Theory of X-ray natural circular dichroism

A theoretical approach is presented to calculate the natural circular dichroism recently discovered in the x-ray range (XNCD). XNCD is shown to be due to an interference of electric dipole and quadrupole transitions. The basic formula represents XNCD as an odd second-rank tensor. The crystal symmetries compatible with XNCD are determined. Sum rules are derived that relate XNCD to the mixing of odd and even orbitals on the absorbing site in the ground state. A multiple-scattering theory of XNCD is presented. The results are analyzed to show that XNCD is sensitive to the relative orientation of the cluster shells. A scattering path analysis is carried out to identify the paths responsible for the signal.