Fission dynamics with microscopic level densities

¹ Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
² Mathematical Physics, Lund University, 221 00 Lund, Sweden
³ Niels Bohr Institute, 2100 Copenhagen Ø, Denmark
⁴ Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

^* e-mail: JRandrup@LBL.gov

Published online: 6 March 2018

Abstract

Working within the Langevin framework of nuclear shape dynamics, we study the dependence of the evolution on the degree of excitation. As the excitation energy of the fissioning system is increased, the pairing correlations and the shell effects diminish and the effective potential-energy surface becomes ever more liquid-drop like. This feature can be included in the treatment in a formally well-founded manner by using the local level densities as a basis for the shape evolution. This is particularly easy to understand and implement in the Metropolis treatment where the evolution is simulated by means of a random walk on the five-dimensional lattice of shapes for which the potential energy has been tabulated. Because the individual steps between two neighboring lattice sites are decided on the basis of the ratio of the statistical weights, what is needed is the ratio of the local level densities for those shapes, evaluated at the associated local excitation energies. For this purpose, we adapt a recently developed combinatorial method for calculating level densities which employs the same single-particle levels as those that were used for the calculation of the pairing and shell contributions to the macroscopic-microscopic deformation-energy surface. For each nucleus under consideration, the level density (for a fixed total angular momentum) is calculated microscopically for each of the over five million shapes given in the three-quadratic-surface parametrization. This novel treatment, which introduces no new parameters, is illustrated for the fission fragment mass distributions for selected uranium and plutonium cases.