  We report the results of the analysis of the temperature broadening of the
momentum distribution of delocalized Positronium (Ps) in Magnesium Fluoride in
terms of optical deformation-potential scattering model (long-wavelength
optical phonons). The Ps optical deformation-potential coupling constant
$D_{o}$ in MgF$_{2}$ has been determined to be $(1.8\pm0.3)\times10^{9}$ eV/cm.
We also show that the Ps momentum distribution is sensitive to second-order
phase transitions in those crystals where optical deformation-potential
scattering is allowed in one and forbidden in another crystalline phase.
