Nuclear pasta structures and symmetry energy

TL;DR

This study models nuclear pasta structures in neutron-rich matter using a relativistic mean field approach, revealing how lattice stability and symmetry energy influence pasta phases relevant to neutron star physics.

Contribution

It introduces an improved 3D modeling method for nuclear pasta structures and explores the impact of symmetry energy slope on their properties.

Findings

FCC lattice becomes more stable than BCC at higher densities.

Honeycomb lattice is more stable than simple lattice for rod/tube phases.

Reducing the symmetry energy slope increases the onset density for pasta formation.

Abstract

In the framework of the relativistic mean field model with Thomas-Fermi approximation, we study the structures of low density nuclear matter in a three-dimensional geometry with reflection symmetry. The numerical accuracy and efficiency are improved by expanding the mean fields according to fast cosine transformation and considering only one octant of the unit cell. The effect of finite cell size is treated carefully by searching for the optimum cell size. Typical pasta structures (droplet, rod, slab, tube, and bubble) arranged in various crystalline configurations are obtained for both fixed proton fractions and $\beta$-equilibration. It is found that the properties of droplets/bubbles are similar in body-centered cubic (BCC) and face-centered cubic (FCC) lattices, where the FCC lattice generally becomes more stable than BCC lattice as density increases. For the rod/tube phases, the honeycomb lattice is always more stable than the simple one. By introducing an $\omega$-$\rho$ cross coupling term, we further examine the pasta structures with a smaller slope of symmetry energy $L = 41.34$ MeV, which predicts larger onset densities for core-crust transition and non-spherical nuclei. Such a variation due to the reduction of $L$ is expected to have impacts on various properties in neutron stars, supernova dynamics, and binary neutron star mergers.