I Is the degeneracy of N2+ different from N2?

[BlackPowder]

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.

 

[DrClaude]

Can you clarify what you mean by degeneracy (degeneracy of what)?

 

[BlackPowder]

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(C³π_u) and N₂⁺(B²Σ_g⁺). 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).

 

[DrClaude]

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.

 

[BlackPowder]

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⁺(B²Σ_g⁺). 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, g_rot=(2J+1)g_sg_i, where g_s and g_i 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 g_s = 6, but I have no idea how to find g_s 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.