States of Carbon-12 in the Skyrme Model

TL;DR

This paper analyzes two Skyrmion solutions in the Skyrme model for Carbon-12, calculating their rotational spectra and radii, which align well with experimental nuclear data.

Contribution

It provides a detailed recalculation of moments of inertia for Skyrmions with baryon number 12, linking their quantized states to observed nuclear structures of Carbon-12.

Findings

Good match with Carbon-12 ground-state band

Reproduces rotational band of Hoyle state

Accurately predicts matter radii

Abstract

The Skyrme model has two Skyrmion solutions of baryon number $12$, with $D_{3h}$ and $D_{4h}$ symmetries. The first has an equilateral triangular shape and the second an extended linear shape, analogous to the triangle and linear chain structures of three alpha particles. We recalculate the moments of inertia of these Skyrmions, and deduce the energies and spins of their quantized rotational excitations. There is a good match with the ground-state band of Carbon-12, and with the recently established rotational band of the Hoyle state. The ratio of the root mean square matter radii also matches the experimental value.