Macroscopic model of rotating nuclei

Abstract

I present a macroscopic model for the energy of rotating nuclei which has several refinements relative to the rotating-liquid-drop model. Of most importance are the inclusion of finite-range effects in the nuclear surface energy by means of a Yukawa-plus-exponential potential, finite surface diffuseness effects in the Coulomb energy and in the rotational moments of inertia, and an improved specification of nuclear shapes. With this model I calculate the properties of points of equilibrium corresponding to nuclear ground states and fission saddle points. The results are qualitatively similar to those of the rotating-liquid-drop model, but there are significant quantitative differences in fission-barrier heights and moments of inertia. Fission barriers for nonrotating nuclei are calculated for nuclei with atomic numbers varying from 14 to 117. For rotating nuclei, detailed results are given for the entire range of angular momentum for which a fission barrier exists, for nuclei with atomic numbers from 20 to 100, and for mass numbers which exceed the range of known nuclei. The calculated barriers are lower than liquid-drop-model barriers for lighter nuclei and are consistent with those deduced from experimental fission-fusion data over a wide range of nuclear species. The present calculations indicate that super-deformed rotating ground states, which are predicted in the liquid-drop model, would not survive fission long enough to undergo electromagnetic decay. Multiparameter functions which approximately reproduce the calculated results for barrier heights and moments of inertia are described.