Self-trapping at the liquid-vapor critical point: a path-integral study.

Experiments suggest that localization via self-trapping plays a dominant role in the behavior of a low-mass particle, e.g., an electron, positron, or positronium atom, in both liquids and supercritical fluids. In the latter case, the behavior is dominated by the liquid-vapor critical point. However, because of its large isothermal compressibility, the critical point is difficult to probe both experimentally and theoretically. Here we present the results of path-integral computations of the characteristics of a generic self-trapped particle at the critical point of a Lennard-Jones fluid for a positive particle-atom scattering length. We carefully investigate the dependence of the properties of both the self-trapped quantum particle and the proximal fluid on the range of the direct particle-atom interaction. To the extent that the generic particle mimics the behavior of ortho-positronium, qualitative information is provided on the pick-off decay rate. In general, compared with self-trapping at higher temperature, we find that the localized quantum defect has a much larger range of influence on the host fluid. In particular, it appears that long-range density oscillations are induced in the fluid surrounding the defect. The results also suggest that, even at the critical point, there is a minimum interaction range below which self-trapping does not occur.