# Effect of Coulomb energy on Skyrmions

## TL;DR

This paper investigates the Coulomb energy's impact on Skyrmions within the Skyrme model, using numerical calculations and an alpha-like particle approximation, revealing insights consistent with nuclear physics and potential for modeling nuclear structures.

## Contribution

It introduces an effective alpha-like particle approximation for large Skyrmions and demonstrates its agreement with numerical Coulomb energy calculations, enhancing the Skyrme model's nuclear relevance.

## Key findings

- Coulomb energies match well between numerical and approximate methods.
- The Coulomb effect increases with baryon number but remains small overall.
- The Skyrme model reproduces known Coulomb energy results for nuclei.

## Abstract

The Coulomb effect, an essential ingredient in nuclear systems, is quantitatively investigated for certain Skyrmions within the Skyrme model. To do this we calculate the Coulomb energy from numerically generated multi-Skyrmions and, simultaneously, introduce an effective alpha-like particle approximation for large Skyrmions with baryon number $B$, where $B$ is a multiple of four. The calculated Coulomb energies and the corresponding fitted curve from this approximation match well with the results from the numerical method, as well as the behavior of the Coulomb energy in the semi-empirical mass formula. The Skyrme model correctly reproduces the well known results for the Coulomb energy of nuclei. This suggests that the alpha-particles can be used as the fundamental degrees of freedom in the Skyrme model. The Coulomb effect on the binding energy of the Skyrmions increases with baryon number but has a small effect overall. However, the effect could be significantly more pronounced for loosely bound Skyrme models.