/Multiple Scattering

Short summary of discussions/breakouts:

• Reflection and refraction should be excluded from multiple scattering
• Need to agree on a common nomenclature
• There are certain constraints for multiple scattering: mean free path length & coherence length, sample size / curvature / geometry
  • They have to be identified before each experiment

Detailed:

• X-ray comparison (overlapping with topic Background):
  • MS in the end gives extra background
  • Some people use MS to enhance the signal explicitly. Or you make additional layer to enhance reflections
  • Comparing X-ray and neutron background, X-rays behave nicer in terms of MS. When absorption is strong all the scattering is from near the surface. For neutrons the absorption is weak and therefore scattering is of higher intensity.
  • Incoherent scattering cross section for hydrogen is very high and scattering attenuation of the beam penetration is limited. One has to be careful about comparing the theory for X-ray and neutrons.
  • Diffuse scattering for X-rays at Liq-Liq interface is comparable to neutrons. The beam is below the horizon and there is an attenuated pattern seen.
  • X-ray Software packages we can take inspiration from? Brookhaven, Ben Ocko, BornAgain

• • Sub-cases of multiple coherent scattering and distinction from incoherent multiple scattering:

In the framework of the distorted-wave Born approximation (DWBA), it is essential to distinguish between two distinct processes: (i) the propagation of the incident wave through the stratified medium, which is incorporated _exactly_ in the formalism; and (ii) the scattering from embedded “particles” (additional scattering centers) which is treated perturbatively within the 1st-order Born approximation. Both (i) and (ii) are within the quantum theory (‘coherent’). Only in (i), each layer is represented by an effective static potential, simplifying the description of the background medium.

The term “multiple scattering” refers to the situation in which successive scattering events are not treated independently but are combined quantum mechanically, i.e., the amplitudes from different scattering paths are added coherently.

In contrast, “incoherent multiple scattering” denotes an approximation in which scattering from each center is treated quantum mechanically, but the subsequent propagation of scattered waves is represented within a semi-classical or ray-optical picture (Gaussian optics). This approach is conceptually analogous to the semi-classical treatment of transport phenomena based on the Boltzmann equation, where phase relations between successive scattering events are neglected.

• How to measure?
  • GIXOS grazing incidence X-ray offspecular scattering. Scattering from the object is modulated by the reflectivity, you can deduce reflectivity if you estimate the form factor.
    • When you move a liquid surface and wait for it to stop, the measurement duty cycle is poor (2 min vs seconds)

If you rotate the solid sample there is much less need to wait.

• • • ID10 at the ESRF has a good setup. DCM beam tilting is used instead to avoid moving the sample.
    • Get inspiration from X-rays to improve the way we measure GISANS
    • Most productive groups are writing their own code and have their own ways to do experiments. Leading groups spend years analysing the data from an experiment. Writing their own code. Sharing is not common.