Momentum density for Compton scattering from random alloys

We derive an explicit expression for the average momentum density $〈\rho \left(\overrightarrow{\mathrm{p}}\right)〉$ measured by a Compton-scattering experiment on a disordered binary alloy. Our treatment is based on the use of muffin-tin atomic potentials within the framework of the average $t$-matrix approximation. In the case of a perfect crystal the momentum density is also derived directly from the usual Korringa-Kohn-Rostoker wave functions, and the formula so obtained is shown to be identical to the crystalline limit of $〈\rho \left(\overrightarrow{\mathrm{p}}\right)〉$.