Skyrmions, Tetrahedra and Magic Numbers

Abstract

Michael Atiyah’s interest in Skyrmions and their relationship to monopoles and instantons is recalled. Some approximate models of Skyrmions with large baryon numbers are then considered. Skyrmions having particularly strong binding are clusters of unit baryon number Skyrmions arranged as truncated tetrahedra. Their baryon numbers, $B = 4 \,, 16 \,, 40 \,, 80 \,, 140 \,, 224$ , are the tetrahedral numbers multiplied by four, agreeing with the magic proton and neutron numbers $2 \,, 8 \,, 20 \,, 40 \,, 70 \,, 112$ occurring in the nuclear shell model in the absence of strong spin-orbit coupling.