Dichroism and resonant diffraction in x-ray scattering by complex materials

We survey universal concepts that influence dichroism and resonant Bragg diffraction, aiming to reach across the range of scientific disciplines that benefit from x-ray techniques, namely, chemistry, physics, life-sciences, and the science of materials. To this end, we adopt a top down discussion of the aspects of symmetry and concomitant selection rules. Starting from selection rules that can be deduced from the global condition that an observable quantity is unchanged on reversing the directions of both space and time separately, to selection rules that flow from bulk symmetry properties of electrons imposed by elements of a point group or crystal class to, finally, atomic selection rules that emerge from the details of the electronic structure. As a motivation for the latter we discuss, with a new calculation of the x-ray scattering length, E1 - M1 absorption and scattering events that particularly interest scientists studying the chirality of life. In the main text there is modest use of mathematics, with appropriate details relegated to a few appendices.