Coulomb scattering in the Born approximation and the use of generalized functions

TL;DR

This paper compares three methods for deriving the Born approximation in Coulomb scattering, highlighting the use of generalized functions as an instructive and valuable approach for physicists.

Contribution

It introduces and discusses the use of generalized functions in deriving the Coulomb scattering Born approximation, emphasizing its pedagogical value.

Findings

The generalized functions approach is effective for Coulomb scattering analysis.

Different methods for Born approximation yield consistent results.

The approach enhances understanding of scattering theory techniques.

Abstract

We discuss three ways of obtaining the Born approximations for Coulomb scattering: The standard way, making use of a convergence factor ("screening"), Oppenheimer's way using cylindrical (instead of spherical) coordinates, and finally Landau and Lifshitz' way. The last one although it does require some background from the theory of generalized functions is nevertheless a very instructive and important technique deserving more exposure to physicists.