K. Someda et al., SYSTEMATICS OF THE AVERAGE RESONANCE WIDTHS IN OVERLAPPING RESONANCE-SCATTERING AND ITS CONNECTION WITH THE RRKM THEORY, Chemical physics, 187(1-2), 1994, pp. 195-209
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.