Nuclear deformations in the pairing-plus-quadrupole model (III). Static nuclear shapes in the rare-earth region

The potential energy of deformation (β, γ), is calculated with the pairing-plus-quadrupole model for nuclei with N=82–126, Z=50–82. There is a sudden onset of deformation in the N=86–90 region, and the static nuclear shape, the lowest minimum of the potential function, changes from spherical to prolate. The disappearance of deformation in the Z=74–80 region is more gradual, and the static shape changes from prolate to asymmetric to oblate to spherical. The energy of zero-point motion is calculated, and it is concluded that all the stable deformed shapes of the region are prolate. Proton and neutron energy gaps, intrinsic quadrupole moments, moments of inertia and gyromagnetic ratios of the doubly even nuclei of the rare-earth region are calculated and compared with the experimental data.