Method for calculating charge densities in impurities and disordered alloys

Based on the linear response of the density of states to the scattering strength, an expression for the electron-density function is derived for a system of muffin-tin potentials of arbitrary separation and composition. This expression readily leads to useful formulas for various systems including (i) a single potential, (ii) pure crystals, (iii) impurities in crystal environments, and (iv) disordered alloys using the average-$t$-matrix approximation and the coherent-potential approximation. The charge densities in this formalism can be computed on the same basis as the density of states, and thus allow a self-consistent treatment of the potential problem in impurities and disordered alloys.