Memory effects on descent from the nuclear fission barrier

Non-Markovian transport equations for nuclear large amplitude motion are derived from the collisional kinetic equation. The memory effects are caused by Fermi surface distortions and depend on the relaxation time. It is shown that nuclear collective motion and nuclear fission are influenced strongly by memory effects at the relaxation time $\ensuremath{\tau}>~5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23} \mathrm{s}.$ In particular, the descent of the nucleus from the fission barrier is accompanied by characteristic shape oscillations. The eigenfrequency and the damping of the shape oscillations depend on the contribution of the memory integral in the equations of motion. The shape oscillations disappear at the short relaxation time regime at $\stackrel{\ensuremath{\rightarrow}}{\mathrm{\ensuremath{\tau}}}$0, which corresponds to the usual Markovian motion in the presence of friction forces. We show that the elastic forces produced by the memory integral lead to a significant delay for the descent of the nucleus from the barrier. Numerical calculations for the nucleus ${}^{236}\mathrm{U}$ show that due to the memory effect the saddle-to-scission time grows by a factor of about 3 with respect to the corresponding saddle-to-scission time obtained in liquid drop model calculations with friction forces.

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