Path-integral approach to density fluctuations in self-trapping systems

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Abstract
We introduce an approximate path-integral approach to model the localization of a light particle (electron, positron, or positronium) in a dense fluid. The path integral is defined as an integral over the whole Hilbert space H and then approximated by considering a subset comprised of a function family with one parameter. The integration over the parameter is weighted by a Jacobian which is the infinitesimal length of a curve traced out by this family in H. We found that the integration diverges for all one-parameter families. This difficulty is removed by inserting a second (fixed) parameter. We apply the method to the computation of the decay rate of positronium in ethane. The fit is especially good in the transition region between trapped and extended states.