THEORY OF POSITRONIUM INTERACTIONS WITH POROUS MATERIALS

The work in this thesis is focused on studying the behavior of a positronium atom (Ps) inside matter and especially in porous materials. The need for im- proved theoretical models is justified by the lack of a simple explanation for the well known phenomenon of the lowering of the contact density, a parameter describing the electron density at the positron position. Given that this parameter is experimentally accessible, connecting its value to specific properties would be extremely useful in the context of structural analysis of materials. In the first two chapters we will give an introduction to positronium physics and an overview of methods and models commonly used by the positron community. In the third chapter we analyze a simple two-particle model we formulated to describe Ps confined in nanopores. This model is based on the observation that the confining potential acting on Ps is a net result of two independent and different contributions, acting on the electron and on the positron separately. In particular, a positive value for the positron work function, as derived by theoretical models and found, for example, in silica, suggests that the positron is attracted toward the medium and then is not confined a priori. The well known confining behavior of Ps is then related to the repulsive electron-electron interaction at short distances and to the strong Pauli exchange forces with bulk electrons. In this picture, it is the electron in o-Ps that prevents large overlap between Ps and electrons in matter. By applying approximate semi-analytical techniques, a variational method approach, and finally a quantum montecarlo code, we were able to demonstrate that our model correctly describe the lowering of the contact density, obtaining also promising results in the comparison with experimental data. However this model was not fully satisfactory because it is based on a macro- scopic parameter (the positron work function) which is not easy to obtain ex- perimentally. For this reason in the fourth chapter we will provide some theoretical insight about Ps interactions with external electrons, taking into account correlation as well as exchange interactions. Given the difficulty of the general problem itself we focused on a system of Ps interacting with a homogeneous electron gas (HEG). We will show that this calculation recover the same result obtained for a positron-HEG system in the limit of high density, while on the opposite limit we recover two different annihilation rates for o-Ps and p-Ps as expected fo Ps in a free space region. We will formally prove that the pickoff annihilation rate has the same expression both for o-Ps and p-Ps , a result which was never proved for a system of N electrons. Finally we will show how the presence of a low external electron density manage to screen the positron charge effectively lowering the contact density, with a mechanism which can be seen as a Ps negative ion formation. In the last chapter we will give a comparison of our results with experimental data.