Abstract
Nuclear binding energies are investigated in two variants of the Skyrme model: the first replaces the usual Skyrme term with a term that is sixth order in derivatives, and the second includes a potential that is quartic in the pion fields. Solitons in the first model are shown to deviate significantly from ansätze previously assumed in the literature. The binding energies obtained in both models are lower than those obtained from the standard Skyrme model, and those obtained in the second model are close to the experimental values.
Highlights
The Skyrme model is a candidate model of nuclear physics in which nuclei appear as topological solitons
One class of quantities which are not accurately predicted within the standard Skyrme model is that of nuclear binding energies: typically, these are too large by an order of magnitude
The problem is that the skyrmions start to develop singularities, and become numerically inaccessible, before the regime of very low binding energy is reached
Summary
The Skyrme model is a candidate model of nuclear physics in which nuclei appear as topological solitons It can be derived from QCD as an effective theory valid in the limit of an infinite number of colours [1]. U (x) is an SU(2)-valued field, Rμ = (∂μU )U † is its right-invariant current, Fπ and mπ denote the pion decay constant and mass, and g is a dimensionless parameter This Lagrangian should be understood as defining an effective field theory, and the ellipsis represents additional terms which are higher order either in derivatives or in the pion fields 1 − U. Numerical approximations to energy minima in both models will be presented for baryon numbers one to eight These results are consistent with the hypotheses that low binding energies are attainable in both models.
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