Application of Group Theory to the Alpha Particle Model of the S32 Nucleus

In the alpha particle model for a nucleus one assumes that the system is composed of alpha clusters, in so far as possible, bound in some symmetrical configuration. This model is supported by the observation that many nuclei emit alpha rays. Since these nuclei are presumably constructed from alpha particles alone, bonding within such particles is apparently much stronger than that between two alpha particles and between an alpha particle and a nucleon. In the simple implementation of the model, lower excited states are associated with excitation of the 3-3 rotational and vibrational degrees of freedom. The rotational levels are not characteristic of the particular configuration chosen while the vibrational levels are. A more serious objection is that the amplitudes of vibration which the simple model yields are as large as the intercluster distance. Thus, the alpha particles are smeared out through the nucleus as if they were not really distinct. Calculation by Dennison4 and Kameny5 of the nuclear energy levels of O16 suing the alpha particle model produced a system of levels remarkably close to know the experimental values. By attempting to correlate the levels of these models with known experimental values, one eliminates incorrect structures. If the alpha particle model is valid, at least one of these structures should give a scheme corresponding to the experimental data. For the requisite group theory, the reader may consult various references on the subject