Many-Cluster Problem by the Orthogonality Condition Model: General Discussion and 12C Problem

Abstract

Treatment of many-cluster problem by the orthogonality condition model (OCM) is formulated as an approximation to the many-cluster resonating group method (RGM), and its significance is discussed in detail mainly by analysing the results of its application to the 3α problem of 12C. Non-redundant OCM basis states which are at the same time the nonredundant eigenvectors of the RGM overlap kernel are clssified by the Elliott SU3 scheme, through which the relation of OCM or RGM with the shell model is clarified. Calculated wave functions of 01+ and 02+ of 12C are analysed from this point. Possible truncation schemes are discussed and K-harmonics-type truncation scheme is shown to work well by applying it to the 3α problem. The OCM for 3α gives a binding energy for the ground state about twice as deep as the previously reported results with the phenomenological α-α potentials which have repulsive core. It is shown that this large difference is due to the difference of the treatment of the inner repulsive effect arising from the Pauli exclusion principle; one is the orthogonality condition and the other is the repulsive core. Since the OCM treatment of the inner repulsive effect is considered to be more plausible theoretically, the importance of the OCM to the many-cluster problem is emphasized. On the basis of the investigation on the inner repulsive effect in many-cluster system, we also give some comments on the mechanism of the coexistence of shell- and molecule-like structures.