GENERALIZED LLOYD FORMULA FOR THE ELECTRON-DENSITY OF STATES

An expression is derived for the electron density of states of an arbitrary collection of scattering potentials, described with respect to another, related collection of scatterers. This latter system, serving as a reference system, replaces free space, being the reference system for Lloyd's formula. The expression is very similar in form compared with the original expression. It contains the system t-matrix defined with respect to the reference system. The generalized Lloyd formula is very useful in describing defects in dilute alloys. The derivation is accomplished by evaluating the trace operation in the formal density-of-states expression in the r representation, by integrating over all space explicitly, and by using a generalized form of the equality due to Jacobs and Zaman.