A Skyrme-type proposal for baryonic matter

TL;DR

This paper introduces a Skyrme-type model with Bogomolny solutions that naturally reproduces nuclear mass growth and captures key features of nuclear structure, offering a new analytical approach to baryonic matter.

Contribution

It proposes a submodel within the Skyrme framework that admits Bogomolny solutions, enabling classical reproduction of nuclear mass scaling and structural features.

Findings

The model reproduces linear nuclear mass growth with baryon number.

It captures the main features of the liquid droplet model.

The sextic term's topological nature aids in describing nuclear properties.

Abstract

The Skyrme model is a low-energy effective field theory for QCD, where the baryons emerge as soliton solutions. It is, however, not so easy within the standard Skyrme model to reproduce the almost exact linear growth of the nuclear masses with the baryon number (topological charge), due to the lack of Bogomolny solutions in this model, which has also hindered analytical progress. Here we identify a submodel within the Skyrme-type low energy effective action which does have a Bogomolny bound and exact Bogomolny solutions, and therefore, at least at the classical level, reproduces the nuclear masses by construction. Due to its high symmetry, this model qualitatively reproduces the main features of the liquid droplet model of nuclei. Finally, we discuss under which circumstances the proposed sextic term, which is of an essentially geometric and topological nature, can be expected to give a reasonable description of properties of nuclei.