Positronium in alkali halides: Tunneling from the delocalized to the self-trapped state

The tunnel transition of positronium (Ps) from its stable delocalized state to the metastable localized state in alkali halides is investigated theoretically using the formalism developed by Nasu and Toyozawa for excitons [J. Phys. Soc. Jpn. 50, 235 (1981)]. The tunneling rate between these two states is found to have the exponential dependence on the parameter $B/ħ\omega$ $(B$ is half of the Ps bandwidth, $\omega$ is the averaged frequency of the longitudinal acoustic phonons), whereas the potential barrier height between the two states is mainly determined by the bandwidth $B$ and is proportional to $B$. A fitting procedure taking into account the quantum tunneling of Ps between the delocalized and the self-trapped state is proposed for the theoretical interpretation of the experimental data on Ps self-trapping. The procedure yields the numerical values of the parameters of Ps self-trapping (the tunneling rate and the potential barrier height) in qualitative agreement with those calculated theoretically.