I am aware of the fact that selection rules for transitions between two different quantum states, are obtained via an assessment of the corresponding transition matrix elements [1,2].
When we consider the spectrum of a pure rotational spectrum, with different states identified by the rotational quantum number $J$, allowed transitions follow the selection rule $\Delta J = \pm 1$, i.e. only one unit (positive or negative) changes [3].
However, when we consider the pure rotational Raman spectrum (i.e. polarizibility changes purely due to molecular rotations), the relevant selection rules are stated [4] to be - $\Delta J = 0, \pm 2$, i.e. $\Delta J = 1$ is no longer followed for these transitions.
One would expect that the rigorous derivation would once again be based on some transition matrix element calculations, but certainly this change cannot be devoid of any physical meaning!
So, in essence, my question is two-fold:
Is there any reference for the detailed calculation of the above $\Delta J = \pm 2$ rule?
Is there any simple explanation for why are $\Delta J = 1$ transitions forbidden and $\Delta J = 2$ transitions allowed in Rotational Raman spectra?
[1] E. Merzbacher - Quantum Mechanics 3e/d; Ex 17.11.
[2] D. J. Griffiths - Quantum Mechanics 1e/d; Section 9.3.3.
[3] C. Banwell, E. McCash - Fundamentals of Molecular Spectroscopy, Section 2.3.
[4] C. Banwell, E. McCash - Fundamentals of Molecular Spectroscopy, Section 4.2.
