X-ray Resonant Magnetic Scattering : Polarisation Dependence in the non-spherical case

We develop a simple tensorial contraction method to obtain analytical formula for X-ray resonant magnetic scattering. We apply the method considering first electric dipole-dipole and electric quadrupole-quadrupole scattering in the isolated atom approximation and compare the results with previous works. Then we apply the method to derive phenomenological original formulas which account also for non-spherical systems and for dipole-quadrupole mixing.