Surface Coupling Mechanism for Approaching Statistical Equilibrium in Compound Nucleus Formation, with Application to Fission

In a particular representation where the state vectors are not eigenstates of the Hamiltonian, coupling terms remain which cause "virtual" or "real" transitions among states. An appropriate choice of representation depends upon the physical processes involved. The decay of a compound nucleus, expecially by fission, is considered. The strong coupling representation of the unified model is employed, with surface oscillations inducing transitions among states of the representation. A diffusion equation is derived to describe the flow of probability among the states available within constraints. An estimate of the characteristic relaxation time for arriving at statistical equilibrium is obtained. Only when the relaxation time is short compared with a basic reaction time are statistical arguments valid to evaluate the reaction rate. As an example the relevant reaction time in the fission process is a collective vibrational period. The necessary condition appears to be satisfied for excitation energies more than a few Mev above threshold. Arguments are presented to show why equilibrium may not be maintained at lower energy. Thus the usual estimate of the number of open channels, $\frac{2\pi {\overline{\Gamma }}_f}{D}$, would give a number lower than what one would estimate simply from penetrability of the fission barrier. This seems to explain, at least in part, the anomalously low numbers of channels obtained in this manner. Problems relating to the validity of oft made statistical assumptions at scission are also discussed.