THEORY OF ACTIVATED RATE-PROCESSES IN THE WEAK AND INTERMEDIATE FRICTION CASES - NEW ANALYTICAL RESULTS FOR ONE AND MANY DEGREES OF FREEDOM

Simple analytical expressions for the reaction rate of activated rate processes are derived in the weak/intermediate friction limit for one and many degrees of freedom and for finite microcanonical reaction rat es. The expressions are obtained by analytical solution of-the steady- state integral master equations (in energy variables). The microcanoni cal reaction rate is taken to be independent of energy (higher than th e activation energy). Irreversible transitions from one state and reve rsible transitions between many states are discussed in detail. A simp le interpolation formula for the reaction rate is derived which descri bes a turnover from the weak friction regime to a strong friction one. The formula takes into account an interplay between activation and re action at energies close to the activation energy. When applied to uni molecular gas phase reactions this interpolation formula bridges betwe en the weak and strong collision limits. The formulas obtained are gen eralized to multidimensional activated rate processes.