Hydrodynamic model wavefunctions in intrinsic coordinates and their application to the structure of even-even nuclei

A closed expression is presented for intrinsic-coordinate (β, γ, thetai) eigenfunctions of the hydrodynamic, quadrupole-vibration Hamiltonian of A. Bohr. These functions are used as an expansion basis for the treatment of more general collective Hamiltonians. Two classes of such Hamiltonians are considered. In each the potential energy term of the Bohr Hamiltonian, 1/2Cβ2, has been replaced with a more general function of the shape coordinates, V(β, γ). The potential of Gneuss and Greiner is used to demonstrate the soundness of the calculational technqiues, and to illustrate convergence properties of calculated energies. Potentials possessing a single minimum on 0 less than or equal to γ less than or equal to 600 are considered through the study of a quadratic-potential [QP] Hamiltonian having V(β, γ) = 1/2Cβ(β - β0)2 + Cγ(γ - γ0)2. The smooth development from spherical to asymmetrically deformed nuclear shapes is investigated by systematic variation of the parameters β0 and Cγ. Model energies and E2 transition rates are traced during this process. The QP model is then applied to 106Pd, 166Er, 182W, 122Te, and sup 186,188,190,192/Os. Low-energy γ vibrations appear to play a prominent role in the latter five nuclei, and the QP model offers a better accounting of experimental spectra than does the model of Davydov and Chaban