States of Carbon-12 in the Skyrme Model

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.