A Unified Phenomenological Description of Quadrupole Excitations in Even-Even Nuclei

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Abstract
A phenomenological model is developed for the collective quadrupole properties of all even-even nuclei. Rotational. vibrational and transitional nuclei are included in the model on an equal footing. A Bohr-type intrinsic Hamiltonian for harmonic quadrupole vibrations about an axially deformed shape is solved exactly. States of good angular momentum are projected out of the intrinsic states, and they are made orthogonal by a Schmidt scheme. The angular-momentum and phonon-number composition of the states is analyzed at various stages; states with K = 1 are found spurious. Excitation energies for the ground, β, and γ bands are calculated as expectation values of a radically simplified nuclear Hamiltonian in our projected and orthogonalized states. With increasing deformation the calculated energies evolve smoothly from the evenly spaced phonon spectrum to the Bohr-Mottelson rotational-vibrational spectrum according to the scheme of Sheline and Sakai. Our basic model contains only two parameters (deformation d and energy scale) to fix the entire quadrupole spectrum of a nucleus. Our results are given in the form of graphs suitable for immediate application; numerical results are readily produced by our computer code. The ground bands are fitted comparably to the VMI model, while the β and γ bands are reproduced qualitatively. The nuclei 152Sm, 152Gd, and 114Cd are used as test cases. Quadrupole moments and E2 transition rates are also calculated. Intraground-band transition ratios and branching ratios from the β and γ bands are given in terms of the single parameter d. The results are applied to 152Sm with fair success. Finally we extend the model to include two more parameters (anisotropy). The improvement over the basic model is modest in view of the added parameters and computational effort.