An implementation of the multiple-scattering approach to x-ray magnetic circular dichroism (XMCD) in K-edge x-ray absorption spectroscopy is presented. The convergence problems due to the cluster size and the relativistic corrections are solved using an expansion of the Dirac Green function for complex energies up to the second order in 1/$c$. The Fermi energy is dealt with via a complex plane integration. Numerical methods used to obtain the semi-relativistic Green function in the whole complex plane are explained. We present a calculation of the magnetic circular dichroism at the K-edge of bcc-iron including the core hole effect. A good agreement is found at high energy. The physical origins of the XMCD spectrum near the edge and far from the edge are analyzed. The influence of the core hole, the possibility of a multiple-scattering expansion and the relation of XMCD with the spin-polarized density of states are discussed. A simple interpretation of XMCD at the K-edge is presented in terms of a rigid-band model.
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