Modeling Nuclear Pasta and the Transition to Uniform Nuclear Matter with the 3D Skyrme-Hartree-Fock Method at Finite Temperature I: Core-Collapse Supernovae

TL;DR

This paper presents a 3D finite-temperature Skyrme-Hartree-Fock+BCS study of inhomogeneous nuclear matter, modeling nuclear pasta structures and their transition to uniform nuclear matter relevant for core-collapse supernovae.

Contribution

It introduces a self-consistent 3D modeling approach to study nuclear pasta and the transition to uniform matter at finite temperature, incorporating effects like neutron drip and shell effects.

Findings

Diverse nuclear shapes emerge in the pasta regime.

Thermodynamic properties change smoothly within pasta phases.

Transition to uniform matter involves a discontinuous change in properties.

Abstract

The first results of a new three-dimensional, finite temperature Skyrme-Hartree-Fock+BCS study of the properties of inhomogeneous nuclear matter at densities and temperatures leading to the transition to uniform nuclear matter are presented. Calculations are carried out in a cubic box representing a unit cell of the locally periodic structure of the matter. A constraint is placed on the two independent components of the quadrupole moment of the neutron density in order to investigate the dependence of the total energy-density of matter on the geometry of the nuclear structure in the unit cell. This approach allows self-consistent modeling of effects such as (i) neutron drip, resulting in a neutron gas external to the nuclear structure, (ii) shell effects of bound and unbound nucleons, (iii) the variety of exotic nuclear shapes that emerge, collectively termed `nuclear pasta' and (iv) the dissolution of these structures into uniform nuclear matter as density and/or temperature increase. In part I of this work the calculation of the properties of inhomogeneous nuclear matter in the core collapse of massive stars is reported. Calculations are performed at baryon number densities of $n_{\rm b}$ = 0.04 - 0.12 fm$^{\rm -3}$, a proton fraction of $y_{\rm p}=0.3$ and temperatures in the range 0 - 7.5 MeV. A wide variety of nuclear shapes are shown to emerge. It is suggested that thermodynamical properties change smoothly in the pasta regime up to the transition to uniform matter; at that transition, thermodynamic properties of the matter vary discontinuously.