Nuclear descent from the fission barrier in the presence of long--range memory effects

We have investigated the peculiarities of nuclear descent from a parabolic fission barrier within a generalized Langevin equation with power–law $f(t-t^{\mathrm{\prime }})=(\mathrm{\mid }t-t^{\mathrm{\prime }}\mathrm{\mid }\mathrm{/}\tau {)}^{-\alpha }$ memory function. We have observed much stronger slowing down of the nuclear descent in the presence of long–range memory effects, caused by the power–law memory function at $0<\alpha <1$, than in the presence of short–range memory effects, generated by exponential $f(t-t^{\mathrm{\prime }})=\mathrm{e}\mathrm{x}\mathrm{p}(-\mathrm{\mid }t-t^{\mathrm{\prime }}\mathrm{\mid }\mathrm{/}\tau )$ memory function. At a specific value of the exponent $\alpha =1\mathrm{/}2$ of the power–law memory function, it turned out possible to find analytically the trajectory of the descent and demonstrate that the long–range memory effects give rise to complex time oscillations of nuclear shape, becoming more frequent and damped with the correlation time $\tau$. We have found fairly long ($>{10}^{-20}\mathrm{s}$) times of the descent of ${}^{236}\mathrm{U}$ at the values of the correlation time $\tau \sim [{10}^{-24}÷{10}^{-23}]\mathrm{s}$.