Pressure Corrections to the Equation of State in the Nuclear Mean Field

TL;DR

This paper explores how pressure affects the nuclear equation of state in a Relativistic Mean Field model, proposing modifications to maintain fundamental sum rules and aligning results with empirical and advanced theoretical models, impacting neutron star studies.

Contribution

It introduces modifications to the RMF model to preserve the Momentum Sum Rule at high pressures, improving agreement with empirical data and neutron star observations.

Findings

Modified RMF model satisfies the Momentum Sum Rule at high pressure.

Equation of State closely matches semi-empirical and DBHF results.

Proper stiffness of EoS constrains neutron star mass and radius, ruling out some exotic matter models.

Abstract

We show the connection between stiffness of equation of state in a Relativistic Mean Field (RMF) of Nuclear Matter (NM) and the existence of a strong violation of longitudinal Momentum Sum Rule (MSR) in RMF for a finite pressure. The increasing pressure between nucleons starts to increase the ratio of nucleon Fermi to average single particle energy and according to the Hugenholtz-van Hove theorem valid for NM the MSR is broken. In order to satisfy that MSR we propose changes which modify the nucleon Parton Distribution Function (PDF) above a saturation density. The course of Equation o State in our modified RMF model is very close to semi-empirical estimation and to results obtained from extensive DBHF calculations with a Bonn A potential. Other features of the model includes a good values saturation properties including spin-orbit term. Specially the proper stiffness of EoS recently discussed in an application to compact and neutron stars is important when studying star properties (mass-radius constraint), especially the mass of "PSR J1614-2230" the most massive known neutron star, which rules out many soft equations of state including exotic matter. An admixture of additional hyperons are discussed in our approach.