Anderson-McMillan prescription for the density of states of liquid iron

An intensive numerical investigation reveals a gross error in the density of states reported in 1967 by Anderson and McMillan. Whereas they obtained a broad double-peaked resonance that appeared sufficiently reasonable to justify their prescription, correct evaluation of their formula yields a single structureless resonance far too narrow to be representative of a transition-metal $d$ band. This conclusion is verified by algebraically reducing their expression for the density of states to a form that is easily evaluated by hand. Anderson and McMillan also err in claiming that their dispersion relation leads to a vanishing wave number at resonance. The zero wave number is on an extraneous branch and would have led to a nonintegrable singularity in their density of states. Evidently the Anderson-McMillan prescription is inadequate as a description of the effects of $s-d$ hybridization on the density of states of transition metals.