Statistical Properties of Kawai-Kerman-McVoy T-matrix

Kawai, Kerman and McVoy (KKM) derived an optical background-plus-fluctuations representation of T-matrix, T = Topt+Tfluct, so that an energy average of Tfluct over a single-particle resonance width is expected to be negligibly small (Ann. of Phys. 75, 156 [1973]). We investigate this property numerically in a simple model with 1,600 compound nuclear levels and 40 channels, coupled via a random interaction. We find that the energy average of the fluctuating term is much smaller than the optical background, Topt, in support of the KKM result. A self-contained derivation of KKM T-matrix is presented.