Liquid Drop Model for Nuclear Matter in the Low Density Limit

TL;DR

This paper rigorously derives the asymptotic behavior of nuclear matter energy in the dilute limit using a liquid drop model, confirming droplet arrangements akin to the astrophysical gnocchi phase.

Contribution

It provides the first rigorous derivation of the gnocchi phase in nuclear matter within the liquid drop model framework.

Findings

Two-term asymptotics for ground state energy per volume

Optimal configurations are droplets of unit size

Droplet arrangements correspond to Jellium minimizers

Abstract

We consider the liquid drop model with a positive background density in the thermodynamic limit. We prove a two-term asymptotics for the ground state energy per unit volume in the dilute limit. Our proof justifies the expectation that optimal configurations consist of droplets of unit size that arrange themselves according to minimizers for the Jellium problem for point particles. In particular, we provide the first rigorous derivation of what is known as the gnocchi phase in astrophysics.