Temperature-activated transition of positronium from self-trapped to delocalized state inCaF2

Abstract

Temperature dependence of the momentum distribution of positronium (Ps) in $\mathrm{Ca}{\mathrm{F}}_{2}$ single crystal has been investigated in a temperature range from $10\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}297\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Temperature activated transition of Ps from the stable self-trapped state to the metastable delocalized state has been observed. The self-trapping barrier height and the under-barrier tunnel self-trapping rate have been determined to be $0.17\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and $2.9\ifmmode\times\else\texttimes\fi{}{10}^{10}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, respectively, and an important role of the under-barrier tunneling has been demonstrated. The bottom of the delocalized Ps band is $6.6\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ higher in energy than the ground self-trapped state. The observed effective mass of the delocalized Ps is considerably larger than the free Ps mass in vacuum.