On the Spin of the B=7 Skyrmion

TL;DR

This paper studies the quantum properties of the B=7 Skyrmion with icosahedral symmetry, revealing new relationships between classical solutions and quantum states, and exploring symmetry breaking effects relevant to lithium and beryllium isotopes.

Contribution

It introduces a novel connection between quantum states and the rational map approximation, and analyzes symmetry breaking effects on allowed spin states.

Findings

Identified a quantum state preserving classical symmetries.

Established a relationship between quantum states and rational map approximation.

Predicted spin 3/2 states for partially broken symmetries.

Abstract

We investigate the collective coordinate quantization of the icosahedrally symmetric B=7 Skyrmion, which is known to have a ground state with spin 7/2 and isospin 1/2. We find a particular quantum state maximally preserving the symmetries of the classical solution, and also present a novel relationship between the quantum state and the rational map approximation to the classical solution. We also investigate the allowed spin states if the icosahedral symmetry is partially broken. Skyrme field configurations with $D_5$ residual symmetry can be quantized with spin 3/2, giving a realistic model for the ground states of the $^7{\rm Li}/^7{\rm Be}$ isospin doublet