Non-Markovian fission rate within the Kramers model

We investigate possible non-Markovian effects in fission dynamics of highly excited nuclei by using the generalized Langevin approach for a single nuclear shape parameter. We estimate the effective friction and stiffness coefficients of the non-Markovian dynamics for different values of the correlation time of the random force in the Langevin equation of motion. We discuss the found nonmonotonic dependence of the fission rate on the correlation time. We also show how to extend the Kramers theory of fission rate in the case of non-Markovian thermal diffusion over barrier.

Figure 1

The memory-induced renormalization (18) of the potential energy of the non-Markovian system (1, 2, 3, 4, 5), calculated at ${\kappa }_0/\left|C_B\right|=0.15$, is shown by the dashed line. The Kramers potential $E_{\mathrm{pot}}$ (2) is given by the solid line.

Figure 2

Time dependences of the functions $\gamma \left(t\right),C^{\prime }\left(t\right)$ (22), defining the general friction-conservative splitting (19) of the time-retarded force in the Langevin equation of motion (1), for the motion near the barrier top and at correlation times $\tau <{\tau }_{\mathrm{thresh}}$.

Figure 3

The correlation-time dependence of the effective friction coefficient ${\gamma }_{0,B}$ and the memory-induced correction $C_{0,B}^{\prime }$ to the stiffness (29) and (31) of the non-Markovian Langevin system (1, 2, 3, 4, 5) for the motion near the barrier top.

Figure 4

The correlation-time dependence of the effective friction coefficient ${\gamma }_{0,A}$ and the memory-induced correction $C_{0,A}^{\prime }$ to the stiffness (32) of the non-Markovian Langevin system (1, 2, 3, 4, 5) for the motion near the potential minimum.

Figure 5

Time dependence of the probability rate $R\left(t\right)$ (33) at the correlation times $\tau =2\times {10}^{-23}\mathrm{s}$ and $\tau =10\times {10}^{-23}\mathrm{s}$.

Figure 6

The fission rate $R_f$ as an asymptotic value of the probability rate (33) (solid line) as a function of the correlation time $\tau$. The standard Kramers formula (34) for the fission rate with the $\tau$-dependent friction coefficient ${\gamma }_{0,B}$ of Eqs. (29) and (31) is given by the dashed line.

Figure 7

The fission rate $R_f$ as an asymptotic value of the probability rate (33) (solid line) vs the correlation time $\tau$. The non-Markovian extension of the Kramers theory (49) for the fission rate is shown by the dashed line. The dotted line represents the fission rate $R_f$ calculated as inverse first-passage time (51).