Parametrization of the Relativistic ($\sigma-\omega$) Model for Nuclear Matter

TL;DR

This paper analyzes the equation of state for nuclear matter using the $(\sigma-\omega)$ model, providing analytical expressions for key properties and demonstrating that the quartic self-coupling constant $G_4$ is unnecessary for reproducing saturation properties.

Contribution

The paper develops an analytical method to determine strong coupling constants and shows that the $G_4$ term is not needed in the model to match saturation properties.

Findings

Nuclear matter ceases to saturate at $ ext{eta} > 0.8$

Analytical expressions for compression modulus and coupling constants

Reproduction of saturation properties without $G_4$

Abstract

We have investigated the zero-temperature equation of state (EoS) for infinite nuclear matter within the $(\sigma-\omega)$ model at all densities $n_{\mathrm{B}}$ and different proton-neutron asymmetry $\eta\equiv(N-Z)/A$. We have presented an analytical expression for the compression modulus and found that nuclear matter ceases to saturate at $\eta$ slightly larger than $0.8$. Afterward, we have developed an analytical method to determine the strong coupling constants from the EoS for isospin symmetric nuclear matter, which allow us to reproduce all the saturation properties with high accuracy. For various values of the nucleon effective mass and the compression modulus, we have found that the quartic self-coupling constant $G_4$ is negative, or positive and very large. Furthermore, we have demonstrated that it is possible (a) to investigate the EoS in terms of $n_{\mathrm{B}}$ and $\eta$; and (b) to reproduce all the known saturation properties without $G_4$. We have thus concluded that the latter is not necessary in the $(\sigma-\omega)$ model.