Uniform WKB approximation of Coulomb wave functions for arbitrary partial wave

TL;DR

This paper derives analytical asymptotic formulas for Coulomb wave functions applicable across all energies and partial waves, including complex parameters, facilitating easier numerical computation at low energies.

Contribution

It introduces new asymptotic formulas for Coulomb wave functions valid for arbitrary energies and partial waves, extending to complex parameters.

Findings

Formulas valid for all energies and partial waves

Extension to complex parameter values

Improved numerical computation methods

Abstract

Coulomb wave functions are difficult to compute numerically for extremely low energies, even with direct numerical integration. Hence, it is more convenient to use asymptotic formulas in this region. It is the object of this paper to derive analytical asymptotic formulas valid for arbitrary energies and partial waves. Moreover, it is possible to extend these formulas for complex values of parameters.