  We present an equation of motion coupled cluster approach for calculating and
understanding intrinsic inelastic losses in core level x-ray absorption spectra
(XAS). The method is based on a factorization of the transition amplitude in
the time-domain, which leads to a convolution of an effective one-body spectrum
and the core-hole spectral function. The spectral function characterizes these
losses in terms of shake-up excitations and satellites, and is calculated using
a cumulant representation of the core-hole Green's function that includes
non-linear corrections. The one-body spectrum also includes orthogonality
corrections that enhance the XAS at the edge.
