Energy sharing based on microscopic level densities

¹ Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
² Yukawa Institute for Theoretical Physics, Kyoto 606-8502, Japan
³ Mathematical Physics, Lund University, S-221 00 Lund, Sweden
⁴ Niels Bohr Institute, DK-2100 Copenhagen ø, Denmark
⁵ Moller Scientific Graphics and Computing, Los Alamos, New Mexico 87545, USA

^* e-mail: JRandrup@LBL.gov

Published online: 15 December 2021

Abstract

The transformation of a moderately excited heavy nucleus into two excited fission fragments is modeled as a strongly damped evolution of the nuclear shape. The resulting Brownian motion in the multi-dimensional deformation space is guided by the shape-dependent level density which has been calculated microscopically for each of nearly ten million shapes (given in the three-quadratic-surfaces parametrization) by using a previously developed combinatorial method that employs the same single-particle levels as those used for the calculation of the pairing and shell contributions to the five-dimensional macroscopic-microscopic potential-energy surface.

The stochastic shape evolution is followed until a small critical neck radius is reached, at which point the mass, charge, and shape of the two proto-fragments are extracted. The available excitation energy is divided statistically on the basis of the microscopic level densities associated with the two distorted fragments. Specific fragment structure features may cause the distribution of the energy disvision to deviate significantly from expectations based on a Fermi-gas level density.

After their formation at scission, the initially distorted fragments are being accelerated by their mutual Coulomb repulsion as their shapes relax to their equilibrium forms. The associated distortion energy is converted to additional excitation energy in the fully accelerated fragments. These subsequently undergo sequential neutron evaporation which is calculated using again the appropriate microscopic level densities. The resulting dependence of the mean neutron multiplicity on the fragment mass, as well as the dependence of on the initial excitation energy of the fissioning compound nucleus, exhibit features that are similar to the experimentally observed behavior, suggesting that the microscopic energy sharing mechanism plays an important role in low-energy fission.