0
$\begingroup$

Scattering from a single scattering centre can be described by the (differential) cross section, which tells us the proportion of particles scattered into a given solid angle.

However, what if the target is an extended body composed of many scattering centres? Can one desribe the scattering from such a target using the cross section for a single centre? I have tried to find information about this, but did not find anything useful.

The way I imagine this could go is - e.g., for a very dilute gas of scatterers, we can assume that each incident particle is only scattered once. The scattered intensity will then depend on the number density $n$ of the scattering centres. For less dilute gases, this suggests to me that a series in powers of $n$ could describe the situation quite well, with the 2nd order term representing double scattering, etc.

For gases, the scattering centres are randomly distributed, which makes the problem easier (I suppose). For solids, we would also have to consider interference, giving rise to things like Bragg's law.

And lastly, for the case of high number density, I assume the particles would just scatter in every direction randomly, and the propagation would follow the diffusion equation.

My question therefore is - is there a theory that can describe some (or all) of these phenomena in a unified way, probably as a series expansion in the number density $n$ of scattering centres? (It seems like a problem that someone has already studied, so I am probably just missing the right search keywords.)

$\endgroup$

1 Answer 1

0
$\begingroup$

I would suggest you to look for Clausius-Mossoti relation (it helps to calculate the correction to the polarizability of medium, caused by the particles in it). For higher concentrations I would consider searching for keywords 'effective medium model': it tells how to treat the mixture of some shapes of materials in given volume as one material with one dielectric function.

$\endgroup$
1
  • $\begingroup$ What does this have to do with scattering of particles? $\endgroup$ Commented Aug 16, 2023 at 22:37

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.