Comparison of the Interacting Boson Approximation with AN Exact Shell Model Calculation on the OXYGEN-16 Nucleus.

The validity of the interacting Boson approximation (IBA) was examined, and the degree of success that this approximation has in explaining the structure of the O-16 nucleus was investigated. An extension of the IBA, the hybrid Boson approximation (HBA), is proposed which corrects some of the deficiencies of the IBA. The results of the two approximate methods are compared with an exact shell model calculation in the case of the (0+,0) and 2+,0) two hole-two particle states. These calculations were done for a Gaussian and a zero-range two-body interaction, and within the configuration space chosen, the holes were restricted in the p shell and the particles in the s-d shell. The relevant matrix elements of the Hamiltonian are given in detail, and the spuriocity of the center of mass motion is almost completely removed in the exact calculation.