A study of local approximation for polarization potentials

TL;DR

This paper explores methods to derive an l-independent polarization potential for heavy ion scattering, assessing its validity against the l-dependent Feshbach potential through applications to low-energy halo nucleus scattering.

Contribution

It introduces three methods for deriving an l-independent polarization potential and evaluates their effectiveness in modeling heavy ion scattering.

Findings

l-independent polarization potential has limited validity

The derived potentials are not perfect substitutes for l-dependent Feshbach potentials

Application to $^{11}$Li scattering demonstrates practical relevance

Abstract

We discuss the derivation of an equivalent \textit{l}-independent polarization potential for use in the optical Schr\"{o}dinger equation that describes the elastic scattering of heavy ions. Three diffferent methods are used for this purpose. Application of our theory to the low energy scattering of the halo nucleus $^{11}$Li from a $^{12}$C target is made. It is found that the notion of \textit{l}-independent polarization potential has some validity but can not be a good substitute for the \textit{l}-dependent local equivalent Feshbach polarization potential.