Polarizability if a molecule in raman scattering

[Mr Boom]

Hello. I'm reviewing background information on Raman scattering and I've noticed that the polarizability scales with v+1 for Stokes transitions and v for anti-Stokes. Why is this and what assumptions are used in the derivation? An explanation or pointing me to a good reference would be appreciated.

Thanks

 

[Andy Resnick]

I don't understand your question- what is 'v'?

 

[DrDu]

I think v is the quantum number n of the oscillator involved.
I can only give you a scetch:
In Raman scattering you have matrix elements $\langle v|x,y,z|v\pm 1\rangle \langle v\pm 1 | x,y,z |v\rangle$. If the vibrations are harmonic these expressions scale like v or v+1. Try to express x, y or z in terms of generation and anihilation operators b+ and b to prove this.