Dynamical α-cluster model of ¹⁶O

We calculate the low-lying spectrum of the ¹⁶O 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 ¹⁶O and make predictions for the energies of 6¯ states that have yet to be observed experimentally

Electromagnetic transition strengths for light nuclei in the Skyrme model

We calculate reduced $B(E2)$ electromagnetic transition strengths for light nuclei of mass numbers $B=8,12,16,20,24$ and $32$ within the Skyrme model. We find that the predicted transition strengths are of the correct order of magnitude and the computed intrinsic quadrupole moments match the experimentally observed effective nuclear shapes. For the Hoyle state we predict a large $B(E2)\!\uparrow$ value of $0.0521\, \rm{e}^2\rm{b}^2$. For Oxygen-16, we can obtain a quantitative understanding of the ground state rotational band and the rotational excitations of the second spin-0 state, $0_2^+$.This work was partly undertaken on the COSMOS Shared Memory system at DAMTP, University of Cambridge operated on behalf of the STFC DiRAC HPC Facility. This equipment is funded by BIS National E-infrastructure capital grant no. ST/J005673/1 and STFC grants no. ST/J001341/1, ST/H008586/1, ST/K00333X/1. M.H. has been partially funded by the UK Science and Technology Facilities Council under grant no. ST/J000434/1. M.H. thanks Andrzej Wereszczynski and the Jagiellonian University, Krakow for hospitality. P.H.C.L. thanks Ling-Yan Hung and Fudan University in Shanghai for hospitality. P.H.C.L. acknowledges support as an International Research Fellow of the Japan Society for the Promotion of Science (JSPS).This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevC.93.03430

Dynamical α-cluster model of 16^{16}O

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.C.J.H. and C.K. are supported by STFC studentships

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

Five vortex equations

The Taubes equation for Abelian Higgs vortices is generalised to five distinct U(1) vortex equations. These include the Popov and Jackiw–Pi vortex equations, and two further equations. The Baptista metric, a conformal rescaling of the background metric by the squared Higgs field, gives insight into these vortices, and shows that vortices can be interpreted as conical singularities superposed on the background geometry. When the background has a constant curvature adapted to the vortex type, then the vortex equation is integrable by a reduction to Liouville's equation, and the Baptista metric has a constant curvature too, apart from its conical singularities. The conical geometry is fairly easy to visualise in some cases

Interactions of B = 4 Skyrmions

It is known that the interactions of single Skyrmions are asymptotically described by a Yukawa dipole potential. Less is known about the interactions of solutions of the Skyrme model with higher baryon number. In this paper, it is shown that Yukawa multipole theory can be more generally applied to Skyrmion interactions, and in particular to the long-range dominant interactions of the B = 4 solution of the Skyrme model, which models the alpha-particle. A method that gives the quadrupole nature of the interaction a more intuitive meaning in the pion field colour picture is demonstrated. Numerical methods are employed to find the precise strength of quadrupole and octupole interactions. The results are applied to the B = 8 and B = 12 solutions and to the Skyrme crystal.Comment: 21 pages, 11 figure

Quantized Skyrmions from SU(4) weight diagrams

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

Rolling Skyrmions and the Nuclear Spin-Orbit Force

We compute the nuclear spin-orbit coupling from the Skyrme model. Previous attempts to do this were based on the product ansatz, and as such were limited to a system of two well-separated nuclei. Our calculation utilises a new method, and is applicable to the phenomenologically important situation of a single nucleon orbiting a large nucleus. We find that, to second order in perturbation theory, the coefficient of the spin-orbit coupling induced by pion field interactions has the wrong sign, but as the strength of the pion-nucleon interactions increases the correct sign is recovered non-perturbatively

On the curvature of vortex moduli spaces

We use algebraic topology to investigate local curvature properties of the moduli spaces of gauged vortices on a closed Riemann surface. After computing the homotopy type of the universal cover of the moduli spaces (which are symmetric powers of the surface), we prove that, for genus g>1, the holomorphic bisectional curvature of the vortex metrics cannot always be nonnegative in the multivortex case, and this property extends to all Kaehler metrics on certain symmetric powers. Our result rules out an established and natural conjecture on the geometry of the moduli spaces.Comment: 25 pages; final version, to appear in Math.

Soliton pair creation in classical wave scattering

We study classical production of soliton-antisoliton pairs from colliding wave packets in (1+1)-dimensional scalar field model. Wave packets represent multiparticle states in quantum theory; we characterize them by energy E and particle number N. Sampling stochastically over the forms of wave packets, we find the entire region in (E,N) plane which corresponds to classical creation of soliton pairs. Particle number is parametrically large within this region meaning that the probability of soliton-antisoliton pair production in few-particle collisions is exponentially suppressed.Comment: 16 pages, 8 figures, journal version; misprint correcte