Tunnelling of a molecule

A quantum-mechanical description of tunnelling is presented for a one-dimen sional system with internal oscillator degrees of freedom. The 'charged dia tomic molecule' is frustrated on encountering a barrier potential by its ce ntre of charge not being coincident with its centre of mass, resulting in t ransitions amongst internal states. In an adiabatic limit, the tunnelling o f semiclassical coherent-like oscillator states is shown to exhibit the Har tman and Buttiker-Landauer times t(H) and t(BL), with the time dependence o f the coherent state parameter for the tunnelled state given by alpha(t) = alpha e(-iw(t+Delta t)), Delta t = t(H)-it(BL). A perturbation formalism is developed, whereby the exact transfer matrix can be expanded to any desire d accuracy in a suitable limit. An 'intrinsic' time, based on the oscillato r transition rate during tunnelling, transmission or reflection, is introdu ced. In simple situations the resulting intrinsic tunnelling time is shown to vanish to lowest order. In the general case a particular (nonzero) param etrisation is inferred, and its properties discussed in comparison with the literature on tunnelling times for both wavepackets and internal clocks.