Unified shell-model description of nuclear deformation

A unified shell-model description of nuclear deformation valid throughout the periodic table is presented. Microscopic calculations for the Zr and Mo isotopes are carried out in the frameworks of the shell model and the Hartree-Fock-Bogoliubov method, respectively, to study the shape transition in these nuclei. It is shown that deformation is produced by the isoscalar component of the neutron-proton ($n-p$) interaction in this region, as in the lighter ($2s$,$1d$)-shell region. Deformation sets in when the $T=0\mathrm{}$ $n-p$ interaction dominates over the sphericity-favoring pairing interaction between $T=1\mathrm{}$ pairs of nucleons. When shell effects are important, as for the light and medium-weight regions mentioned above, the simultaneous occupation of neutrons and protons of spin-orbit "partner" orbitals plays a crucial role in determining the onset of deformation. However, their effect is probably less important in the rare-earth and transuranic regions due to the rapid accumulation of single-particle orbitals.