Symmetric ground states for a stationary relativistic mean-field model for nucleons in the nonrelativistic limit

TL;DR

This paper analyzes a relativistic nucleon-meson interaction model in the nonrelativistic limit, demonstrating the existence of symmetric ground states and accurately modeling mesonic density distributions within nuclei.

Contribution

It establishes the existence of symmetric ground states for a broad range of parameters in a relativistic nucleon-meson model in the nonrelativistic limit.

Findings

Existence of ground states with specified angular momentum.

Accurate description of mesonic density shapes inside and outside the nucleus.

Model parameters can be chosen to match observed density distributions.

Abstract

In this paper we consider a model for a nucleon interacting with the $\omega$ and $\sigma$ mesons in the atomic nucleus. The model is relativistic, but we study it in the nuclear physics nonrelativistic limit, which is of a very different nature from the one of the atomic physics. Ground states with a given angular momentum are shown to exist for a large class of values for the coupling constants and the mesons' masses. Moreover, we show that, for a good choice of parameters, the very striking shapes of mesonic densities inside and outside the nucleus are well described by the solutions of our model.