Coulomb-distorted plane wave: partial wave expansion and asymptotic forms

TL;DR

This paper derives the partial wave expansion and asymptotic forms of Coulomb-distorted plane waves, providing explicit formulas and asymptotic behaviors useful for quantum scattering analysis.

Contribution

It presents a detailed derivation of the partial wave expansion and asymptotic forms of Coulomb-distorted plane waves, including hypergeometric function simplifications.

Findings

Explicit partial wave expansion formulas derived.

Asymptotic expansion terms identified and analyzed.

Hypergeometric functions expressed and simplified.

Abstract

Partial wave expansion of the Coulomb-distorted plane wave is determined and studied. Dominant and sub-dominant asymptotic expansion terms are given and leading order three-dimensional asymptotic form is derived. The generalized hypergeometric function $_2F_2(a,a;a+l+1,a-l;z)$ is expressed with the help of confluent hypergeometric functions and the asymptotic expansion of $_2F_2(a,a;a+l+1,a-l;z)$ is simplified.