A ug 2 02 1 Memory effects in Langevin approach to nuclear fission process

We present the calculations within the schematic Langevin approach to investigate the dependence of fission width on the memory time and the excitation energy at low temperatures where the quantum fluctuations play an important role. For this, we consider the simple one-dimensional model with the potential energy given by the two parabolic potentials (Kramers potential). For the friction and mass parameters, we use the deformation independent values fitted to the results obtained earlier within the microscopic linear response theory. We have found out that at small excitation energies (comparable with the fission barrier height) the memory effects in the friction and random force acts on the fission width in opposite direction. The total effect depends very much on the value of damping parameter η. In the low viscosity region the fission width Γf grows as function of η and decreases as function of τ . In the high viscosity region, the tendency is opposite. The fission width Γf decreases as function of η and increases as function of τ . Such dependence is common both for small and large excitation energies.