Tunnelling in a double-well system with allowance made for the relaxation

Abstract

Tunnelling in a one-dimensional double-well system with five turning points can be considered as one of the simplest models for a unimolecular chemical reaction. It is assumed that a potential barrier separating reactants from products is sufficiently high, so that the reaction rate constant decreases exponentially. The height of the second potential barrier is related to the widths of the energy levels in a product well imitating relaxation processes of reaction products. An analytical expression is derived for the width of an initial energy level in a reactant well. It depends exponentially on the value of 2W ₁ (W ₁ is a quasiclassical phase integral under the potential barrier separating reactants from products). The preexponential factor is expressed in terms of matrix elements of the propagator connecting solutions of the Schrödinger equation in asymptotic regions. Quantum and quasiclassical calculations of the propagator were performed. Under resonance conditions, when reactant and product energy levels coincide, the width of a reactant level is shown to be 4 exp 2W ₂ times as large as its value in the absence of the resonance (W ₂ is a quasiclassical phase integral under the second potential barrier).