Time-Dependent Hartree-Fock Approach to Nuclear Pasta at Finite Temperature

TL;DR

This paper uses time-dependent Hartree-Fock simulations to study the formation of nuclear pasta shapes in neutron-rich matter at finite temperatures, providing a detailed morphological analysis.

Contribution

It introduces a novel morphological analysis method using Minkowski functionals to identify all pasta shapes and proposes a variance measure to distinguish pasta from uniform matter.

Findings

Nuclear pasta shapes form at subnuclear densities in simulations.

All eight pasta shapes can be uniquely identified by Euler characteristic and mean curvature.

Variance in cell density helps differentiate pasta from uniform matter.

Abstract

We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of $\alpha$ particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature. In addition, we propose the variance in the cell density distribution as a measure to distinguish pasta matter from uniform matter.