Oxygen-16 spectrum from tetrahedral vibrations and their rotational excitations

A reinterpretation of the complete energy spectrum of the Oxygen-16 nucleus up to 20MeV, and partly beyond, is proposed. The underlying intrinsic shape of the nucleus is tetrahedral, as in the naive 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 works. 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 6.05MeV is modeled 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 analyzed as in the classic works 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 11MeV. Altogether, about 80 states with isospin zero are predicted below 20MeV, and these match rather well the more than 60 experimentally tabulated states. Several high-spin states are predicted, up to spin 9 and energy 30MeV, 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.