Path-integral simulation of positronium in a hard sphere

Abstract

We employ the path-integral Monte Carlo method to study the binding energy of positronium trapped within a hard sphere. The two-body density matrix and the total- and kinetic-energy matrices are obtained by matrix squaring. The pair-product approximation is then used to obtain the entire density and estimator matrices for the Monte Carlo simulation. Ground-state binding energies are obtained as a function of sphere radius and the system is found to become unbound near a radius of 4 bohrs. Annihilation times are calculated which vary from 125 ps for free-space positronium down to 76 ps at a sphere radius of 4 bohrs.