# A Selection rules in IXS and EELS

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1. Jul 10, 2016

### EdB

Hello everybody,

since I have to plan an experiment to map the energy-momentum dispersion of a bosonic excitation, I have a question related to the difference between the excitations probed by Inelastic X-ray Scattering (IXS) and Electron Energy Loss Spectroscopy (EELS). Both the techniques are useful for mapping the energy-momentum dispersion of "some" excitations in solids (phonons, plasmons, excitons...).

When one is in the limit q = 0 (which is probed by optics), every kind of excitation can be labelled in terms of its symmetry. For a solid with inversion symmetry, the excitations can be labelled as dipole-allowed (sometimes called IR-active when the photon energy for exciting them is in the IR) or Raman-active. Some modes are also silent in both spectroscopies but I would like to neglect this aspect. Therefore, in general, we can have IR-active phonons, Raman-active phonons, transverse plasmons that are dipole-allowed (they absorb light in the IR or in the visible range) etc.

Now let's suppose we want to map the energy-momentum dispersion of such excitations (i.e. far from q = 0). Is the symmetry selection rule that governs the physics at q = 0 valid anymore?
This question arises from a general observation: I noticed in many papers that EELS is a very sensitive probe to surface plasmons, which are dipole-allowed excitations in the q = 0 limit (they can be excited by light). So EELS can map "dipole-allowed modes". I expected that the inelastic scattering of x-ray photons followed more or less the same phenomenology as the inelastic scattering of electrons, because both particles are highly energetic and because the information is impinged in the energy shift of the detected particle. However, I have not found any IXS experiment probing a surface plasmon at q far from zero!

Close to a resonance, IXS becomes RIXS (Resonant Inelastic X-ray Scattering) and this can be seen more as a Raman-like process. However, far from a resonance and at large q's, I expect both techniques to probe the same kind of excitations. The relative cross-sections for sure will vary, but I don't see a limitation in IXS itself as a process...

Thanks a lot for any help!

2. Jul 15, 2016