Nuclear friction and lifetime of induced fission.

Abstract

Induced nuclear fission is described as a transport process of the fission degree of freedom over the fission barrier. The lifetime of the event is defined in terms of the probability of finding the nuclear system in the potential well corresponding to the ground-state deformation. This definition appears as a natural generalization to nonstationary transport processes of the usual expression for the lifetime. Using the conservation law for the current we relate the lifetime to the time-integrated escape rate across the collective potential barrier.We envisage a schematic model in which the escape rate attains a constant value only after a certain transient time \ensuremath{\tau}. In this case we show that the lifetime evaluated at the saddle point of the collective potential is made up of two contributions: one---\ensuremath{\Elzxh}/${\ensuremath{\Gamma}}_{f}^{\mathrm{stat}\mathrm{---}}$identified as the quasistationary transition-state expression of the statistical model and one proportional to \ensuremath{\tau}, hence directly related to the transient behavior of the transport process. As long as \ensuremath{\Elzxh}/${\ensuremath{\Gamma}}_{f}^{\mathrm{stat}\mathrm{\ensuremath{\gg}}\mathrm{\ensuremath{\tau}}}$, fission can well be described as a quasistationary transport phenomenon. For \ensuremath{\Elzxh}/${\ensuremath{\Gamma}}_{f}^{\mathrm{stat}\ensuremath{\ll}\mathrm{\ensuremath{\tau}}}$, which occurs for excitation energies of a few hundreds of MeV and small fission barriers, the fission process becomes a transient phenomenon of duration of the order of \ensuremath{\tau}.For a single collective variable and its canonically conjugate momentum, we study the transient time \ensuremath{\tau} as a function of the nuclear friction constant \ensuremath{\beta}. Thereby we extend and complete the findings of earlier studies. For a specific system of mass A=248, we calculate the lifetime at the saddle point of the collective potential and find results in keeping with our schematic model. We assume further that the collective potential beyond the saddle point can be correctly represented by an inverted parabola and we obtain an analytical expression for the current evaluated at the scission point. We find that this current can be expressed reliably as the current evaluated at the saddle point but delayed by a constant time \ensuremath{\tau}${\ifmmode\bar\else\textasciimacron\fi{}}_{1}$ which we obtain and interpret. Thereby we bring support to the conjectures made in several studies of fissioning systems within the same framework.As a result we also extend trivially the schematic model to the escape rate evaluated at the scission point and obtain the lifetime evaluated at scission as the sum of the lifetime evaluated at the saddle point and of the time delay \ensuremath{\tau}${\ifmmode\bar\else\textasciimacron\fi{}}_{1}$.