Circular dichroism effects in atomic x-ray scattering

It is shown that a specific beyond-dipole-approximation polarization effect in elastic photon-atom scattering, resulting in circular dichroism when the scattered photon has a suitable observed linear polarization, has significance in the x-ray regime. Ground-state atoms are considered, assumed to be randomly oriented. The cross section, given our assumptions, is written in terms of photon Stokes parameters and four real photon-polarization-independent atomic parameters (which depend on the vectors of the problem and the two invariant scattering amplitudes). Numerical results are given for the case of scattering from ground-state atoms with $Z=29,$ $Z=54,$ and $Z=92.\mathrm{}$ Attention is given to determining the regime where the dichroism effect may be experimentally observable. An ideal experiment would involve measuring the difference between the cross sections for right-handed and left-handed circularly polarized incident photons, observing a fixed linear polarization for the scattered photon which makes an angle of $45°$ with respect to the scattering plane. The effect is seen to be largest for intermediate angles, high Z and high (hundreds of keV) photon energies, increasing to an approximately 20% effect in cross sections. The parameter determining this effect is also responsible for the appearance of elliptically polarized scattered photons for the case of a suitable linearly polarized incident beam.