Abstract
Lloyd's formula (1967) for the density of single-particle states in an energy-dependent pseudo-potential W(E) is not valid when the latter is singular. A modified formula, valid for a resonant model formula V(E)+U/(E-E) (where the Hermitian operator U is related to the resonance width and E to the resonant level, is derived. It is used to show that the rank of U must be exactly equal to the number of resonant states (i.e. 2*5 per atom for a d-band metal).