Abstract
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.
Highlights
The lightly bound Skyrme model, developed by the Leeds group [1,2,3], gives new insight into the structure and symmetries of Skyrmions for a large range of baryon numbers, B
Four orientations are needed, arranged periodically. These are specified by four SO(3) matrices, but it is convenient to replace them by the four quaternions 1,i,j,k. (This involves a sign choice that is unimportant here but becomes more significant when we consider quantization.) Skyrmions which lie at points of the form (0,0,0) mod 4 have orientation 1, and points (0,2,2), (2,0,2), and (2,2,0) mod 4 have, respectively, orientations i, j, and k. These orientations are copied onto any weight cluster of quadrality 0, which is a subcluster of the face-centered cubic (FCC) lattice
This paper has focused on those clusters that correspond to SU(4) weight diagrams, which are all tetrahedrally symmetric subclusters of the FCC lattice, and sometimes octahedrally symmetric
Summary
The lightly bound Skyrme model, developed by the Leeds group [1,2,3], gives new insight into the structure and symmetries of Skyrmions for a large range of baryon numbers, B. And the weight diagrams of these irreps are invariant under O, the full octahedral subgroup of O(3), with 48 elements These symmetries are important for us—they are the bodyfixed symmetry groups of the Skyrmion clusters and have a crucial influence on the allowed combinations of spin, isospin, and parity of quantum states. Weights of the quadrality 1 irrep 4 form a regular tetrahedron with center of mass at the origin, but only after a shift do they form a cluster in the FCC root lattice with one point at the origin, for example, as the set of points (0,0,0), (2,2,0),.
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