Constraining the nonanalytic terms in the isospin-asymmetry expansion of the nuclear equation of state

TL;DR

This paper investigates the high-order isospin-asymmetry expansion of the nuclear equation of state, focusing on nonanalytic logarithmic terms and their impact on nuclear matter properties using chiral forces.

Contribution

It introduces a new finite difference method to accurately extract high-order symmetry energy coefficients, including nonanalytic logarithmic terms, from perturbation theory calculations.

Findings

Logarithmic terms' coefficients are larger in magnitude than normal terms.

Normal terms dominate the overall contribution to the ground state energy.

High-order terms significantly influence proton fraction at large densities.

Abstract

We examine the properties of the isospin-asymmetry expansion of the nuclear equation of state from chiral two- and three-body forces. We focus on extracting the high-order symmetry energy coefficients that consist of both normal terms (occurring with even powers of the isospin asymmetry) as well as terms involving the logarithm of the isospin asymmetry that are formally nonanalytic around the expansion point of isospin-symmetric nuclear matter. These coefficients are extracted from numerically precise perturbation theory calculations of the equation of state coupled with a new set of finite difference formulas that achieve stability by explicitly removing the effects of higher-order terms in the expansion. We consider contributions to the symmetry energy coefficients from both two- and three-body interactions. It is found that the coefficients of the logarithmic terms are generically larger in magnitude than those of the normal terms from second-order perturbation theory diagrams, but overall the normal terms give larger contributions to the ground state energy. The high-order isospin-asymmetry terms are especially relevant at large densities where they affect the proton fraction in beta-equilibrium matter.