Fano-Feshbach approach for calculation of Auger decay rates with equation-of-motion coupled-cluster wave functions

X-ray absorption creates electron vacancies in a core shell. These highly excited states often relax by the Auger decay - an autoionization process in which one valence electron fills the core hole and another valence electron is ejected into the ionization continuum. Despite the important role of Auger processes in many experimental settings, their first-principle modeling remains challenging, mainly due to the necessity to describe many-electron continuum. We present a novel approach to calculate Auger decay rates by combining Fano-Feshbach resonance theory with equation-of-motion coupled-cluster (EOM-CCSD) framework and core-valence separation (CVS) scheme. The continuum many-body decay states are represented by products of an appropriate EOM-CCSD state and a continuum orbital describing the outgoing electron. The Auger rates are expressed in terms of two-body Dyson amplitudes (reminiscent of two-particle transition density matrix) contracted with two-electron bound-continuum integrals. Two approximations to the state of the outgoing electron are considered: a plane wave and a Coulomb wave with an effective charge. Numerical results are provided for core-ionized and core-excited benchmark systems (Ne, H₂O, CH₄, and CO₂), and compared with available experimental spectra.