Nuclear binding energies from a Bogomol'nyi-Prasad-Sommerfield Skyrme model

Abstract

Recently, within the space of generalized Skyrme models, a BPS submodel was identified which reproduces some bulk properties of nuclear matter already on a classical level and, as such, constitutes a promising field theory candidate for the detailed and reliable description of nuclei and hadrons. Here we extend and further develop these investigations by applying the model to the calculation of nuclear binding energies. Concretely, we calculate these binding energies by including the classical soliton energies, the excitation energies from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies and a small explicit isospin symmetry breaking, which accounts for the mass difference between proton and neutron. The integrability properties of the BPS Skyrme model allow, in fact, for an analytical calculation of all contributions, which may then be compared with the semi-empirical mass formula. We find that for heavier nuclei, where the model is expected to be more accurate on theoretical grounds, the resulting binding energies are already in excellent agreement with their physical values. This result provides further strong evidence for the viability of the BPS Skyrme model as a distinguished starting point and lowest order approximation for the detailed quantitative investigation of nuclear and hadron physics.

Skyrme models and nuclear matter equation of state

“…4) whereL 0 is a further potential. Then, an improved proposal which might also be valid for the high baryon charge regime, is given by the near-BPS Skyrme model [12] 5) where the usual Skyrme model only provides rather small corrections to masses (binding energies), as is assumed to be a small parameter. Let us remark that the sextic term L 6 can be effectively introduced by a coupling with the ω meson [13]- [18].…”

Baryon chemical potential and in-medium properties of BPS skyrmions

“…Then, λ 2 ≤ 47 MeV fm 3 . Let us remark that all previously used potentials led to λ 2 slightly bigger than the optimal value, but significantly below the upper bound [16,26,29]. Undoubtedly, this bound on the BPS Skyrme model parameter may help to constrain the potential part of the action.…”

“…In particular, the BPS Skyrme model (the BPS restriction of the near-BPS Skyrme model) already provides quite accurate binding energies of the most abundant higher nuclei (after taking into account the semiclassical rotational and iso-rotational corrections as well as the Coulomb interaction and a small isospin breaking [16]). It also leads to a perfect fluid energy-momentum tensor with SDiff symmetries.…”

Skyrmions in models with pions and rho mesons

“…The first of these is a BPS Skyrme model [15,16], including only a term of sixth order in derivatives and a potential term. As binding energies vanish in this BPS model then it provides a good starting point to approach small binding energies [17,18]. A problem with the BPS model is an embarrassment of riches, in that there is an infinite symmetry group that allows Skyrmions to take arbitrary shapes.…”