I often hear that Rayleigh scattering is several orders of magnitude more common than Raman scattering; for instance here is one description. However, i have not come across any explanations as to why this is so. I presume it has something to do with Raman being an inelastic process. Does anyone know of any quantum or classical derivations showing why Rayleigh is so much more common than Raman scattering?

Raman scattering doesn't happen in all systems. As the link points out, it requires an anisotropic polarizability. So not all systems can (spontaneously) Raman scatter. Since J has to change by 2, this is effectively a second-order interaction (dipole interactions are strongest) — basically, two things have to happen, each with some probability.  Two probabilities multiplied gives you a smaller number, since they are < 1.

 

 

This is the best answer i have yet received on this topic, but my understanding is lacking. I will revise quantum numbers and come back - i think they cropped up during the solutions to solving SE due to the imposition of certain constraints.

I found this PPT presentation which I've converted to PDF. I've uploaded it. Note the print is rather large, so shrink the doc. In it, it says:

Quote

Rayleigh scattering has a considerably higher probability of occurring than Raman because the most probable event is the energy transfer to molecules in the ground state and re -emission by the return of these molecules to the ground state.

 

Chapter 18.pdf

Thanks. I can understand why molecules will most likely start in the ground state - although the proportion of molecules in this state must follow some kind of Boltzmann distribution dependent on temperature. But in Raman scattering we see stokes and anti-stokes scattering, energy lost and gained, so i'm not sure how the starting state influences the type of scattering. The latter part of that statement suggests return to the ground state is most probable - i assume this has something to do with selection rules and quantum numbers so i'm slowly reading up on these (probably the former part too).

What i really want is a mathematical description of these: i will likely need to revise my physics a bit to understand it, but until i do i won't understand. Any hints or resources on the maths i should be reading up on would be greatly appreciated.