Positronium (Ps) is a valuable probe to investigate nanometric or sub-nanometric cavities in non-metallic materials, where Ps can be confined. Accessible experimental measurements concern the lifetime of trapped Ps, which is largely influenced by pick-off processes, depending on the size of the cavity as well as on the density of the electrons belonging to the surface of the host trap. Another relevant physical quantity is the contact density, that is the electron density at the positron position, which is usually found to be well below the vacuum value. Here, we review the principal models that have been formulated to account and explain for these physical properties of confined Ps. Starting with models, treating Ps as a single particle formulated essentially to study pick-off, we go on to describe more refined two-particle models because a two-body model is the simplest approach able to describe any change in the contact density, observed in many materials. Finally, we consider a theory of Ps annihilation in nanometric voids in which the exchange correlations between the electron of Ps and the outer electrons play a fundamental role. This theory is not usually taken into account in the literature, but it has to be considered for a correct theory of pick-off annihilation processes.
Keywords: exchange correlations; nanoporous materials; positronium lifetime spectroscopy.