SYSTEMATICS OF THE AVERAGE RESONANCE WIDTHS IN OVERLAPPING RESONANCE-SCATTERING AND ITS CONNECTION WITH THE RRKM THEORY

Decay processes of densely distributed quasi-bound states are studied numerically by randomly generating the Hamiltonian matrices. The avera ge decay rate obtained from the Feshbach theory of resonance scatterin g exhibits systematic behavior against the average density of states ( rho), the number of continua (K) and the average coupling strength to the continua (upsilon). The distribution of the decay rates bifurcates into long-lived and short-lived branches when rho is larger than a ce rtain critical value rho(c), which is found to be roughly equal to the inverse of the 0-th order partial width [gamma(part.)]. Thus one can clearly distinguish the isolated resonance regime in the region rho < rho(c) and overlapping resonance regime in the region rho > rho(c). Th e states belonging to the short-lived branch exhibit a very broad ener gy spectrum and are recognized as background continua. They are not qu asi-bound states in practice. The decay rates of the long-lived branch , on the other hand, systematically decrease with rho at rho much-grea ter-than rho(c). The average of these decay rates is proportional to [ gamma(part.)]-1K(rho)-2. When the short-lived branch is excluded, the average decay rate, [GAMMA/HBAR], roughly agrees with that of the RRKM rate in the region rho almost-equal-to rho(c), where the spectral pro file becomes most diffuse. Outside the region of rho almost-equal-to r ho(c), [GAMMA/HBAR] is always smaller than the RRKM rate. The above ob servational is confirmed also by a square-well potential model and asc ertains the conventional belief that the RRKM theory holds only when r esonances overlap and that it gives the upper bound. It is noteworthy that this RRKM regime corresponds to the critical overlap, rho[gamma(p art.)] almost-equal-to 1.