Collective Motion in Finite Many-Particle Systems. III. Foundations of a Theory of Rotational Spectra of Deformed Nuclei

The generalized Hartree-Fock approximation developed in previous papers is here applied to provide a microscopic and fully quantum-mechanical self-consistent theory of the rotational spectra of deformed nuclei. Starting from a rotation- and inversion-invariant Hamiltonian, the equations of the method are derived for the present application, including the effect of pairing correlations. The equations of motion yield the description of a quasiparticle (hole) self-consistently coupled to a rotator. Within a consistent approximation, all the usual observables associated with the notion of deformed nuclei-moments of inertia, collective gyromagnetic ratios, quadrupole moments, and transition probabilities-can be obtained in terms of the solutions of these equations, which are developed as a power series in the reciprocal of the moment of inertia. The zero-order theory is equivalent to the best current theory of nuclear shapes and also describes, therefore, the quadrupolar properties of the nucleus. The first-order solution suffices for the calculation of the moment of inertia and the collective gyromagnetic ratio. Here again familiar results are obtained in the only case considered in detail, that of a single band with unlimited angular-momentum states available. The second-order solution is also found and used to study the spectrum of the neighboring odd nuclei. The main new results of this paper are contained in the formulas for the moment of inertia and decoupling parameter for odd-particle or hole-based bands, where the self-consistency requirements yield terms not hitherto noticed in the case of an odd nucleus.