Infinite matter properties and zero-range limit of nonrelativistic finite-range interactions

TL;DR

This paper analyzes the properties of finite-range nuclear interactions, specifically Gogny and M3Y, in infinite matter, revealing insights into their components and the connection to zero-range Skyrme interactions, highlighting potential improvements.

Contribution

It provides a detailed analysis of Gogny and M3Y interactions in infinite matter and links their zero-range limits to N3LO Skyrme interactions, suggesting enhancements.

Findings

Central Gogny interaction may benefit from a third Gaussian.

Tensor parameters can be derived from partial wave combinations.

Zero-range limit aligns with N3LO Skyrme interaction form.

Abstract

We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin-orbit terms from the spin-isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin-orbit of the M3Y interaction is not compatible with local gauge invariance. Finally, we show that the zero-range limit of both families of interactions coincides with the specific form of the zero-range N3LO Skyrme interaction and we emphasize from this analogy the benefits of N3LO.