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

The ground-state energy of excitonic molecules is evaluated as a function of the ratio of electron and hole masses, $\sigma$, with use of the Green's-function Monte Carlo method. For all $\sigma$, 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 ($\sigma =1\mathrm{}$) is predicted to be - 0.06 and for $\sigma \ll 1$, the Green's-function Monte Carlo energies agree with the "exact" limiting behavior, $E=-2.346+0.764\mathrm{}\sqrt{\sigma }$.