Linear Response Theory with finite-range interactions

TL;DR

This review discusses methods for calculating nuclear matter response functions with finite-range interactions, comparing approximations and exact techniques, and analyzing stability against finite-size instabilities.

Contribution

It provides a comprehensive comparison of approximate and exact methods for response function calculation with finite-range interactions in nuclear matter.

Findings

Landau approximations offer quick estimates

Multipolar and continued fraction methods yield accurate results

Two or three terms in expansions are sufficient for convergence

Abstract

This review focuses on the calculation of infinite nuclear matter response functions using phenomenological finite-range interactions, equipped or not with tensor terms. These include Gogny and Nakada families, which are commonly used in the literature. Because of the finite-range, the main technical difficulty stems from the exchange terms of the particle-hole interaction. We first present results based on the so-called Landau and Landau-like approximations of the particle-hole interaction. Then, we review two methods which in principle provide numerically exact response functions. The first one is based on a multipolar expansion of both the particle-hole interaction and the particle-hole propagator and the second one consists in a continued fraction expansion of the response function. The numerical precision can be pushed to any degree of accuracy, but it is actually shown that two or three terms suffice to get converged results. Finally, we apply the formalism to the determination of possible finite-size instabilities induced by a finite-range interaction.