Fission dynamics with microscopic level densities

Jørgen Randrup,Daniel Ward,Thomas Døssing,Gillis Carlsson,Sven Åberg,Peter Möller,F.-J Hambsch,I Ruskov,N Carjan

doi:10.1051/epjconf/201816900019

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.

Highlights

Soon after the discovery of nuclear fission in 1938 [1], it was recognized that the process can be viewed qualitatively as an evolution of the nuclear shape from that of a single compound nucleus to two receding fragments [2, 3] and that Langevin transport theory provides an appropriate model framework [3, 4]
For a specified shape χ, the single-particle levels for protons and neutrons needed for the combinatorial calculation of the level density are obtained by solving the Schrödinger equation in the associated folded-Yukawa potential. These are the same levels as those previously used in Ref. [11] to calculate the microscopic shell and pairing energies in the construction of the deformation energy surface, guaranteeing consistency of the treatment
The opposite situation is encountered at the symmetric barrier, where a high density of single-particle states around the Fermi energy results in a large positive shell correction energy, while at the same time delivering particle-hole states at a low cost in energy, providing a rapid increase of the level density with local excitation energy

Summary

Fission dynamics with microscopic level densities

Jørgen Randrup1, , Daniel Ward, Gillis Carlsson, Thomas Døssing, Peter Möller, and Sven Åberg2 1Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 2Mathematical Physics, Lund University, 221 00 Lund, Sweden 3Niels Bohr Institute, 2100 Copenhagen Ø, Denmark 4Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

Introduction

Backshifted energy

Brownian shape evolution

Energy dependence of the fragment yields

Fragment proton number Zf

Conclusions and outlook