Normal Modes of the B=4 Skyrme Soliton

The Skyrme model of nuclear physics requires quantisation if it is to match observed nuclear properties. A simple technique is used to find the normal mode spectrum of the baryon number B=4 Skyrme soliton, representing the $\alpha$ particle. We find sixteen vibrational modes and classify them under the cubic symmetry group $O_h$ of the static solution. The spectrum possesses a remarkable structure, with the lowest energy modes lying in those representations expected from an approximate correspondence between Skyrmions and BPS monopoles. The next mode up is the `breather', and above that are higher multipole breathing modes.