On the spin excitation energy of the nucleon in the Skyrme model

Abstract

In the Skyrme model of nucleons and nuclei, the spin excitation energy of the nucleon is traditionally calculated by a fit of the rigid rotor quantization of spin/isospin of the fundamental Skyrmion (the hedgehog) to the masses of the nucleon and the Delta resonance. The resulting, quite large spin excitation energy of the nucleon of about $ 73\, \mbox{MeV}$ is, however, rather difficult to reconcile with the small binding energies of physical nuclei, among other problems. Here we argue that a more reliable value for the spin excitation energy of the nucleon, compatible with many physical constraints, is about $ 16\, \mbox{MeV}$. The fit of the rigid rotor to the Delta, on the other hand, is problematic in any case, because it implies the use of a nonrelativistic method for a highly relativistic system.Comment: Latex, 8 pages, no figure

Exploring the generalized loosely bound Skyrme model

“…That is, if we make˜ 1 small then so is 5˜ 1 , see ref. [39]; more concretely, if we want the spin/isospin contribution to the mass of the nucleon,˜ 1 , to be less than the binding energy of roughly 16 MeV, which is approximately the binding energy of nuclear matter, then it is impossible for 5˜ 1 to be as large as 366 MeV [39] 4 . As further pointed out in ref.…”

“…As further pointed out in ref. [39], the ∆ resonance probably needs a fully relativistic treatment and should be considered as a resonance with a complex mass pole.…”

Generalized Skyrme model with the loosely bound potential

“…This issue of the large size of the spin-isospin contribution to the 1-Skyrmion has been addressed recently in Ref. [46], where it was suggested by an indirect argument of relating the spin contribution to the nucleon mass and the moment of inertia of the nucleon, that the spin contribution should actually be more than twice as large as the standard Skyrme model (direct) argument suggests. The spin contribution to the mass of 29 the nucleon needed should, by comparing the nucleon to Helium-4, be as low as 7.2 MeV.…”

“…[5], but again with the inclusion of the contribution from the BPS-Skyrme term, see Eq. (46). The result of the axial coupling in the chosen parameter space is shown in Fig.…”

Neutron stars within the Skyrme model

“…5 by quantizing the B = 1 Skyrmion and fitting the parameters to the mass values of the nucleon and the delta baryon 1 (different values have been also proposed, see for instance Ref. 58).…”