Polaron theory of positronium localization and annihilation in xenon.

Abstract

We investigate the quantum states of a light particle (positronium, or Ps) in a disordered medium (fluid xenon). The Ps atom is modeled as a hard sphere which has thermalized in a Lennard-Jones fluid. The purpose of this paper is threefold: first, to test the efficacy of a recent analytic theory by comparing its predictions with available results of path-integral Monte Carlo (PIMC) simulations; second, to explore the Ps-xenon system over a much wider range of circumstances than is possible with PIMC; third, to report predictions for the lifetime of ortho-Ps and the momentum distribution of para-Ps at high density which should be of interest to condensed-matter experimentalists. In sharp contrast with the case of an electron or positron, the reference-interaction-site-model (RISM)-polaron theory produces Ps-fluid pair-distribution functions in good agreement with the PIMC results. As a result, the pick-off decay rate of ortho-Ps in the transition region between localized and extended states is reproduced successfully. We also find that the variance of the momentum distribution of para-Ps agrees qualitatively with experimental measurements of the angular correlation of the annihilation photons. Compared with the behavior at low density, above the critical density up to about 3${\mathrm{\ensuremath{\rho}}}_{\mathit{c}}$ the RISM-polaron theory predicts strong confinement of the localized Ps atom and different distortion of the local fluid density, resulting in the monotonic increase of the decay rate and the momentum variance with mean fluid density. As a consequence, the slope of the decay rate is much greater than the extrapolated low density limit predicted by the older density functional theories. These predictions of RISM-polaron theory for the behavior of positronium in a dense fluid suggest that the traditional picture of self-trapping in a fluid is incomplete and call for more careful experimental investigations to resolve this issue.