The self-consistent quasiparticle-phonon coupling equations are solved for deformed superfluid nuclei in the rare earth region. Parameters are chosen to agree with previous calculations, and the solutions for $\gamma$-, $\beta$-, and octupole-vibrational states are compared to experiments and to previous descriptions of both even- and oddmass nuclei. The importance of exclusion principle violations in the rare earth region is noted as well as the interference of pairing and quadrupole correlations in the even nuclei with $A\sim 164$. An "intruder" state is predicted in the Eu and Tb isotopes. The splitting of the $K\pm 2$ states in ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$ and ${}_{}{}^{167}{}_{}{}^{}\mathrm{Er}$ is derived from higher-order contributions to the self-energy.

NUCLEAR THEORY Green's function method with pairing. Self-consistent RPA, collective effects in odd-$H$ rare earth nuclei.

• Received 18 June 1976

DOI:https://doi.org/10.1103/PhysRevC.15.1103