Effect of the Coulomb energy on Skyrmions

The Coulomb effect, an essential ingredient in nuclear systems, is quantitatively investigated for certain Skyrmions with charge greater than 1. This is the first time such a calculation has been done. 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 4. 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 semiempirical 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, like the proposals in many other models. 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.

Figure 1

A surface of constant baryon density for the $B=12,16,32,108$ Skyrmion (upper row); different colors indicate the direction of the pion field. The corresponding simplified subfigures in the alpha-like particle framework (bottom row).

Figure 2

(a) Two groups of Coulomb energies for $B=4,8,12,16,32,108$ Skyrmion, APA–magenta spheres, NM–olive crosses. The Coulomb term in MF, two fitted curves—APA as magenta dashed line and NM as olive line, in various of the baryon numbers.