Tunnelling of a molecule

A quantum-mechanical description of tunnelling is presented for a one-dimensional system with internal oscillator degrees of freedom. The 'charged diatomic molecule' is frustrated on encountering a barrier potential by its centre of charge not being coincident with its centre of mass, resulting in transitions amongst internal states. In an adiabatic limit, the tunnelling of semiclassical coherent-like oscillator states is shown to exhibit the Hartman and Bueuttiker-Landauer times tH and tBL, with the time dependence of the coherent state parameter for the tunnelled state given by α(t) = α e-iω(t+Δt) , Δt = tH - itBL. A perturbation formalism is developed, whereby the exact transfer matrix can be expanded to any desired accuracy in a suitable limit. An 'intrinsic' time, based on the oscillator transition rate during tunnelling, transmission or reflection, is introduced. In simple situations the resulting intrinsic tunnelling time is shown to vanish to lowest order. In the general case a particular (nonzero) parametrisation is inferred, and its properties discussed in comparison with the literature on tunnelling times for both wavepackets and internal clocks. Copyright (1998) CSIRO Australia