The density of states in dilute solid solutions

The difference in the density of states in energy in a dilute solid solution, relative to its value in the pure solvent, is derived. It is shown to be simply related to the energy level shift induced by virtual electron scattering off the solute ions and to the density of states in the pure solvent. The result, which follows from a brief physical argument, is shown to be completely equivalent to that obtained from a far more laborious derivation by means of Green function techniques. An application to the determination of the specific heat of dilute metallic solid solutions is given and a former incomplete result, as derived by Jones from an approximate evaluation of the Green function method, is amended.