Self-consistent large-$N$ expansion for normal-state properties of dilute magnetic alloys

Finite-temperature properties of the infinite-$U$ Anderson model for rare-earth alloys are calculated within a unified approach. The impurity-electron density of states and magnetic moment spectrum provide a natural framework for describing both static and dynamic properties. The density of states and moment spectrum exhibit low-energy "Kondo resonances" with approximate single-parameter scaling, which persists for impurity valences in the range 1.0-0.7. The position of the resonance in the zero-temperature density of states, $T_0$, sets the scale for all low-temperature properties. Results are reported for the impurity valence, resistivity, thermopower, thermal conductivity, magnetic susceptibility, specific heat, photoemission and inverse-photoemission spectra, and neutron scattering linewidth. The effect of spin-orbit interactions is incorporated in the theory. The calculation is a diagrammatic approximation motivated by the simplifying concept of large angular momentum degeneracy ($N$). The approximate solution is thermodynamically consistent and satisfies all pertinent sum rules. Static properties (magnetic susceptibility and specific heat) are in good agreement with exact results of the Bethe ansatz. Experimental results on both dilute and concentrated Ce alloys are described quantitatively with use of a one-parameter ($T_0$) theory.