Band Structure Approach to the X-Ray Spectra of Metals

Abstract

The non-trivial part in the computation of the X-ray absorption spectrum (XAS)

$$ {{\mu }_{i}}(E) = const\sum\limits_{f} { < {{\psi }_{i}}|\vec{r} \cdot \hat{\varepsilon }|{{\psi }_{f}}{{ > }^{2}}\delta (E - {{E}_{f}} + {{E}_{i}}),} $$

((1))

due to excitation of a core level i = (nℓJ), is the evaluation of the final states ψ_f. From a mathematical point of view, the scattering and the band structure formalisms are two different ways of calculating the same quantity (1). In the scattering formalism one takes ψ_f to be a solution for the excited atom potential and improves it systematically by including the single backscattering from neighboring atoms [1,2], the spatial variation of the scattered wavelets [3], and multiple scattering events [4], as needed. In the alternative approach presented here ψ_f is a Bloch state resulting from a band structure calculation. Unlike the scattering approach, which is of general applicability, the band structure approach requires a periodic potential. The appealing feature of the scheme is that it includes multiple scattering to infinite order. Fiqure 1 shows that the band structure result reproduces all features of the single-particle spectrum.