Mean First Passage Time for Nuclear Fission and the Emission of Light Particles

The concept of a mean first passage time is used to study the time lapse over which a fissioning system may emit light particles. The influence of the “transient” and “saddle to scission times” on this emission are critically examined. It is argued that within the limits of Kramers’s picture of fission no enhancement over that given by his rate formula needs to be considered.

Figure 1

The current across the barrier for different initial conditions (see text).

Figure 2

Samples of initial points which overcome the saddle within a time ${\tau }_s$: left part: ${\tau }_s\simeq {\tau }_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}}$; right part: ${\tau }_s\simeq {\tau }_{\mathrm{K}}$.

Figure 3

MFPT for a cubic potential normalized to its asymptotic value, shown by the solid, dashed, dot-dashed, and dotted curves which correspond to $T/E_b=0.1$, 0.2, 0.5, and 1.0. The dash-double-dotted curve represents a calculation within the Langevin approach for $T/E_b=1$.

Figure 4

The MFPT for the case of small and vanishing barriers for $T=2$, 3, and 4 MeV from top to bottom. The $Q_{\mathrm{s}\mathrm{c}}$ corresponds to a scission point 20 MeV below the barrier.