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.
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