Reduced equations of motion and reduced S matrix for scattering processes
Shaul Mukamel · The Journal of Chemical Physics · 1981
Reduced equations of motion (REM) are derived for the reduced density matrix of some of the degrees of freedom taking part in a scattering process. The derivation is made making use of the Zwanzig–Mori projection operator technique and utilizing a partial time ordering prescription (POP) which results in simple REM which contain no convolution in time. The present formulation is convenient for the direct calculation of reduced information on scattering events since it avoids the necessity of calculating the complete S matrix. The entire dynamical information relevant for the present description is expressed in terms of a hierarchy of correlation functions which in turn depend on the potential surface only in the region of interest. We further develop an exponential approximation for the reduced tetradic scattering S matrix in Liouville space, which forms a convenient framework for systematic approximations.