Oxygen-16 spectrum from tetrahedral vibrations and their rotational excitations

Abstract

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

Realistic classical binding energies in the ω-Skyrme model

“…The traditional approach is "rigid body quantisation", in which the action of the field theory is restricted to the spin-isospin orbit of a degree B classical energy minimiser. Recent studies of the standard Skyrme model suggest that this is, for B > 1, often too restrictive: the Skyrme field should instead be restricted (for each fixed t) to lie in some finite dimensional manifold M of configurations which includes the spin-isospin orbits of the global energy minimiser and all nearby local minima, and field configurations interpolating between these [29][30][31][32][33][34]. In general, determining M is a difficult task, more art than science at present.…”

Electromagnetic transition rates of C12 and O16 in rotational-vibrational models

“…The expression (4.4) is only valid in the red region of the complex plane (for the colouring, see Figure 4). The wavefunctions were calculated in [9] and classified further in [10]. Four of them will be relevant for our calculation -labeled ψ + T 0 , ψ + T 1 , ψ − S0 and (u + 1 , v + 1 ).…”

Evidence for Tetrahedral Structure of Calcium-40

“…It was initiated by Wheeler [1] and by Dennison [6], and followed up by Robson [7], Bijker and Iachello [8], and others. The most detailed model was constructed recently by Halcrow, King and the present author [9,10]. Our model was based on Skyrmion solutions [11] in which alpha particles are extended structures of the Skyrme field, stabilised by their topological charge (baryon number).…”

“…In Oxygen-16, the E-mode has lowest frequency, and in [9,10] the first excited 0 + state at 6.05 MeV is interpreted as a state with two E-phonons. The E-mode, if extended to large amplitude, can deform a tetrahedron of four alpha particles through a square configuration into the dual tetrahedron (the spatial inversion of the initial tetrahedron).…”

“…Quantum mechanics on this E-manifold replaces the harmonic oscillator quantisation of the E-mode, but states can still be classified in terms of E-phonons (by examining the wavefunctions close to the initial tetrahedral configuration). The contributions of A-phonons and F-phonons were added in [10]; these were treated harmonically.…”