We calculate the low-lying spectrum of the 16 O nucleus using an α-cluster model which includes the important tetrahedral and square configurations. Our approach is motivated by the dynamics of α-particle scattering in the Skyrme model. We are able to replicate the large energy splitting that is observed between states of identical spin but opposite parities. We also provide a novel interpretation of the first excited state of 16 O and make predictions for the energies of 6 − states that have yet to be observed experimentally.

We consider the inclusion of the most important vibrational modes in the quantisation of the dodecahedral B = 7 Skyrmion. In contrast to a rigid body quantisation, this formalism allows a spin 3 2 state to lie below the spin 7 2 state, in agreement with experimental data. There is also a low lying spin 1 2 state and two spin 5 2 states. We find that the excited spin 7 2 state has a smaller root mean square charge radius than the other states. This prediction is an important signature of the Skyrme model, in conflict with more conventional nuclear models. * C.J.Halcrow@damtp.cam.ac.uk 1 arXiv:1511.00682v1 [hep-th] 2 Nov 2015

We study the vibrational modes of Skyrmions with baryon numbers one through eight in the standard Skyrme model. The vibrational modes are found in the harmonic approximation around the classical soliton solution and the real parts of the frequencies of the modes are extracted. We further classify the vibrational modes into representations of the symmetries possessed by the Skyrmion solutions. We find that there are approximately 7B low-lying modes for a Skyrmion with baryon number B, in addition to an infinite continuum of scattering modes. This result suggests that the instanton moduli space, which is 8Bdimensional, does not accurately describe the deformation space of Skyrmions as previously conjectured.

We derive the nucleon-nucleon isoscalar spin-orbit potential from the Skyrme model and find good agreement with the Paris potential. This solves a problem that has been open for more than 30 years and gives a new geometric understanding of the spin-orbit force. Our calculation is based on the dipole approximation to skyrmion dynamics and higher order perturbation theory.

A reinterpretation of the complete energy spectrum of the Oxygen-16 nucleus up to 20 MeV, and partly beyond, is proposed. The underlying intrinsic shape of the nucleus is tetrahedral, as in the naïve alpha-particle model and other cluster models, and A, E and F vibrational phonons are included. The A-and F-phonons are treated in the harmonic approximation, but the E-vibrations are extended into a twodimensional E-manifold of D 2 -symmetric, four-alpha-particle configurations, following earlier work. This allows for the underlying tetrahedral configuration to tunnel through a square configuration into the dual tetrahedron, with the associated breaking of parity doubling. The frequency of an E-phonon is lower than in other models, and the first-excited 0 + state at 6.05 MeV is modelled as a state with two E-phonons; this allows a good fit of the lowest 2 + and 2 − states as excitations with one E-phonon. Rotational excitations of the vibrational states are analysed as in the classic work of Dennison, Robson and others, with centrifugal corrections to the rotational energy included. States with F-phonons require Coriolis corrections, and the Coriolis parameter ζ is chosen positive to ensure the right splitting of the 3 + and 3 − states near 11 MeV. Altogether, about 80 states with isospin zero are predicted below 20 MeV, and these match rather well the more than 60 experimentally tabulated states. Several high-spin states are predicted, up to spin 9 and energy 30 MeV, and these match some of the observed high-spin, natural parity states in this energy range. The model proposed here is mainly phenomenological but it receives some input from analysis of Skyrmions with baryon number 16.1 email: C.J.Halcrow@leeds.ac.uk 2