Theory of Localized Magnetic Moments in Metals. II

The electron-hole Green's function for the resonant state of a nondegenerate impurity is constructed in the $\Omega$ approximation, using the Anderson Hamiltonian. The magnitude of the localized moment is found always to attain its maximum possible value (i.e., one Bohr magneton), provided that a moment exists at all. The linearity of the impurity contribution to the specific heat is demonstrated. The homogeneous equation for a band electron-hole Green's function in the presence of a localized moment is solved. This leads to the Suhl-Abrikosov transition temperature. It is thus shown that at this temperature the band becomes unstable towards the formation of a band electron-hole resonant state with its spin opposite to that of the impurity electron-hole resonant state. The treatment does not use any perturbation theory. Finally the $\Omega$ approximation is compared with the decoupling approximation of the interacting one-particle Green's functions.