4f level width

The relatively large Sommerfeld constant (0.79 J/(mol K )) of Sm3Se4 points towards the formation of heavy quasiparticles and, despite the fact that all Sm3X4 compounds are non-metallic, they have been discussed as low-carrier-density HF systems. Optical measurements on Sm3Sc4 (Batlogg et al. 1976) placed the 4f level inside the gap ( 4 eV width) about 0.7 eV below the bottom of the conduction band. Hence, conduction electrons do not play an essential role in the valence fluctuations. 

B) In MV compounds the 4f level is closer to the Fermi level and real charge fluctuation processes lead to a non-integer occupation rtf. T ranges from a few hundred Kelvins in the weakly MV compounds to a few thousand Kelvins in the strongly MV compounds. In the latter case, T corresponds directly to the hybridization width F. Reviews have been cited in the introduction. 

Another intriguing question is why should the spectrum of the medium-sized cluster (Z) = 190 1) resemble closely that of SmS and, to a lesser, extent that of the vapour (the structure is similar, but the widths and the intensities of M[v and My lines differ in fig. 10) The similarity between the cluster spectrum and that of SmS suggests that a parallel mechanism, independent of temperature in these bulk materials, could be responsible for the population of the low-lying states of the manifold. If the natural width of the 4f level is smaller than the Fq- F 1 separation, this mechanism may also... 

In the limit of weak hybridization of the 4f and conduction electrons, the charge fluctuations are strongly suppressed and there remain only spin fluctuations. In this Kondo limit the f-electron level width is small compared to the (negative) f-electron energy Sf as well as small compared to the Coulomb energy U. At low temperatures these systems exhibit an unusually high electronic specific heat coefficient y or a large effective mass m and are therefore called heavy-fermion systems. 

The parameters of the model are the band width D (with the Fermi energy assumed to be zero), the 4f-electron energy S[, the f-electron interaction energy U and the mixing energy V. An important new parameter is the 4f-electron level width for U = 0,... 

The one-electron theory, discussed previously, explains satisfactorily the features observed in the spectra of simple and 3d transition metals. The theory is valid for systems having a continuous DOS above Ep. Discrepancies between theory and experiment were observed for lanthanides. The breakdown of the one-electron model occurs because the excited core electron and/or projectile electron may occupy 4f orbitals, which are quite localized about the excited ion. Wendin (1974) has made an attempt to explain the spectral features on the basis of a two densities of states model one for the scattered projectile electron and the other for the excited ion with an electron-hole pair. This model is able to explain some of the spectral features. More theoretical work, taking into account the core-level widths, core-hole lifetime broadening, many-body and other effects contributing to the spectrum, is needed to provide a more plausible explanation for the APS spectra. 

Fig. 23. Calculated 4f contribution to the EDC of o-Ce for different values of the hybridization matrix element, V. The bare 4f level was placed at a binding energy of 2.5 eV, the f-f repulsive interaction, V, was SeV, and the elliptical conduction band width was 6eV with p at its center. The calculated spectra were convolved with a Lorentzian of full width at half maximum of 0.5 eV to simulate experimental broadening. (After Gunnarsson and Schonhammer 1985a,b.)...

For Ce atoms the 4f level has the total angular momentum S = f and a total number of rotational levels N( = 2S +1 = 6. The crystal field usually splits the degeneracy, but if the level splitting is sufficiently small, all N( substates can participate in spin fluctuation. The theory of the resonance level remains qualitatively the same, but the large Nf value allows the so-call l/N approximation, which helps to simplify the calculation of the level width (Bickers et al. 1985, 1987). At zero temperature the resonance is found to have an asymmetric lineshape with a level width measured by k T. When the temperature is increased the line drops in height and shifts in energy as shown in fig. 28. Although the theory introduces a new parameters in addition... 

The energy distribution curves of the photoelectron emission from cleaved single crystals at 300 K for photon energies hv = 6.5 to 9.7 eV (see Fig. 115) reveal peaks attributed to4f levels at 1.6 eV below Ep with a peak location and peak width independent of exciting photon energy, and to p states ca. 3 eV below Ep. The peak at 5.5 eV below Ep, observable only for hv>9 eV, cannot be explained it may result from scattered electrons [1,3]. Earlier studies at hv = 6.5 eV on single crystals [2] and at hv = 6.5 to 10.2 eV on (ordered) polycrystalline films [6] showed that the 4f levels lie above the p valence band but that emission from 4f is very weak. Studies with 40 eV synchrotron radiation photons reveal the intense 4f peak at 1.8 eV below Ep and a broad p band peak around 3 eV below Ep. But there also is an unidentified broad peak between 8 and 11 eV (not observable for 61 eV photons) and a weak broad peak at 13 eV below Ep (not studied for 61 eV), which was tentatively attributed to the outermost s band of selenium, Sato etal. [7]. 

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