Quantum Monte Carlo treatment of elastic exciton-exciton scattering

We calculate cross sections for low energy, elastic, bulk, s-wave exciton-exciton scattering within the single-band effective mass approximation. Unlike previous theoretical approaches, we give a complete, nonperturbative treatment of the four-particle scattering problem. Diffusion Monte Carlo is used to calculate the essentially exact energies of scattering states, from which phase shifts are determined. For the case of equal-mass electrons and holes, which is equivalent to positronium-positronium scattering, we find $a_s{=2.1a}_x$ for scattering of singlet excitons and $a_s{=1.5a}_x$ for triplet excitons, where $a_x$ is the excitonic radius. The spin dependence of the cross sections arises from the spatial exchange symmetry of the scattering wave functions. A significant triplet-triplet to singlet-singlet scattering process is found, which is similar to the reported effects in recent experiments and theory for excitons in quantum wells. We also show that the scattering length can change sign and diverge for some values of the mass ratio $m_h{/m}_e,$ an effect not seen in previous perturbative treatments.