I will discuss three x-ray spectroscopies:
(1) X-ray absorption (XAS)
(2) X-ray photoemission (XPS)
(3) Resonant inelastic scattering of X-rays (RIXS)

INTERPRETATION: The general interpretation of the spectral shapes is outlined, noting that there is no practical unified theory for the interpretation of x-ray spectroscopies and both one-particle (excitation) models based on (time-dependent) Density Functional Theory as well as model Hamiltonians are used for specific spectra [1,2,3,4]

RIXS: In 2p3d resonant inelastic x-ray scattering (RIXS) one scans through the 2p X-ray absorption edge and measures the low energy excitations, including phonons, magnons, plasmons and orbitons. The present experimental resolution of 20 meV allows the detailed observation of the electronic and magnetic structure. Energy-resolved RIXS to determine the energy positions of the (multi)-magnons, phonons and orbitons [5]. Momentum-resolved RIXS can be used to determine the momentum dependence of these excitations, for example the electron-hole pair band structure of LaCoO3 [6].

OPERANDO: An important advantage of XAS and RIXS is that they can be performed as a photon-in photon-out experiment, in contrast to XPS where electrons are detected. This implies that XAS and RIXS can be used under extreme conditions and/or to study the inside of materials or reactors [7].

[1] Core Level Spectroscopy of Solids, Frank de Groot and Akio Kotani (2008)
[2] Simulation software at www.anorg.chem.uu.nl/CTM4XAS
[3] Ghiasi et al. Phys. Rev. B. 100, 7, 075146 (2019)
[4] J. Elec. Spec. 249, 147061 (2021)
[5] Elnaggar et al. Nature Comm 14, 2749 (2023)
[6] Wang et al. Phys. Rev. B. 98, 035149 (2018)
[7] Che et al. J. Phys. Chem. C. in press (2024)