Symmetric Excited States for a Mean-Field Model for a Nucleon

TL;DR

This paper investigates a relativistic mean-field model for a nucleon interacting with mesons, proving the existence of infinitely many solutions with specific angular momentum properties using a shooting method.

Contribution

It introduces a novel approach to establish the existence of multiple solutions in a relativistic nucleon-meson interaction model via a shooting method.

Findings

Proved existence of infinitely many solutions with fixed angular momentum.

Solutions are ordered by the number of nodes in each component.

Applied a shooting method to a nuclear physics nonrelativistic limit.

Abstract

In this paper, we consider a stationary 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. By a shooting method, we prove the existence of infinitely many solutions with a given angular momentum. These solutions are ordered by the number of nodes of each component.