Ground State of Excitonic Molecules by the Green's-Function Monte Carlo Method

Abstract

The ground-state energy of excitonic molecules is evaluated as a function of the ratio of electron and hole masses, $\ensuremath{\sigma}$, with use of the Green's-function Monte Carlo method. For all $\ensuremath{\sigma}$, the Green's-function Monte Carlo energies are significantly lower than the variational estimates and in favorable agreement with experiments. In excitonic rydbergs, the binding energy of the positronium molecule ($\ensuremath{\sigma}=1$) is predicted to be - 0.06 and for $\ensuremath{\sigma}\ensuremath{\ll}1$, the Green's-function Monte Carlo energies agree with the "exact" limiting behavior, $E=\ensuremath{-}2.346+0.764\sqrt{\ensuremath{\sigma}}$.