Screened final-state

It is worthwhile to mention the ample use of screening final states models in understanding core levels as well as valence band spectra of the oxides. The two-hole models, for instance, which have been described here, are certainly of relevance. Interpretational difference exists, for instance, on the attribution of the 10 eV valence band peak (encountered in other actinide dioxides as well), whether due to the non-screened 5f final state, or to a 2p-type characteristics of the ligand, or simply to surface stoichiometry effects. Although resonance experiments seem to exclude the first interpretation, it remains a question as to what extent a resonance behaviour other than expected within an atomic picture is exhibited by a 5 f contribution in the valence band region, and to what extent a possible d contribution may modify it. In fact, it has been shown that, for less localized states (as, e.g., the 3d states in transition metals) the resonant enhancement of the response is less pronounced than expected. 

Photoemission and neutron diffraction measurements are limited only to UBe13. The combined XPS-BIS experiments of Wuilloud et al. (1984) displayed a picture similar to other very narrow-band compounds with 5f states extended to 2 eV below Ep, while the 5f intensity is spread above 5 eV about EF. Pronounced satellites corresponding to poorly screened final states accompany the core 4f lines of U, but the XPS spectrum of the Be Is level remains unaffected by hybridization with U electron states. A temperature-dependent narrow feature was distinguished at EF by means of high-resolution studies (Arko et al. 1984). The existence of a low intensity 5f-tail extended far below EF, which can be resolved by resonant photo-emission, is taken as an indication for the hybridization of 5f states with Be-derived conduction-band states (Parks et al. 1984). 

Now ( (ion) is a measure of the correlation accompanying the excitation of a 4f electron alone, while represents the correlation associated with 4f->5d conversion. The bracketed quantity in the above expression is thus an estimate of the correlation energy associated with the additional conduction electron which is present in the neutral (completely screened) final state of zl (4f" -> 4f ) and absent in the ionic (unscreened) final state of zl (4f ion). 

Of direct interest for photoemission of supported catalysts is that similar increases in the width of d-bands have been observed by Mason in UPS spectra of small metal particles deposited on amorphous carbon and silica substrates [48]. Theoretical calculations by Baetzold et al. [49] indicate that the bulk density of states is reached if Ag particles contain about 150 atoms, which corresponds to a hemispherical particle 2 nm in diameter. Concomitant with the appearance of narrowed d-bands in small particles is the occurrence of an increase in core level binding energies of up to 1 eV. The effect is mainly an initial and only partly a final state effect [48], although many authors have invoked final state - core hole screening effects as the only reason for the increased binding energy. 

The efficient screening approximation means essentially that the final state of the core, containing a hole, is a completely relaxed state relative to its immediate surround-ing In the neighbourhood of the photoemission site, the conduction electron density of charge redistributes in such a way to suit the introduction of a core in which (differently from the normal ion cores of the metal) there is one hole in a deep bound state, and one valence electron more. The effect of a deep core hole (relative to the outer electrons), may be easily described as the addition of a positive nuclear charge (as, e.g. in P-radioactive decay). Therefore, the excited core can be described as an impurity in the metal. If the normal ion core has Z nuclear charges (Z atomic number) and v outer electrons (v metallic valence) the excited core is similar to an impurity having atomic number (Z + 1) and metalhc valence (v + 1) (e.g., for La ion core in lanthanum metal, the excited core is similar to a Ce impurity). 

Fig. 7 a-c. Schematic representation of final state screening models for lanthanide and d-metal core level responses (a) and c)) (c.b. means conduction band). In part b), the possible situations for light and heavy actinides (before and after the Mott-Hubbard transition) are also represented... 

In d-metals, the opposite is true the d-wavefunctions hybridize easily with conduction band states. The main peak can in this case be coordinated with the well screening outer d s, and the shake-up satellite, when observed, is due to the poorly screening process (Fig. 7c). For d-metals, furthermore, the very high density of d-states at Ep is the cause of many secondary electron excitation from just below Ep to empty states just beyond Ep which results in the asymetric high energy tailing of the main peak. Final state multiplet splitting, explained above, can in addition overlap the split response. 

Because of the much reduced itinerant 5 f character of Pu one would expect a similar, but even more pronounced multielectron satellite structure as observed at 2.3 eV in U. In contrast to U, this satellite due to a localized 5f hole state screened by (6d7s) conduction electrons should not be a single line but show three or even four separate components as calculated for the 5 f 5 f final state multiplet . The fact that such a multiplet satellite is not observed in the XPS valence band spectrum is confusing. It could... 

Final state screening effects have been described generally, although qualitatively, in Part II. A more quantitative model interpreting the relative intensities of the different... 

The most important information (by Baer and Schoenes ) obtained when using the combined XPS/BIS method is the Coulomb interaction energy Uh that we have discussed in Part II. For UO2, Uh = 4.6 0.8 eV has been obtained. This large separation between the two final states (2(5f ) —> 5f + 5f ) is in itself a hint to the localized character of the 5 f states in UO2. Baer and Schoenes compared the value for Uh with theoretical values they found an agreement with Uh = 4 eV as calculated by Herbst et al. for a U" " metal core. As discussed in Chap. A, intraatomic calculations of Uh in metals possibly underestimate screening by conduction electrons nevertheless, they should be valid in the case of an insulating solid as UO2. 

We should finally briefly discuss the calculation of spectra for the surface adsorbates which we will use to verify the theoretical models and to assign peaks in the spectra. The calculation of XES spectra has been discussed extensively previously [3]. Briefly we have shown that the ground state orbitals provide a balanced description of initial and final state and calculate the spectrum as the dipole transition between the valence orbitals and the selected Is core level [21]. The success of this approach relies on similar charge transfer screening in the core-ionized initial (or intermediate) state as for the valence-ionized levels. XES thus reflects the ground state molecular orbitals. 

The surface core level shift is defined as the shift in the core level binding energy for a surface atom relative to that of a bulk atom. Different theoretical approaches have been used to calculate surface shifts5,9 and for metals it has recently been shown21 that both initial- and final-state effects have to be included in ab initio calculations to obtain consistent agreement between experimental and calculated results. The basic assumption in this theoretical approach is that the final state is completely screened so the... 

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