Many-body approach to the calculation of the exciton binding energies in quantum wells

The study of the exciton binding energies and the joint density of states in quantum well heterostructures presented by Traetta, Coli, and Cingolani [Phys. Rev. B 59, 13 196 (1999)] using many body approach is improved to give the correct description even for well widths larger than the exciton Bohr radius, where the previous model is less accurate. The dependence of the Coulomb matrix elements on the density of states in the well is discussed. Our analytical correction to the scattering amplitude through the form factor using perturbation theory leads to the values of the exciton binding energies that agree very well with those calculated using a variational approach and at the same time preserves the analytical structure of the many body model.