  Experiments suggest that localization via self-trapping plays a central role
in the behavior of equilibrated low mass particles in both liquids and in
supercritical fluids. In the latter case, the behavior is dominated by the
liquid-vapor critical point which is difficult to probe, both experimentally
and theoretically. Here, for the first time, we present the results of
path-integral computations of the characteristics of a self-trapped particle at
the critical point of a Lennard-Jones fluid for a positive particle-atom
scattering length. We investigate the influence of the range of the
particle-atom interaction on trapping properties, and the pick-off decay rate
for the case where the particle is ortho-positronium.
