Application of Renormalization to Potential Scattering

TL;DR

This paper applies a renormalization scheme to nonrelativistic potential scattering with ultraviolet divergences, demonstrating a model-independent low-energy result through numerical methods and discussing off-shell behavior.

Contribution

It introduces a numerical implementation of a renormalization scheme for potential scattering with divergences, providing a way to obtain physical results independent of cut-offs.

Findings

Successfully removes cut-off dependence in potential scattering

Obtains model-independent low-energy scattering results

Discusses off-shell behavior variations of the t matrix

Abstract

A recently proposed renormalization scheme can be used to deal with nonrelativistic potential scattering exhibiting ultraviolet divergence in momentum space. A numerical application of this scheme is made in the case of potential scattering with $r^{-2}$ divergence for small r, common in molecular and nuclear physics, by the use of cut-offs in momentum and configuration spaces. The cut-off is finally removed in terms of a physical observable and model-independent result is obtained at low energies. The expected variation of the off-shell behavior of the t matrix arising from the renormalization scheme is also discussed.