Theory of Polar Corrections to Donor Binding
  We calculate the optical phonon correction to the binding energy of electrons to donors in cubic materials. Previous theories calculated the Rydberg energy reduced by the effective mass and the static dielectric function. They omitted an important energy term from the long-range polarization of the ionized donor, which vanishes for the neutral donor. They also omitted the donor-phonon interaction. Including these terms yields a new formula for the donor binding energy. 
G. D. Mahan and Kristian Berland
cond-mat.mtrl-sci cond-mat.mes-hall quant-ph