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

TL;DR

This paper reevaluates the spin excitation energy of the nucleon in the Skyrme model, suggesting a significantly lower value (~16 MeV) than traditionally estimated (~73 MeV), due to issues with the rigid rotor approximation.

Contribution

It proposes a more reliable estimate for the nucleon spin excitation energy, challenging the conventional rigid rotor fit and highlighting relativistic considerations.

Findings

Traditional estimate of 73 MeV is problematic

Proposed more consistent value is about 16 MeV

Rigid rotor fit to Delta resonance is problematic

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.