# Combination differences with spin

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• Malamala
In summary, the person asking the question is trying to analyze diatomic molecular spectra using pgopher. They are unsure if they can use the Combination Differences method due to the presence of electron spin and other molecular parameters. The expert responds that Combination Differences can still be used, but it is important to know the energy differences between ground states sharing a common excited state. They also note that the task will be different depending on whether the molecule being analyzed is known or new.
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!

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.

## 1. What is combination difference with spin?

Combination difference with spin is a concept in quantum mechanics that refers to the difference in energy levels between two atomic or molecular states with different spin orientations. This difference is caused by the interaction of the spin of the electrons or nuclei within the atom or molecule.

## 2. How is combination difference with spin related to the Pauli exclusion principle?

The Pauli exclusion principle states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously. Combination differences with spin arise from the application of this principle, as the spin of fermions affects their energy levels and thus their ability to occupy certain states.

## 3. What are some real-world applications of combination difference with spin?

Combination difference with spin is an important concept in understanding the behavior of atoms and molecules, which has many practical applications. For example, it is used in nuclear magnetic resonance (NMR) spectroscopy, which is used in medical imaging and chemical analysis. It also plays a role in the functioning of electronic devices such as transistors and magnetic storage media.

## 4. Can combination difference with spin be observed directly?

No, combination difference with spin cannot be directly observed as it is a theoretical concept. However, its effects can be observed through experiments and measurements, such as in NMR spectroscopy, which indirectly confirms the existence of combination differences with spin.

## 5. How does combination difference with spin impact the properties of materials?

The combination difference with spin of atoms and molecules affects their electronic and magnetic properties, which in turn impact the properties of materials made from these atoms and molecules. For example, the spin of electrons in a material can determine its electrical conductivity and magnetic properties. Understanding combination differences with spin is therefore crucial in materials science and engineering.

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