Quantum Monte Carlo treatment of elastic excitonexciton scattering
Abstract
We calculate cross sections for low energy, elastic, bulk, swave excitonexciton scattering within the singleband effective mass approximation. Unlike previous theoretical approaches, we give a complete, nonperturbative treatment of the fourparticle 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 equalmass electrons and holes, which is equivalent to positroniumpositronium 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 triplettriplet to singletsinglet 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.
 Publication:

Physical Review B
 Pub Date:
 April 2001
 DOI:
 10.1103/PhysRevB.63.165209
 arXiv:
 arXiv:condmat/9907309
 Bibcode:
 2001PhRvB..63p5209S
 Keywords:

 71.35.Cc;
 36.10.Dr;
 Intrinsic properties of excitons;
 optical absorption spectra;
 Positronium muonium muonic atoms and molecules;
 Condensed Matter
 EPrint:
 6 pages, 6 figures. Revision has updated figures, improved paper structure, some minor corrections