Tunneling Process from Free State to Self-Trapped State of Exciton

The tunneling of the Wannier exciton from its metastable free state to the stable self-trapped state is described in the context of the multi-phonon nonradiative transition. The escape path through the adiabatic potential barrier is determined by a variational method: the tunneling is assumed to occur along a trial interaction mode, with its degree of localization being the variational parameter determined so as to maximize the rate of the tunneling. The rate is obtained as a function of the exciton band width, coupling constants and the Wannier radius, and the tunneling is found to be more probable than the radiative annihilation in a wide range of these parameters. The rate is also found to depend exponentially on the band width and the Wannier radius, in agreement with the experimental results in alkali iodides and rare gas solids.