Exact three-dimensional wave function and the on-shell t-matrix for the sharply cut off Coulomb potential: failure of the standard renormalization factor

TL;DR

This paper derives the exact 3D wave function for a sharply cut-off Coulomb potential and demonstrates that the standard renormalization factor fails, challenging its assumed universality in screened Coulomb interactions.

Contribution

The paper provides an analytical derivation of the wave function for a sharply cut-off Coulomb potential and shows the breakdown of the standard renormalization factor.

Findings

Standard renormalization factor fails for sharply cut-off Coulomb potential

Analytical wave function derived for the cut-off Coulomb potential

Challenging the universality of the renormalization approach

Abstract

The 3-dimensional wave function for a sharply cut-off Coulomb potential is analytically derived. The asymptotic form of the related scattering amplitude reveals a failure of the standard renormalization factor which is believed to be generally valid for any type of screening.