Numerical solution of a two-particle model of positronium confined in small cavities

The positronium atom (Ps) is widely used as a probe to characterize nanoporous and mesoporous materials. Existing theoretical models for describing Ps annihilation rates by pick-o processes generally treat Ps as a point particle confined in a potential well. Hence these models do not justify any change in the internal structure of Ps, which is experimentally accessible by means of the contact density parameter. Recently we formulated a two-particle model in which only the electron is confined in the cavity, while the positron is moving freely and feels the medium via a positive work function. We present here a numerical treatment of the problem of calculating contact densities and pick-o annihilation rates, by using a variational method. Results are in agreement with experimental data for a large class of materials, and suggest a way to connect these data with pore sizes and positron work functions.