The intrinsic state as a sum of two determinants for a degenerate Hartree-Fock problem

The lowest deformed Hartree-Fock (HF) solutions of the 4n- 2s-1d shell nuclei are approximately doubly degenerate, a typical example being 28Si. The projected spectra from one of these degenerate HF (i.e. the oblate) solutions of this nucleus is in violent disagreement with the observed states. This points to the construction of an intrinsic state as a sum of two Slater determinants (ISTD) which could break the degeneracy. The fully self-consistent (SC) ISTD theory has been applied to 28Si. Firstly an ISTD is chosen with Nilsson-orbitals as the single-particle orbits and the energy is minimised in the ISTD by varying the two quadrupole deformations and one mixing variable. Then using the formalism of B. Bremond, this problem is solved in a fully SC way by the method of diagonalizing coupled SC Hamiltonians. The result of the SC calculation tallies with that of Nilsson-Slater determinants. In either case the energy is not lowered substantially below the HF value. (auth.)