The quantization of the B=1 and B=2 Skyrmions

Abstract

We propose to set the Skyrme parameters F_{\pi} and e such that they reproduce the physical masses of the nucleon and the deuteron. We allow deformation using an axially symmetric solution and simulated annealing to minimize the total energy for the B=1 nucleon and B=$ deuteron. First we find that axial deformations are responsible for a significant reduction (factor of \approx 4) of the rotational energy but also that it is not possible to get a common set of parameters F_{\pi} and e which would fit both nucleon and deuteron masses simultaneously at least for m_{\pi}= 138 MeV, 345 MeV and 500 MeV. This suggests that either m_{\pi}>500 MeV or additional terms must be added to the Skyrme Lagrangian.