Towards an Accurate Wave Function for Positronium Hydride

Abstract

A variational wave function for the ground state of positronium hydride is presented. The wave function is considerably more accurate than any previously reported. The only simplifications used are (a) only kinetic and Coulombic potential energy terms are included in the Hamiltonian, (b) the motion of the proton is ignored, and (c) the nucleus-positron distance is excluded from the wave function. The last assumption is the major source of error, but it enables us to evaluate all integrals exactly. Several trial wave functions are examined, the one giving the lowest energy being an open-shell exponential function times a 12-term power series through second-degree terms in the five remaining interparticle coordinates. Positronium hydride is found to be stable with respect to separation into hydrogen and positronium by at least 0.657 eV. The annihilation rate for two-photon events is found to be 2.095 ${\mathrm{nsec}}^{-1\mathrm{}}$ for the trial wave function giving the lowest energy, and 2.265 ${\mathrm{nsec}}^{-1\mathrm{}}$ for the trial wave function which most nearly satisfies the positron-electron cusp condition. A search for bound excited states of PsH and a bound state for the system $e^{+}\mathrm{He}$ was unsuccessful.