Densities and energies of nuclei in dilute matter

TL;DR

This paper investigates the properties of nuclear clusters in dilute matter using microscopic calculations, proposing analytical models for their densities and energies, with implications for astrophysical equations of state.

Contribution

It introduces a microscopically motivated analytical modeling of cluster densities and energies in dilute nuclear matter, accounting for gas effects.

Findings

Cluster volume energies relate to saturation properties.

Surface energies are significantly influenced by the surrounding gas.

Density profiles and energies are strongly affected by the nucleon gas presence.

Abstract

We explore the ground-state properties of nuclear clusters embedded in a gas of nucleons with the help of Skyrme-Hartree-Fock microscopic calculations. Two alternative representations of clusters are introduced, namely coordinate-space and energy-space clusters. We parameterize their density profiles in spherical symmetry in terms of basic properties of the energy density functionals used and propose an analytical, Woods-Saxon density profile whose parameters depend, not only on the composition of the cluster, but also of the nucleon gas. We study the clusters' energies with the help of the local-density approximation, validated through our microscopic results. We find that the volume energies of coordinate-space clusters are determined by the saturation properties of matter, while the surface energies are strongly affected by the presence of the gas. We conclude that both the density profiles and the cluster energies are strongly affected by the gas and discuss implications for the nuclear EoS and related perspectives. Our study provides a simple, but microscopically motivated modeling of the energetics of clusterized matter at subsaturation densities, for direct use in consequential applications of astrophysical interest.