WHY ARE DEFORMED-NUCLEI PROLATE

We address the general question of the predominance of prolate shapes among deformed nuclei. For that purpose, we show that the kinetic energy of a deformed intrinsic state is a minimum when the deformation is such that the mean square components of the momentum are isotropically distributed. In this way we generalize Mottelson's self-consistency equation to apply to a general class of deformed shell-model wave functions. The generalized equation is then used to show that states of maximum deformation compatible with the Pauli principle have lowest kinetic energy and, as a consequence, prolate shapes are preferred over oblate shapes. © 1990.