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In previous papers we have introduced a simple model for backbending nuclei which satisfactorily describes the essential experimental features of those nuclei. In this paper we show that the basic assumptions of this model can be deduced by a more microscopic treatment. [ABSTRACT FROM AUTHOR]

In an earlier paper we have extended the new Tamm-Dancoff method to the 'New Tamm-Dancoff method with intermediate states'. This extension makes it possible to treat the effect of nearby levels in many body systems with Green's functions. In addition to well-known approximations, such as the Hartree-Fock theory and the Hartree-Bogoliubov theory, we obtain a series of new approximations. The 'Hartree-Fock theory with intermediate states', which is the subject of the present investigation, is one of these. By using time reversal invariance we have succeeded in clarifying its structure, and we give the solution procedure. The exchange terms in the N-particle intermediate states can be represented by an additional potential Y, which (as is the case for the generalized density matrix ρ) has to be determined selfconsistently. In this way we have overcome the difficulties, that Kerman and Klein met in their 'generalized Hartree-Fock approximation', which has some close similarities with our Hartree-Fock theory with intermediate states. We demonstrate our method for the exactly soluble rotational-vibrational model of Klein et al. Hereby we show how to treat conservation laws and the degeneracy of levels. The Hartree-Fock equations with three intermediate states turn out to give analytical expressions for the energies and the matrix elements. These agree excellently with the exact values in the rotational part of the spectrum. [ABSTRACT FROM AUTHOR]