Double occupancy of the f orbital in the Anderson model for Ce compounds.

Abstract

The Anderson model at zero temperature is studied as a function of the f-level position ${\ensuremath{\varepsilon}}_{f}$ and the f-level--conduction-electron hopping matrix element V. The f-f Coulomb interaction U is assumed to be finite, and double occupancy of the f level is taken into account. For a large value of the f-level degeneracy ${N}_{f}$, there is an important asymmetry between ${f}^{0}$ and ${f}^{2}$ configurations. Even for ``symmetric'' parameters, 2${\ensuremath{\varepsilon}}_{f}$+U=2${\ensuremath{\varepsilon}}_{F}$=0, the ${f}^{2}$ weight is much larger than the ${f}^{0}$ weight if V is small. The effect of this asymmetry on other properties is studied for ${N}_{f}$\ensuremath{\rightarrow}\ensuremath{\infty}. The static susceptibility is primarily determined bythe ${f}^{0}$ weight, while the shape of the valence photoemission spectrum close to the Fermi energy ${\ensuremath{\varepsilon}}_{F}$ also has an important dependence on the ${f}^{2}$ weight. The valence photoemission spectrum can have a pronounced two-peak character, with one peak close to ${\ensuremath{\varepsilon}}_{f}$ and a second structure close to ${\ensuremath{\varepsilon}}_{F}$. For ${\ensuremath{\varepsilon}}_{f}$ well below ${\ensuremath{\varepsilon}}_{F}$ (``spin-fluctuation'' limit) the weight of the second structure can be strongly enhanced compared to the U=\ensuremath{\infty} limit, and its shape and position depends on the conduction density of states. This structure can therefore have a peak below ${\ensuremath{\varepsilon}}_{F}$. The bremsstrahlung isochromat spectroscopy spectrum shows an ${f}^{1}$ peak with an energy separation from ${\ensuremath{\varepsilon}}_{F}$ which is determined by the ``Kondo'' temperature. The tail of this peak contributes to the structure in the valence photoemission spectrum below ${\ensuremath{\varepsilon}}_{F}$.Ground-state properties are calculated variationally, treating 1/${N}_{f}$ as a small parameter. A new technique for performing these calculations is developed. This technique makes it possible to include such a large basis set that accurate results are obtained for the ground-state energy and the f-level occupancy in the limit ${N}_{f}$=1. To calculate the spectra we introduce a time-dependent method which facilitates the inclusion of f2 configurations in the valence photoemission spectrum.