Formal calculation of exchange correlation effects on annihilation lifetimes of positronium confined in small cavities

Positronium atoms (Ps) are widely used as a probe to characterize voids or vacancies in non-metallic materials. The annihilation lifetime of trapped Ps is strongly modified by pickoff, depending on the cavity size and on the appropriate external electron density. The connection between these material characteristics and Ps annihilation lifetimes is usually based on models that do not consider the requirements of full electron indistinguishability, that must be taken into account for a correct description of pickoff annihilation processes. In this report, we provide a formal theoretical framework in which exchange correlation effects between confined Ps and surrounding electrons are introduced in a natural way, giving a clear and versatile picture of the various contributions to pickoff annihilation. Moreover, our results provide a simple explanation of the lowering of the contact density (the Ps-electron density at the positron position) as a direct consequence of the electrons indistinguishability, at variance with previous interpretation based on spatial deformations of Ps wavefunction. Calculations are performed within the 'symmetry adapted perturbation theory' approach, and the results are compared with available experimental data on Ps lifetimes for polymers and molecular solids. Finally, our analysis gives a formal justification to the approximations involved in early models based on the well known Tao-Eldrup approach, and gives a simple interpretation of Ps properties in subnanometric voids.