Is the degeneracy of N2+ different from N2?

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Discussion Overview

The discussion revolves around the degeneracy of the diatomic molecules N2 and its ion N2+. Participants explore the differences in electronic, vibrational, rotational, and nuclear spin statistical weights between these two species, particularly in the context of calculating electron temperature using optical emission spectrum intensity ratios.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses uncertainty about how the degeneracy values differ between N2 and N2+, specifically regarding electronic, vibrational, rotational, and nuclear spin statistical weights.
  • Another participant requests clarification on what is meant by "degeneracy," indicating a need for specificity in the discussion.
  • A participant mentions their goal of calculating electron temperature using the intensity ratio of optical emission spectra, noting the importance of degeneracy values for N2(C3πu) and N2+(B2Σg+).
  • It is noted that N2 is a triplet state while N2+ is a doublet state, which may influence the calculations of degeneracy.
  • Concerns are raised about how the rotational states differ due to the symmetry properties (u vs. g) of the two species, although it is suggested that this may not significantly affect the overall degeneracy.
  • One participant references literature to explain how degeneracy is calculated as a product of electron spin statistical weight, vibrational statistical weight, and rotational statistical weight, providing specific values for N2(C) and N2+(B).
  • There is uncertainty regarding how to determine the rotational quantum number J for N2(C) without access to rotational Raman spectrum data.
  • Discussion includes the complexity of determining state-dependent and state-independent weights for the rotational degeneracy, particularly for N2(C).

Areas of Agreement / Disagreement

Participants express differing views on the implications of the degeneracy differences between N2 and N2+. There is no consensus on how these differences affect calculations, and several uncertainties remain regarding the specific values and methods for determining degeneracy.

Contextual Notes

Limitations include the lack of clarity on the definitions of degeneracy being discussed, the dependence on specific quantum states, and the unresolved nature of how to obtain the necessary rotational quantum numbers for accurate calculations.

BlackPowder
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The calculation of degeneracy of diatomic molecules can be easily found. However, there is no detail introduction of ions. Not sure if the electronic, vibrational, rotational, and nuclear spin statistical weights are differ from N2+ to N2. Please help. Thanks.
 
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Can you clarify what you mean by degeneracy (degeneracy of what)?
 
DrClaude said:
Can you clarify what you mean by degeneracy (degeneracy of what)?
I am trying to calculate the electron temperature using optical emission spectrum intensity ratio. The equation includes degeneracy values of N2(C3πu) and N2+(B2Σg+). I have found the way to get the degeneracy of N2(C), but not sure if I can do the same thing to the excited ion N2+(B).
 
Well, one is a doublet and the other a triplet, so that will have to be taken into account. Also, concerning rotation, you have to consider that one is u and the other g, so that will change which rotational states are allowed, but at first glance I don't see why this should affect the degeneracy.
 
DrClaude said:
Well, one is a doublet and the other a triplet, so that will have to be taken into account. Also, concerning rotation, you have to consider that one is u and the other g, so that will change which rotational states are allowed, but at first glance I don't see why this should affect the degeneracy.
Thanks for the reply.

My trouble is to find the degeneracy of N2(C3∏u) and the degeneracy of N2+(B2Σg+). So far, according to the literature [1], the degeneracy is a product of electron spin statistical weight, vibrational statistical weight, and rotational statistical weight. According to [2], the one of electron spin equals to 2S+1 for Σ states and 2(2S+1) for other states. Thus for N2(C), the value is 6, and for N2+(B), it is 2. Literature [2] also suggests the vibrational degeneracy is unity. However, for the rotational one, grot=(2J+1)gsgi, where gs and gi are "state dependent" and "state independent" weights determined by nuclear spin. My spectrum comes from electron impact excitation in a plasma, rather than light scattering on a target. Therefore, I have no idea how to get J value without rotational Raman spectrum. Also, for N2+(B) which is a Bose system at s level, its gs = 6, but I have no idea how to find gs for N2(C) since it is same for symmetric and antisymmetric rotational level.

[1] M. Simeckova et al, Einstein A-coefficients and statistical weights for molecular absorption transitions in the HITRAN database, J. Quant. Spectrosc. Ra., 98(2006) 130-155.
[2] J. B. Tatum, The interpretation of intensities in diatomic molecular spectra, Astrophys. J. Suppl., 14(1967) p.21.
 

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