  Excitons with a radius of a few lattice constants can be affected by strong
central-cell corrections, leading to significant deviations of the optical
spectrum from the hydrogen-like Rydberg series, and also to an enhancement of
the exciton mass. We present an approach to this situation based on a lattice
model that incorporates the effects of a non-parabolic band structure, short
distance corrections to the Coulomb interaction between electrons and holes,
spin-orbit and exchange coupling. The lattice model allows for observation of
the crossover from large radius Wannier to small radius Frenkel excitons
without invoking a continuum approximation. We apply the lattice model approach
especially to the yellow exciton series in the cuprous oxide, for which the
optical spectrum and exciton mass enhancement are obtained through adaptation
of only a few model parameters to material-specific values. Our results predict
a strongly anisotropic ortho-exciton mass.
