Densities and energies of nuclei in dilute matter at zero temperature
We explore the properties of medium-mass and heavy nuclear clusters embedded in a gas of nucleons with the help of Skyrme-Hartree-Fock microscopic calculations at zero temperature. Two alternative representations of clusters are introduced, namely coordinate-space and energy-space clusters. We parametrize 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 on that 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 equation of state and related perspectives. Our study provides a simple but microscopically motivated modeling of the energetics of clusterized matter at subsaturation densities for applications of astrophysical interest.