Pseudopotential Theory of Exciton and Impurity States

A formalism for studying central-cell corrections to the effective-mass equation is presented. A generalized impurity equation for excitons and impurity states is derived, including the effects of dielectric response and large-$k$ variation of the effective mass. Because of the presence of interband matrix elements of the impurity potential in the general case, this equation is not easily solved. By transforming to a representation in which the core parts of Bloch functions are removed, a pseudo-wave-equation is developed. In this equation the effective impurity potential is substantially cancelled within the central cell, so that interband matrix elements are sharply reduced, and the usual one-band approximation is valid.