The low temperature reactive tunneling in condensed phase. I. The rate expression

We study how the quantization of energy levels affects the deep tunneling r ate expression for a double-well system immersed in a harmonic bath. The mo del of tunneling transitions implies that the energy of a tunneling system is not conserved during a transition because its interaction with the envir onment is explicitly taken into account. The Golden Rule approach invoked u sually cannot be directly applied for such a model. We consider its modific ation in which the expression for the rate constant depends symmetrically o n spectral line shapes of energy levels in both reactant and product wells. The derivation is based on the Breit-Wigner resonance expansion of a dynam ical transition probability which is extended on condensed phase systems an d averaged at the next stage over fluctuations of the energy levels promote d by system/environment interactions. Test computations for a one-dimension al model case demonstrate novel features inherent to this approach which ar e clearly revealed in the low-temperature kinetic regime. (C) 2001 American Institute of Physics.