The $B=5$ Skyrmion as a two-cluster system

TL;DR

This paper models the B=5 Skyrmion as a two-cluster system, quantizes it, and compares the energy spectrum to Helium-5/Lithium-5 nuclei, revealing limitations in reproducing experimental ground states.

Contribution

It introduces a quantization framework for the B=5 Skyrmion as a two-cluster system, adaptable to other B=4n+1 nuclei, and compares theoretical spectra with experimental data.

Findings

Approximate parity doubling not observed experimentally

Incorrect ground state spin obtained in the model

Framework can be adapted for other cluster-based nuclei

Abstract

The classical $B=5$ Skyrmion can be approximated by a two-cluster system where a $B=1$ Skyrmion is attached to a core $B=4$ Skyrmion. We quantise this system, allowing the $B=1$ to freely orbit the core. The configuration space is 11-dimensional but simplifies significantly after factoring out the overall spin and isospin degrees of freedom. We exactly solve the free quantum problem and then include an interaction potential between the Skyrmions numerically. The resulting energy spectrum is compared to the corresponding nuclei -- the Helium-5/Lithium-5 isodoublet. We find approximate parity doubling not seen in the experimental data. In addition, we fail to obtain the correct ground state spin. The framework laid out for this two-cluster system can readily be modified for other clusters and in particular for other $B=4n+1$ nuclei, of which the $B=5$ is the simplest example.