AN ANALYTICAL STUDY OF THE BEREZHKOVSKII-POLLAK-ZITSERMAN THEORY OF RATE-PROCESSES IN THE CRITICAL REGION .2. THE CRITICAL COUPLING PLANE

In a recent paper, we studied analytically the canonical variational t ransition state theory of rate processes, introduced by Berezhkovskii, Pollak and Zitserman (BPZ). We used a quartic potential added to a pa rabolic barrier and a memory friction kernel having an infinite relaxa tion time. We found that their memory suppression region, where the ra te can deviate significantly from the Grote-Hynes (GH) theory, is iden tical to the critical region. We showed that the BPZ rate obeys a scal ing relation in this region and studied the scaling function in differ ent coupling regimes. The most important result of this work was to sh ow the existence of a critical line of singularities in the infinite r elaxation time plane. In this paper, we extend the results to a finite relaxation time and obtain a more general scaling function. We then s tudy this scaling function near the GH limit in order to ascertain the deviations of the BPZ rate from the GH theory due to the finiteness o f the barrier height. We also study the behavior of the rate in the cr itical coupling plane and show that in this plane too, there is a line of critical points where the behavior of the rate is singular and cha nges dramatically as this line is crossed.