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We present an ab initio study of neutral core and valence electronicexcitations in {\alpha}-Al2O3 by solving the Bethe-Salpeter equation (BSE) ofmany-body perturbation theory within an all-electron framework. Calculatedspectra at the Al K and L1 edges are in remarkable agreement with availableexperiments from X-ray absorption (XAS) and X-ray Raman spectroscopy onceexcitonic effects are taken into account. The combination of the BSE spectrafor the two techniques confirms the dipole-forbidden nature of the excitonprepeak as suggested by recent calculations based on density-functional theory.Moreover, we make predictions for resonant inelastic X-ray scattering (RIXS)spectra at K and L1 edges, which strikingly fully overlap also beyond anindependent-particle picture. The RIXS calculations reveal two distinct regimesas a function of incoming photon energy. Below and at the XAS threshold, weobserve Raman-like features, characterised by strong excitonic effects, whichwe directly compare to peaks in the loss function. Above the XAS threshold,instead, fluorescence features become predominant: RIXS spectra can be welldescribed and analyzed within an independent-particle approximation showingsimilarity with the X-ray emission spectrum.

Connections between resonant inelastic x-ray scattering and  complementary x-ray spectroscopies: probing excitons at Al K and L$_1$ edges  of $\alpha$-Al$_2$O$_3$