Electron momentum densities in disordered muffin-tin alloys

The application of average $t$-matrix (ATA) and coherent potential (CPA) approximations to the calculation of average electron momentum density $\rho \left(\overrightarrow{\mathrm{p}}\right)$ in random muffin-tin alloys $A_x{B}_{1-x}$ is considered. The necessary equations for the general matrix elements of the operators describing scattering by the CPA atom and also by an $A$ or $B$ atom embedded in the effective medium are derived. Various versions of the ATA for $\rho \left(\overrightarrow{\mathrm{p}}\right)$ are discussed. Several $\rho \left(\overrightarrow{\mathrm{p}}\right)$ curves calculated on the basis of the CPA and ATA in ${\mathrm{Cu}}_x{\mathrm{Ni}}_{1-x}$ are presented. These results are used to delineate the effects on $\rho \left(\overrightarrow{\mathrm{p}}\right)$ of self-consistency in the treatment of disorder.