Functional integral formulation of the mean-field approximation for many-body systems is used to study the nuclear partition function. Both static and dynamic mean-field solutions with statistical occupations of the single particle wave functions are discussed. These correspond to different physical processes in the nuclear system. In the static case the effect of mean-field fluctuations on the nuclear level density is exhibited. This effect enters consistently along with the usual effects of temperature and chemical potential fluctuations. Together they account for generalized random phase approximation correlations and produce bosonlike terms in the nuclear entropy. Because of the self-consistency of the approach, no overcounting of the collective and single-particle degrees of freedom occurs. The effects of the single particle continuum are included in the discussion. Consequences of a possible multiplicity of static mean-field configurations are briefly discussed. Dynamical mean-field solutions are considered in relation to compound nucleus fission. They provide the extension of the mean-field description of spontaneous fission given recently. A microscopic expression for the energy dependence of the average fission width is presented. It combines both the dynamical and statistical features of the tunneling mean-field solution in the subbarrier region.

NUCLEAR STRUCTURE, FISSION Static and dynamic mean field with statistical occupations, level density, RPA correlations, bosonlike terms in the nuclear entropy, single-particle continuum, mean-field equations for compound nucleus fission.

• Received 8 January 1981

DOI:https://doi.org/10.1103/PhysRevC.24.1029