General trends of positronium pick-off annihilation in molecular substances

The characteristics of positronium (Ps) annihilation in molecular substances (ranging from organic liquids to molecular solids), manifested through the observed lifetimes (tau(p)) for the 'pick-off' process and values of angular correlation (theta(1/2)) of decay gammas, can be shown to be simply related to the size (radius R) of the cavity which the Ps creates in a liquid or finds in a molecular solid. The measured tau(p) and theta(1/2) are in turn calculable from the wavefunction describing the Ps centre-of-mass motion, which is determined from the average potential experienced by it in the confining cavity. Thus the height of this repulsive barrier (U-0) at the wall of this vacant region corresponding to different materials (with varying R) can be obtained by fitting experimental observations, namely tau(p) and theta(1/2). The model we use is an improved version of the usual spherical well description of the cavity (where we take the walls to be diffuse). It is found that the values of U-0 and R, taking into account all available and relevant data for different molecular substances, fall on a universal curve. We attempt to explain the reason behind this 'universality' by relating the potential to the Ps work-function in materials. Finally, the fit provides us with a very convenient linear relationship between the size (R) of the cavity and the pick-off lifetime (tau(p)).