An application of the theory of Bi-determinantal intrinsic states to28Si

For some 4n nuclei in the 2s?1d shell, Hartree-Fock (HF) theory with most two-body interactions predicts nearly degenerate prolate and oblate Intrinsic states. The spectrum ofJ ^π states obtained from these Intrinsic states by projection is too compressed in relation to the observed levels. For such systems with a two-fold degeneracy of HF solutions, a Bi-Determinantal Intrinsic state (BDIS) is the more apt variational state. The equations of the theory of BDIS, which were first derived by B. Bremond, are here simplified and cast in a form suitable for numerical solution. The transformation operators introduced by Bremond are given a suitable representation, compatible with the symmetries of these 4n nuclei, and an independent definition is then given of self-consistent (SC) Hamiltonians. These equations are then iteratively solved in a tripyl-SC way, by the method of diagonalizing the SC Hamiltonions, for the problematic nucleus²⁸Si. By angular momentum projection from this BDIS, the low-lying spectrum is obtained. The discrepancy between this projected spectrum and the observed levels suggests that²⁸Si is not describable by a BDIS. The present results are in reasonable agreement with those of other Multi-Determinantal Theories for this nucleus.