Curvature effect on nuclear pasta: Is it helpful for gyroid appearance?

TL;DR

This study investigates how curvature effects influence nuclear pasta shapes in neutron star crusts, finding that curvature corrections tend to disfavor the formation of gyroid structures, challenging previous suggestions of their relevance.

Contribution

It introduces a curvature-corrected liquid drop model to analyze nuclear pasta and assesses the likelihood of gyroid structures forming in neutron star crusts.

Findings

Curvature effects lower transition densities between nuclear shapes.

Gyroid structures are slightly disfavored by curvature corrections.

Gyroid is unlikely to be part of a family of generalized dimensional spheres.

Abstract

In supernova cores and neutron star crusts, nuclei are thought to deform to rodlike and slablike shapes, which are often called nuclear pasta. We study the equilibrium properties of the nuclear pasta by using a liquid drop model with curvature corrections. It is confirmed that the curvature effect acts to lower the transition densities between different shapes. We also examine the gyroid structure, which was recently suggested as a different type of nuclear pasta by analogy with the polymer systems. The gyroid structure investigated in this paper is approximately formulated as an extension of the periodic minimal surface whose mean curvature vanishes. In contrast to our expectations, we find from the present approximate formulation that the curvature corrections act to slightly disfavor the appearance of the gyroid structure. By comparing the energy corrections in the gyroid phase and the hypothetical phases composed of d-dimensional spheres, where d is a general dimensionality, we show that the gyroid is unlikely to belong to a family of the generalized dimensional spheres.