  For both reactions we use an approach similar to that of compound-nucleus
reaction theory. For neutron-induced fission, we describe the compound system
generated by absorption of the neutron and the nuclear system near the scission
point as two statistically independent systems governed by random-matrix
theory. The systems are connected either by a barrier penetration factor or by
a set of transition states above the barrier. Each system is coupled to a
different set of channels. An analogous model is used for heavy-ion fusion.
Assuming that (seen from the entrance channel) the system on the other side of
the barrier is in the regime of strongly overlapping resonances, we obtain for
fixed spin and parity closed-form analytical expressions for the total
probability for fission and for fusion. Parts of these expressions can be
calculated reliably within existing compound-nucleus reaction theory. The
remaining parts are the probabilities for passage through or over the barrier.
These may be determined theoretically from the liquid-drop model or
experimentally from total fission or fusion cross sections.
