functions are generally true for a class of screened Coulomb potentials.