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A theoretical framework for computing Auger spectra that include spin-orbit interaction is presented. The framework is based on the state-interaction approach using equation-of-motion coupled-cluster wave-functions. The working equations for Auger decay rates are derived within the Feshbach–Fano formalism. The capabilities of the theory are illustrated by the calculation of L-edge Auger spectra of H2S and Ar using the Feshbach–Fano and complex basis function (CBF) approaches. The quality of the Feshbach–Fano results depends critically on the treatment of the free-electron state. In contrast to the K-edge spectra for which both plane wave and Coulomb wave treatments yield reasonable results, the Feshbach–Fano calculations yield accurate results for L-edges only when using Coulomb wave (FF-CW). The FF-CW and CBF calculations of Auger spectra in H2S and Ar agree well with each other and with the available experimental data. The results highlight the importance of spin–orbit interactions for modeling L-edge Auger spectra. 

States with core vacancies, which are commonly created by absorption of X-ray photons, can decay by a two-electron process in which one electron fills the core hole and the second one is ejected. These processes accompany many X-ray spectroscopies. Depending on the nature of the initial core-hole state and the decay valence-hole states, these processes are called Auger decay, intermolecular Coulomb decay, or electron-transfer-mediated decay. To connect many-body wavefunctions of the initial and final states with molecular orbital picture of the decay, we introduce a concept of natural Auger orbitals (NAOs). NAOs are obtained by two-step singular value decomposition of the two-body Dyson orbitals, reduced quantities that enter the expression of the decay rate in the Feshbach--Fano treatment. NAOs afford chemical insight and interpretation of the high-level ab intio calculations of Auger decay and related two-electron relaxation processes.