Determination of fission rate by mean last passage time

The mean last passage time is introduced instead of the mean first passage time for determining the decay rate of a nucleus after induced fission. The stationary fission rate calculated by the inverse of the mean last passage time at the saddle point is in agreement with the result of Langevin simulations and better than that of the mean first passing time at the scission point. In particular, we take into account the backstreaming effect where test particles pass over the potential barrier multiple times. It is shown that the oscillating time of a hot fissioning system around the saddle point is the longest one in time scales of the fission, thus more neutrons might be emitted during this period.

Figure 1

The three kinds of schematic potentials.

Figure 2

Time-dependent fission rate calculated by Langevin simulation using different methods and various potentials. The parameters used are $T=4\text{MeV}$, $\gamma =3.4\text{MeV}∕\hslash$, and the scission position $x_{sc}=2.7$.

Figure 3

Dependence of the stationary fission rate on the temperature $T$ at fixed $\gamma =3.4\text{MeV}∕\hslash$ in (a) and on the friction strength $\gamma$ at fixed $T=4\text{MeV}$ in (b). Here the potential $V_3$ with double saddle potential is used. The solid lines are the results of Langevin simulation, the dashed lines are inverse of the mean last passage time across the saddle point, and the dotted lines are the mean first passage time at the scission point.

Figure 4

The ratio between the resulting rates calculated by theoretical expression and numerical simulation as a function of the exit position. The solid and dashed lines are the results of MLPT across the saddle point and MFPT arriving at the exit point, respectively. The temperatures are equal to 2, 3, and $4\text{MeV}$ from top to bottom and $\gamma =3.4\text{MeV}∕\hslash$.