Undergrad Changes in angular momentum for ro-vibrational transitions

[Malamala]

Hello! If we have a transition between 2 ro-vibrational levels of the same electronic state of a diatomic molecule the selection rules require for the changes in the rotational quantum number J that $\Delta J = \pm 1$. Why can't we have $\Delta J = 0$? The photon carries one unit of angular momentum, so if we start with a state with angular momentum J, shouldn't we be able to obtain J-1, J and J+1 by combining it with the 1 unit of angular momentum from the photon? Thank you!

 

[dRic2]

https://en.wikipedia.org/wiki/Rigid_rotor#Selection_rules

maybe it is what you are looking for

 

[Malamala]

https://en.wikipedia.org/wiki/Rigid_rotor#Selection_rules

maybe it is what you are looking for

I've actually seen that derivation before. In addition, if you do the math, the $\Delta J = \pm 1$ is true for circularly polarized light, too, not only for linearly polarized one. However I was hoping for a more physical/intuitive explanation of this, rather than just: "The math says so". As I said, given that the photon has spin 1, I expected that adding that to a spin J, the resulting spin would be J-1, J, J+1, but it seems like the J case doesn't hold and I was wondering why basic angular momentum addition can't be applied here, without having to go through all the math.

 

[dRic2]

$J_2 - J_1$ is the change in total angular momentum of the molecule, so the photon should carry this momentum ($|J_2 - J_1| < J_{ph} < |J_2 + J_1|$). From an intuitive point of view, I think (I'm not sure) the case $J_{ph} = 0$ is forbidden because it would be associated with a monopole radiation. From classical EM we know that magnetic monopoles do not exist and electric monopoles do not radiate (https://en.wikipedia.org/wiki/Multipole_radiation#Electric_monopole_radiation,_nonexistence). If I remembered correctly, you may be able to prove this by expanding the vector potential in spherical harmonics or something on those lines. I've never actually tried and I'm not sure this is right because I can't remember where I read it. If you succeed let me know.