Normal Modes of the B=4 Skyrme Soliton

Abstract

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.

4 pages, RevTex file and two figures, the former requiring spectrum.eps, the latter requiring 17 eps files sh.sol*.eps which are included. Replaced version corrects one typo in the Table, replacing the representation F_1^- with F_2^- for the omega=.513 mode

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