By use of a time-dependent wave function of the BCS form, we compute microscopically the energy dissipated for a system with a monopole pairing force moving under the influence of a time-dependent single-particle potential. Quasiparticle generation and coupling of the two-quasiparticle modes of the system are included automatically and provide contact with the Landau-Zener formula. The single-particle potential is related to nuclear shapes generated by viscous hydrodynamical calculations of a fissioning U236 nucleus. We attempt to determine the energy dissipated between the saddle point and scission point by requiring that at the scission point the energy dissipated in the microscopic calculations equal that dissipated in the macroscopic hydrodynamical calculations. This procedure leads to 34 MeV of dissipated energy, which is almost twice the value of 18 MeV obtained from macroscopic hydrodynamical calculations that reproduce experimental fission-fragment kinetic energies. The corresponding value of the nuclear viscosity coefficient determined from the microscopic calculations is 0.04 TP, compared to 0.015 0.005 TP obtained from the macroscopic hydrodynamical calculations. The viscosity coefficient determined from the microscopic calculations is even larger if the dissipated energies are compared at a finite scission neck radius. As a possible resolution of this discrepancy, we propose that level splittings arising from axially asymmetric and reflection-asymmetric deformations during the descent from the saddle point to scission reduce the energy dissipation and make the nuclei only moderately viscous. NUCLEAR REACTIONS Fission U236; calculated microscopically energy dissipated between saddle point and scission. Monopole pairing force, time-dependent wave function of BCS form, correspondence with Landau-Zener formula, nuclear viscosity, axially asymmetric and reflection-asymmetric deformations important.
ASJC Scopus subject areas
- Nuclear and High Energy Physics