Effect of the Coulomb energy on Skyrmions

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.

Skyrme Crystals, Nuclear Matter and Compact Stars

“…The formation of nuclear pasta, however, is expected to result from a subtle interplay between the strong and the Coulomb forces. While the coupling of the Skyrme model to the electromagnetic field is known [46], and promising results concerning the computation of Coulomb effect in the case of α-particle Skyrmions have been reported [47], a viable treatment of macroscopic amounts of Skyrmionic matter coupled to electromagnetism which could give rise to the strong inhomogeneities implied by nuclear pasta is currently not available. As a consequence, all currently existing descriptions of nuclear matter based on Skyrme crystals approach zero pressure already at a finite baryon density n B = B cell /V cell , corresponding to the nuclear saturation density n 0 = B cell /V 0,cell .…”

Baby Skyrmion crystals

“…In the Skyrme model, the classical mass of a Skyrmion roughly plays the same role as the volume and surface terms [5]. To be able to address these first two terms, we need to understand the phases of nuclear matter in the Skyrme model.…”