Generalized phase shifts for a cluster of muffin‐tin potentials

Starting with the partial wave method generalized to non‐spherically symmetric potentials by Demkov and Rudakov a purely algebraic scheme is proposed how to calculate the generalized phase shifts for a cluster of non‐overlapping muffin‐tin potentials. These cluster phase shifts and the corresponding partial wave amplitudes are determined by a system of homogeneous linear equations, into which the phase shifts of each muffin‐tin potential and the structure enter separately, completely similar to the KKR method for the band structure of a crystal. By the proposed scheme bound states can also be calculated, the number of which is limited by the properties of cluster phase shifts. As a mathematical remedy an addition theorem about the spherical Neumann functions is derived.