The theory of anharmonic nuclear vibrational motion (nonlinear equations-of-motion method) developed in the preceding paper is applied to ${}_{}{}^{60,62,64}{}_{}{}^{}\mathrm{Ni}$, which exhibit one and two phonon quadrupole collective states. A model Hamiltonian consisting of a modified pairing plus quadrupole interaction is studied first by comparing the results of the nonlinear equations-of-motion method with those of an exact diagonalization. Contrary to popular opinion, the model chosen fails to produce a vibrational spectrum, except in the case of ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$, and, as a consequence, the nonlinear equations-of-motion method, designed specifically to describe vibrational spectra, accords well with the exact calculations only for this case. A simple method is then described, within the framework of the nonlinear equations-of-motion method, for refining the model Hamiltonian so as to bring it into accord with experiment. In practice, it is found that a simple additional parameter in the Hamiltonian suffices to yield descriptions of the quadrupole states in Ni isotopes comparable in precision to the most up-to-date versions (modified, adjusted, etc.) of the surface delta interaction model.

NUCLEAR STRUCTURE Theory of anharmonic nuclear vibrations applied to ${}_{}{}^{60,62,64}{}_{}{}^{}\mathrm{Ni}$. Modified pairing plus quadrupole interactions. Comparison with surface delta models.

• Received 27 November 1978

DOI:https://doi.org/10.1103/PhysRevC.19.2023