Lightly Bound Skyrmions, Tetrahedra and Magic Numbers

Abstract

In the lightly bound Skyrme model, several Skyrmions having particularly strong binding are clusters of unit baryon number Skyrmions arranged as truncated tetrahedra. Their baryon numbers form the sequence B = 4, 16, 40, 80, 140, 224. This is the standard sequence of tetrahedral numbers multiplied by four, and therefore agrees with the sequence of magic proton and neutron numbers 2, 8, 20, 40, 70, 112 that occurs in the nuclear shell model in the absence of strong spin-orbit coupling. This sequence includes several of the magic numbers that are predicted for tetrahedrally deformed nuclei, and also appears in the context of the FCC lattice geometry investigated long ago by Wigner and revived more recently.

arXiv comment25 pages, 4 figures. Appendix on bipyramidal and octahedral clusters of baryons. Minor changes and additional references

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Cited by in corpus (4)

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• Rolling Skyrmions and the Nuclear Spin-Orbit Force
• Fractionalized Quasiparticles in Dense Baryonic Matter
• Quantized Skyrmions from SU(4) Weight Diagrams