Conduction electrons screening effect

In the case of Mahoney et al. (79) performed a detailed examination of conduction electron screening effects in calculating the CFI parameters on a point charge model. The screened Coulomb potential was represented by... 

Table 6. Point charge calculations with and without conduction electron screening effects in NdAl3 to obtain that will yield B = 1.766 K. Zjvjd is taken as + 3 and 03 = 0-5 (79).

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). 

An impurity atom in a solid induces a variation in the potential acting on the host conduction electrons, which they screen by oscillations in their density. Friedel introduced such oscillations with wave vector 2kp to calculate the conductivity of dilute metallic alloys [10]. In addition to the pronounced effect on the relaxation time of conduction electrons, Friedel oscillations may also be a source of mutual interactions between impurity atoms through the fact that the binding energy of one such atom in the solid depends on the electron density into which it is embedded, and this quantity oscillates around another impurity atom. Lau and Kohn predicted such interactions to depend on distance as cos(2A pr)/r5 [11]. We note that for isotropic Fermi surfaces there is a single kp-value, whereas in the general case one has to insert the Fermi vector pointing into the direction of the interaction [12,13]. The electronic interactions are oscillatory, and their 1 /r5-decay is steeper than the monotonic 1 /r3-decay of elastic interactions [14]. Therefore elastic interactions between bulk impurities dominate the electronic ones from relatively short distances on. 

Core photoelectron ejection produces an atom with a vacancy in some level, a final state which is effectively an impurity imbedded in a surrounding host . Herbst et al. and Ley et al., among others, have provided crude estimates of the extraatomic screening of this impurity however, many of the methods available for arriving at such estimates are based on perturbation theory, which is not readily applicable to perturbations as large as a vacancy-bearing atomic impurity . Further from solution is the problem of screening of conduction electron excitations. 

The implications are that conduction electrons confined to the inner-layer slab, in oxides with low d electron counts, may be more spatially screened from electron localizing effects such as chemical or structural disorder in the rock-salt-like slabs, as compared with conduction electrons in single-layer slabs. 

The contribution of the electron-electron Coulomb repulsion in fiillerite is not well defined. The narrow conduction bands in the AaCeo materials and the large values of the electron-electron Coulomb repulsion prompted development of the exotic all-electron pairing models [81]. In this model the electron screening under some conditions results in an effectively attractive interaction between electrons. However, nearly all observations can be understood by a conventional electron-phonon pairing mechanism [78] (although Ceo based compounds do not satisfy Migdal s theorem). 

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