B=5 Skyrmion as a two-cluster system

The classical B=5 Skyrmion can be approximated by a two-cluster system in which a B=1 Skyrmion is attached to a core B=4 Skyrmion. We quantize this system, allowing the B=1 to freely orbit the core. The configuration space is 11 dimensional but simplifies significantly after factoring out the overall spin and isospin degrees of freedom. We exactly solve the free quantum problem and then include an interaction potential between the Skyrmions numerically. The resulting energy spectrum is compared to the corresponding nuclei—the helium-5/lithium-5 isodoublet. We find approximate parity doubling not seen in the experimental data. In addition, we fail to obtain the correct ground-state spin. The framework laid out for this two-cluster system can readily be modified for other clusters and in particular for other B=4n+1 nuclei, of which B=5 is the simplest example

Attractive Spin-Orbit Potential from the Skyrme Model

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

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

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

Quantum soliton scattering manifolds

We consider the quantum multisoliton scattering problem. For BPS theories one truncates the full field theory to the moduli space, a finite dimensional manifold of energy minimising field configurations, and studies the quantum mechanical problem on this. Non-BPS theories — the generic case — have no such obvious truncation. We define a quantum soliton scattering manifold as a configuration space which satisfies asymptotic completeness and respects the underlying classical dynamics of slow moving solitons. Having done this, we present a new method to construct such manifolds. In the BPS case the dimension of the n-soliton moduli space ℳn is n multiplied by the dimension of ℳ1. We show that this scaling is not necessarily valid for scattering manifolds in non-BPS theories, and argue that it is false for the Skyrme and baby-Skyrme models. In these models, we show that a relative phase difference can generate a relative size difference during a soliton collision. Asymptotically, these are zero and non-zero modes respectively and this new mechanism softens the dichotomy between such modes. Using this discovery, we then show that all previous truncations of the 2-Skyrmion configuration space are unsuitable for the quantum scattering problem as they have the wrong dimension. This gives credence to recent numerical work which suggests that the low-energy configuration space is 14- dimensional (rather than 12-dimensional, as previously thought). We suggest some ways to construct a suitable manifold for the 2-Skyrmion problem, and discuss applications of our new definition and construction for general soliton theories

Nucleon-nucleon potential from instanton holonomies

We derive the nucleon-nucleon interaction from the Skyrme model using the instanton and product approximations to skyrmion dynamics. In doing so, we also calculate the classical potential and metric for skyrmion dynamics in each of the approximations. This is the first time they have been compared in detail and the results show major disagreements between the approximations. We derive the eight low-energy nucleon-nucleon interaction potentials and compare them with the Paris model. For the instanton approximation we find strong negative isoscalar and isovector spin-orbit potentials, matching phenomenological models and our geometric intuition. Results for the other potentials are mixed, in part due to the zero pion mass limit used in this approximation

A framework for exploring gender equality outcomes from WASH programmes

This paper aims to assist practitioners and researchers in planning, identifying, and documenting gender outcomes associated with water, sanitation, and hygiene (WASH) programmes by proposing a conceptual framework for classifying gender equality changes. Gender outcomes that have been attributed to WASH initiatives encompass those directly related to improved services as well as outcomes that move into areas of relationships, power, and status. There is a growing body of literature identifying WASH-related gender outcomes; however the types of outcomes described vary considerably and further work is needed to inform a comprehensive picture of WASH and gender links. The framework proposed in this paper is based on a synthesis of outcomes reported in WASH literature to date, empirical research in Fiji and Vanuatu, and insights from gender and development literature. It is hoped that the framework will support practitioners to engage with the inherent complexity of gender inquiry, contributing to sector knowledge about the potential for WASH initiatives to advance gender equality. © Practical Action Publishing, 2013