What is the relationship between FS and HFS in the 3s3p Configuration?

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SUMMARY

The discussion focuses on the relationship between Fine Splitting (FS) and Hyperfine Splitting (HFS) in the 3s3p configuration of atomic states. The user seeks clarification on how to represent HFS alongside FS, specifically regarding the coupling of angular momentum quantum numbers I and J to form F levels, which then yield MF levels. The user also inquires about the degeneracy of Mj levels in the absence of HFS and the representation of hyperfine levels for the 1s orbital, indicating a need for a clearer understanding of these quantum mechanical concepts.

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  • Understanding of quantum mechanics, specifically angular momentum coupling
  • Familiarity with atomic structure and configurations, particularly 3s3p and 1s orbitals
  • Knowledge of Fine Splitting (FS) and Hyperfine Splitting (HFS) concepts
  • Basic grasp of magnetic quantum numbers (Mj and Mf) and their significance
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  • Study the effects of external magnetic fields on hyperfine levels in atomic systems
  • Explore the concept of degeneracy in quantum states, particularly in the context of Mj levels
  • Learn about the implications of Fine and Hyperfine Splitting in spectroscopy
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Henk
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I'm having some problems with the Fine and Hyperfine splitting (FS and HFS). For example the 3s3p Configuration, I understand the FS:
*****************************_______Mj=1
************1P________J=1*****_______ Mj=0
*****************************_______ Mj=-1
*
*
************3P______ Is split into J=0,1,2 and they are split into the Mj levels
*
*
3s3p_____

But where then is the HFS. I understand that I and J couple to F and that gives MF-levels but I don't know where to put in the picture above.

edit: the picture isn't very clear, sorry had to add some stars.
 
Last edited:
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Henk said:
I'm having some problems with the Fine and Hyperfine splitting (FS and HFS). For example the 3s3p Configuration, I understand the FS:
*****************************_______Mj=1
************1P________J=1*****_______ Mj=0
*****************************_______ Mj=-1
*
*
************3P______ Is split into J=0,1,2 and they are split into the Mj levels
*
*
3s3p_____

But where then is the HFS. I understand that I and J couple to F and that gives MF-levels but I don't know where to put in the picture above.

edit: the picture isn't very clear, sorry had to add some stars.
What is the degeneracy of the Mj levels in the absense of the HFS ?

Perhaps, I should ask this first : Do you know where to put the hyperfine levels for the 1s orbital ?
 
For the 1s Orbital: L=0, S=1/2 thus J=1/2. That means the level has FS for J = 1/2 and J = -1/2. I don't know I so I can't give the F values however I suppose that the J-levels are splitted into the F-levels. And that if there is an external magnetic field (weak) the F-levels are splitted into 2F+1 Mf levels. Is this correct?
 

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