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Abstract
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 ofJπ 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.
Published Version
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