Existence of free and self-trapped positronium states in alkali halide crystals: Theoretical analysis and comparison with experiment

A variational calculation is performed of the eigenstates of a positronium atom coupled with a field of longitudinal acoustic phonons in ionic crystals at finite temperatures. On the basis of this calculation a theoretical analysis is made of the possibility of self-localization (self-trapping) of positronium. The self-trapped states of positronium in NaF, NaCl, KCl, and KI crystals are found to be metastable with the energy higher by $\sim 0.01–0.1\hspace{0.5em}\mathrm{eV}$ with respect to the stable delocalized (free) states. The self-trapped states of positronium in ${\mathrm{MgF}}_2$ and $\alpha -{\mathrm{SiO}}_2$ crystals are unstable at absolute zero temperature and become metastable with an increase in temperature for $T>\mathrm{}\sim 300\hspace{0.5em}\mathrm{K}.$ The difference in the energies of such “high-temperature” self-trapped states and the free states of positronium in ${\mathrm{MgF}}_2$ and $\alpha -{\mathrm{SiO}}_2$ is found to be at least one order of magnitude larger than that in the other alkali halides, explaining theoretically experimental evidence for the nonexistence of self-trapped positronium in these crystals. The basic characteristics (energy, effective mass, mean number of surrounding phonons, and localization radius) of the self-trapped and free states as well as the deformation potential constants are calculated for positronium in the crystals above. The results obtained are in good agreement with known experimental data.