Nuclear Pasta at Finite Temperature with the Time-Dependent Hartree-Fock Approach

Bastian Schuetrumpf ,Kei Iida ,J A Maruhn ,Klaus Mecke ,Michael A Klatt ,P.‐G Reinhard

doi:10.1088/1742-6596/665/1/012074

Abstract

We present simulations of neutron-rich matter at sub-nuclear densities, like supernova matter. With the time-dependent Hartree-Fock approximation we can study the evolution of the system at temperatures of several MeV employing a full Skyrme interaction in a periodic three-dimensional grid [1].The initial state consists of α 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.The matter evolves into spherical, rod-like, connected rod-like and slab-like shapes. Further we observe gyroid-like structures, discussed e.g. in [2], which are formed spontaneously choosing a certain value of the simulation box length. The ρ-T-map of pasta shapes is basically consistent with the phase diagrams obtained from QMD calculations [3]. By an improved topological analysis based on Minkowski functionals [4], all observed pasta shapes can be uniquely identified by 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.

Highlights

We observe systems with mean densities of 10% of the nuclear density up to the nuclear density at finite temperatures of an order of 10 MeV
The temperature which was used for the initialization does not stay constant during the fusion of the α particles and background neutrons which takes place in the first few hundred fm/c of the calculation
In this work matter at subnuclear densities was studied by initializing α particles and background neutrons with a certain amount of kinetic energy randomly over a grid with periodic boundary conditions

Summary

Introduction

We observe systems with mean densities of 10% of the nuclear density up to the nuclear density at finite temperatures of an order of 10 MeV. The ρ-T-map of pasta shapes is basically consistent with the phase diagrams obtained from QMD calculations [3]. By an improved topological analysis based on Minkowski functionals [4], all observed pasta shapes can be uniquely identified by only two valuations, namely the Euler characteristic and the integral mean curvature.

Results

Conclusion