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Extra info for Characteristic Absorption of X-rays L. Series (1902)(en)(10s)
32) ρa (X) = (2πβ)−1 ∆[(X − Λ)2 + ∆2 ]−1 . 27). The graphs of the adatom DOS curves are drawn in Fig. 5, which are depicted by the solid and dashed lines, respectively. We note that ρba (X) = 0 at the X = ±1 band edges. 25, βa < β, so the adbond is weaker than the substrate one, and the ρba (X)-curve assumes a typical Lorentzian-shape with a high, narrow central peak. 5, so that βa = β, the peak broadens and shrinks in height until it vanishes, and the ρba (X)-curve becomes a low, wide “plateau”, which is indicative of the increasing strength of the adatomsubstrate interaction.
As a consequence, the chemisorption energy can be calculated in a self-consistent manner. In order to proceed further, we now introduce the language of manyelectron theory, and the concept of occupation number. 1 Second Quantization Formalism The wave function of a many-electron system can be written as a Slater determinant (see App. B). However, a more convenient notation is provided by using the occupation number representation, whereby the N -electron determinantal function takes the form (March et al.
43), µ must be small, because a cyclic crystal supports only delocalized states, so the poles at X = X 0 are located close to the unit-circle contour. 18) shows that X ± ∼ X ∓ iµ. 30 CHAPTER 2. RESOLVENT TECHNIQUE These conditions show that R2 and R1 , respectively,lies outside the unit-circle contour and is excluded. 40). 3 Model representation Let us now consider the interaction of an atom A with the zeroth atom of a monatomic cyclic crystal C, as depicted in Fig. 1. If the site energy of A(C) is αa (α) and the bond energy of C is β, then in the pre- (post-) chemisorption situation the adbond energy βa = 0(βa = 0).