  We investigate the modeling of positronium (Ps) states and their pick-off
annihilation trapped at open volumes pockets in condensed molecular matter. Our
starting point is the interacting many-body system of Ps and a He atom because
it is the smallest entity that can mimic the energy gap between the highest
occupied and lowest unoccupied molecular orbitals of molecules and yet the the
many-body structure of the HePs system can be calculated accurately enough. The
exact-diagonalization solution of the HePs system enables us to construct a
pair-wise full-correlation single-particle potential for the Ps-He interaction
and the total potential in solids is obtained as a superposition of the
pair-wise potentials. We study in detail Ps states and their pick-off
annihilation rates in voids inside solid He and analyse experimental results
for Ps-induced voids in liquid He obtaining the radii of the voids. More
importantly, we generalize our conclusions by testing the validity of the
Tao-Eldrup model, widely used to analyse ortho-Ps annihilation measurements for
voids in molecular matter, against our theoretical results for the solid He.
Moreover, we discuss the influence of the partial charges of polar molecules
and the strength of the van der Waals interaction on the pick-off annihilation
rate.
