Pseudopotential Bethe-Salpeter calculations for shallow-core x-ray absorption near-edge structures: Excitonic effects in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi mathvariant="normal">Al</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>

We present an ab initio description of optical and shallow-core x-ray absorption spectroscopies in a unified formalism based on the pseudopotential plane-wave method at level Bethe-Salpeter equation (BSE) within Green's functions theory. show that norm-conserving pseudopotentials are reliable accurate not only for valence, but also semicore electron excitations. In order to validate our approach, we compare BSE spectra obtained with two different codes: pseudopotential-based code EXC all-electron full-potential Exciting. take corundum $\alpha$-Al$_2$O$_3$ as example, being prototypical material presents strong electron-hole interactions both valence core analyze detail spectrum well Al L$_1$ L$_{2,3}$ edges terms anisotropy, crystal local fields, interference excitonic effects. perform thorough inspection origin localization lowest-energy excitons, conclude highlighting purely electronic character off pre-edge dichroic nature L$_{23}$ spectra.