Collapse of isotropic Raman spectra

The relaxation operator f carries out rotational broadening as well as vibrational dephasing between 0 and 1 states. 

If the interaction V does not depend significantly on vibrational quantum numbers as in Eq. (4.38) then dephasing is negligible and 

That means the frequency exchange operator in the Q-branch coincides with that ruling relaxation of rotational populations Nj = J2m Njm in the ground state  

Thus this operator must satisfy the necessary demands of the particle conservation law and detailed balance principle as was the case for its simpler analogue in Eq. (4.23) and Eq. (4.24). They are 

Now we are well equipped to approach the main problem of spectral collapse theory. Presenting Eq. (4.62) in the form 

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