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We develop a formalism to calculate electromagnetic (EM) transition rates for rotational-vibrational models of nuclei. The formalism is applied to recently proposed models of Carbon-12 and Oxygen-16 which are inspired by nuclear dynamics in the Skyrme model. We compare the results to experimental data, as well as other nuclear models. The results for Carbon-12 are in good agreement with the data across all models, making it difficult to differentiate the models. More experimental data is needed to do this, and we suggest which transitions would be most interesting to measure. The models of Oxygen-16 are less successful in describing the data, and we suggest some possible improvements to our approximations which may help., Comment: 18 pages, 5 figures

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 na\"ive 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 two-dimensional E-manifold of D2-symmetric, four-alpha-particle configurations, following earlier work. This allows for the underlying tetrahedral configuration to deform through a square configuration into the dual tetrahedron, so there is tunnelling between the tetrahedron and its dual, with the associated breaking of parity doubling. However, E-manifold states can still be interpreted in terms of E-phonons. 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 spectrum included. States with F-phonons require Coriolis corrections too. 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. The Coriolis parameter $\zeta$ 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 high-spin, natural parity states in this energy range that have been observed. The model proposed here is mainly phenomenological but it receives some input from analysis of Skyrmions with baryon number 16., Comment: 27 pages, 7 figures. This version accepted for publication in Int. J. Mod. Phys. E

Starting from solutions of the lightly-bound Skyrme model, we construct many new Skyrmion solutions of the standard Skyrme model with tetrahedral or octahedral symmetry. These solutions are closely related to weight diagrams of the group SU(4), which enables us to systematically derive some geometric and energetic properties of the Skyrmions, up to baryon number 85. We discuss the rigid body quantization of these Skyrmions, and compare the results with properties of a selection of observed nuclei., Comment: 31 pages, 5 figures

We calculate the low-lying spectrum of the $^{16}$O nucleus using an $\alpha$-cluster model which includes the important tetrahedral and square configurations. Our approach is motivated by the dynamics of $\alpha$-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, as well as introduce states that were previously not found in other cluster models, such as a $0^-$ state. 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., Comment: 5 pages, 9 figures

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 $\frac{3}{2}$ state to lie below the spin $\frac{7}{2}$ state, in agreement with experimental data. There is also a low lying spin $\frac{1}{2}$ state and two spin $\frac{5}{2} $ states. We find that the excited spin $\frac{7}{2}$ 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., Comment: 24 pages, 6 figures

The spin-orbit force is a vital tool in describing finite nuclei and nucleon interactions; however its microscopic origin is not fully understood. In this paper we study a model inspired by Skyrmions which provides a classical explanation of the force. To simplify the calculations the Skyrmions are approximated as two-dimensional rigid discs which behave like quantum cogwheels., Comment: 18 pages, 9 figures