Combination differences with spin

[Malamala]

Hello! I am trying to analyze some diatomic molecular spectra (I am using pgopher) between a $^2\Sigma_{1/2}$ and a $^2\Pi_{1/2}$ level. Before diving into tying to assign lines by eyes in pgopher I was thinking to use this Combination Differences method, but I am not sure I can do it in my case, given that I have electron spin and hence other molecular parameters (like $\Lambda$-doubling, or spin-rotation coupling). I tried to use some P and R transitions with the same J, but the final formula contains these other spin related parameters, so I can't isolate the rotation parameters alone (B values). Am I doing something wrong, or is that the case for when you have spin? The best I can do is extract the difference in B values for the 2 electronic levels. However, I can do this using, only the R or only P branches, without combining the two of them. Can someone let me know if I can gain anything from using Combination Differences when electronic spin is involved? And in general, can someone advise me on how to get started with assigning lines in pgopher (doing it by eye seems quite daunting). Thank you!

 

[Herzberg137]

Combination differences should still work for quantum number assignment in the sense that the energy differences between ground states sharing a common excited state (or vice versa) must satisfy certain equalities. For example, for the $^2\Pi_{1/2} - ^2\Sigma^+$ case that you mention, you'll find that $R_{11}(N-1) - Q_{12}(N+1) = Q_{11}(N-1) - P_{12}(N+1)$ and $P_{11}(N)-Q_{12}(N) = Q_{11}(N)-R_{12}(N)$.

But there's a bigger question here: what molecule are you trying to analyze? Have either of the states in your transition been observed before? If their constants are known, you'll have a much different task than if you're studying a brand new molecule.