Empty-lattice test for non-muffin-tin multiple-scattering equations

The extension of the Korringa-Kohn-Rostocker band-theory method to non-muffin-tin potentials is studied analytically for the case of an empty lattice with a constant potential. The magnitude of the potential is used as an expansion parameter and to first order the exact eigenvalues are obtained. Second- and third-order corrections are studied and shown to vanish if the correct form of the multiple-scattering equations is used. It is conjectured that also all higher-order corrections vanish in the empty-lattice case. The errors arising from a truncation in the angular-momentum expansion are investigated numerically, and it is shown that the convergence is much better than previously believed.