Scaling theory: Energy sudden and dynamically modified relations

Abstract

An approach is described for dynamically modifying energy sudden (ES) collisional scaling relations. It is based upon a generalized form of perturbation theory (PT), which contains ES dynamics as the zeroth order approximate. The corresponding first order PT scattering matrix is further modified by exponential unitarization (EPT). Our scaling relations take on the following structure: an input column of S-matrix elements (back) projects through first order EPT (and hence in an approximate fashion), onto the corresponding column of ES elements; a set of ES scaling coefficients (forward) projects these elements onto a new column; the new column (forward) projects through again first order EPT, onto the corresponding scaled column. The effectiveness of this approach is illustrated by application to a simple classical path three-state problem. Two slightly different versions of the approach are compared. We also examine how ‘‘column based’’ scaling predictions compare with ‘‘single element based’’ predictions. Finally, a number of avenues for further development and application are discussed.