Ground States for a Stationary Mean-Field Model for a Nucleon

TL;DR

This paper investigates the existence of ground states in a relativistic mean-field model for nucleons interacting with mesons, analyzing a nonrelativistic limit relevant to nuclear physics.

Contribution

It establishes the existence of ground states for a broad range of physical parameters in a relativistic nucleon-meson interaction model.

Findings

Ground states exist for many parameter values.

The model is analyzed in a nuclear physics nonrelativistic limit.

Results differ from atomic physics nonrelativistic limits.

Abstract

In this paper we consider a variational problem related to a model for a nucleon interacting with the $\omega$ and $\sigma$ mesons in the atomic nucleus. The model is relativistic, and we study it in a nuclear physics nonrelativistic limit, which is of a very different nature than the nonrelativistic limit in the atomic physics. Ground states are shown to exist for a large class of values for the parameters of the problem, which are determined by the values of some physical constants.