$\alpha$ particles and the pasta phase

TL;DR

This study investigates the role of alpha particles in nuclear matter at low densities, examining their effects on homogeneous and pasta phases under various conditions using relativistic models.

Contribution

It provides a detailed analysis of alpha particle effects on nuclear matter phases, highlighting their significance near critical temperatures and densities, and introduces the importance of repulsive interactions.

Findings

Alpha particles are present below 0.02 fm$^{-3}$ density in homogeneous matter.

Alpha particle fractions are higher in the pasta phase than in homogeneous matter above 0.01 fm$^{-3}$.

The presence of alpha particles can influence the existence of pasta phases near critical conditions.

Abstract

The effects of the $\alpha$ particles in nuclear matter at low densities are investigated within three different parametrizations of relativistic models at finite temperature. Both homogeneous and inhomogeneous matter (pasta phase) are described for neutral nuclear matter with fixed proton fractions and stellar matter subject to $\beta$-equilibrium and trapped neutrinos. In homogeneous matter, $\alpha$ particles are only present at densities below 0.02 fm$^{-3}$ and their presence decreases with the increase of the temperature and, for a fixed temperature, the $\alpha$ particle fraction decreases for smaller proton fractions. A repulsive interaction is important to mimic the dissolution of the clusters in homogeneous matter. The effects of the $\alpha$ particles on the pasta structure is very small except close to the critical temperatures and / or proton fractions when it may still predict a pasta phase while no pasta phase would occur in the absence of light clusters. It is shown that for densities above 0.01 fm$^{-3}$ the $\alpha$ particle fraction in the pasta phase is much larger than the $\alpha$ particle fraction in homogeneous matter.