Fine Structure Correction to the Edge Singularity in the X-ray Spectra of Metals

Abstract

In 1969, an expression was proposed by Nozières and de Dominicis [1] (ND) and by other authors [2]to describe the edge singularity of X-ray band spectra of metals. This expression is

$$ {{I}_{l}}\left( \varepsilon \right)=I_{l}^{0}\left( \varepsilon \right){{\left( \frac{{{\xi }_{0}}}{\left| \varepsilon \right|} \right)}^{{{\alpha }_{l}}}} $$

(1)

where the frequency ε is measured from the Fermi edge and where I ⁰_l (ε) is the one electron transition intensity. The exponent depends only on the electron phase shifts δ_l at the Fermi level and is given by

$$\alpha _\ell = \frac{2} {\pi }\delta _\ell - 2\sum\limits_{\ell ' = O}^\infty {(2\ell ' + l)} \left( {\frac{{\delta _{\ell '} }} {\pi }} \right)^2$$

(2)