Positronium in xenon: The path-integral approach

Abstract

The ability of a single positronium atom to form a semimacroscopic bubble in helium is a remarkable manifestation of quantum mechanics. Experimental evidence for bubble formation is provided by a dramatic decrease in the decay rate of the triplet state when the ambient conditions favor its formation. The phenomenon is observed near the critical point of helium and is well explained by a mean-field theory in which the positronium atom occupies the ground state of a local potential well induced by its influence on the average local density. Because of the active role played by the positronium atom in producing this localized state, the process is referred to as self-trapping. Similar experiments on other noble gases also show evidence for self-trapping near the liquid-vapor critical point, but the transition from extended to localized behavior is gradual. Mean-field theories, which ignore fluctuations, are not successful at these higher temperatures, suggesting that statistical fluctuations strongly influence the distribution over states of the light atom. This paper presents a theoretical investigation of the localization of positronium in a dense noble gas which employs the path integral to represent the translational degrees of freedom of the light atom. It demonstrates that a theoretical model which properly accounts for fluctuations is able to predict the main features of the experimental measurements.