In rovibrational transitions we have following selection rules

$$ \Delta v = \pm 1 $$

$$ \Delta J = \pm 1 $$

where $v$ is the vibrational quantum number and $J$ is rotational quantum number.

  • All $\Delta J = +1$ transitions give rise to R-branch lines.
  • All $\Delta J = -1$ transitions give rise to P-branch lines.

Literature also notes that R-branch lines are higher in frequency (and thus energy) than P-branch lines.

This is how it's defined but notice how I emphasized transition above? What confuses me is this: it is not specified which transition is meant, is it absorption or emission (of a photon)? Because it seems to me that it makes a difference.

Let's take one example transition, say between levels (v=0, J=0) to the (v=1, J=1) then we have:

  • in case of absorption J goes from 0 to 1 so: $\Delta J = +1$
  • in case of emission J goes from 1 to 0 so: $\Delta J = -1$

So it's the same transition but different $\Delta J $ based on whether it's emission or absorption. So to which branch does this transition belongs then?


You're quite correct that the simple definition for the $R$ branch $\Delta J = +1$ is ambiguous unless you also specify that $\Delta v > 0$. The $R$ branch is the higher energy branch so it's $\Delta J = +1, \Delta v = +1$ in absorption and $\Delta J = -1, \Delta v = -1$ in emission.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.