We have investigated the peculiarities of nuclear descent from a parabolic fission barrier within a generalized Langevin equation with power--law $f(t-t')=(|t-t'|/\tau)^{ -\alpha}$ 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 $f(t-t')={ \rm exp}(-|t-t'|/\tau)$ memory function. At a specific value of the exponent $\alpha=1/2$ 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 ($>10^{ -20}~{ \rm s}$) times of the descent of $^{ \rm 236}{ \rm U}$ at the values of the correlation time $\tau \sim [10^{ -24}\div 10^{ -23}]~{ \rm s}$.
Categories: nucl-th