Irrotational or Rotational Flow Motion in Deformed Nuclei

The "governor model" of Trainor and the author, based on the assumptions of a rotational flow motion and the existence of a rotationally invariant core in nuclei, is completely reformulated in terms of the better-known deformation parameter ${\beta }_0$. It is shown that this model results in an expression for the ground-state moment of inertia which, in agreement with the empirical study of Mariscotti et al. (the variable-moment-of-inertia model), gives a linear dependence on the deformation parameter (${\mathcal{I}}^{\mathrm{}\left(0\right)\mathrm{}}\propto {\beta }_0$). The hydrodynamical model, based on the irrotational flow motion and using the condition ${\mathcal{I}}^{\mathrm{}\left(0\right)\mathrm{}}\propto \beta _0^{}{}_{}{}^2$, is also reformulated to include all the higher-order corrections to the $J(J+1\mathrm{})\mathrm{}$ law. Both the models are then applied to all the even-even nuclei in the mass regions $152\le A\le 188$ and $A\ge 224$, and the results are compared with experiment. The discussion is restricted to the ground-state rotational bands only. In addition to the rotational-state energies and the ground-state moment of inertia, other nuclear properties, such as the variation of the moment of inertia and the quadrupole moment with the angular momentum, are also investigated.