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The different momenta of electron and nucleus are described by different quantum numbers.

(a) l and m$_l$ describe the orbital angular momentum and quantization on its component along an arbitrary direction, respectively.

(b) s and m$_s$ describe the electron spin angular momentum and quantization on its component along an arbitrary direction, respectively.

(c) I and m$_I$ describe the nuclear spin angular momentum and quantization on its component along an arbitrary direction, respectively.

Those space quantizations can be exploited for spectroscopy. For example, m$_I$ $\implies$ the direction of nuclear spin angular momentum w.r.t. external magnetic field is quantized $\implies$ when magnetic field applied, because of the multiple possible directions w.r.t. external field, the energy of initially degenerate states will split according to the direction of angular momentum (i.e. according to the value of $m_I$), and the gaps between the now non-degenerate states can be probed by spectroscopy, and that gives structural information.

magnetic resonance spectroscopy based on $m_I$ = NMR

magnetic resonance spectroscopy based on $m_s$ = EPR

Is there any kind of similar magnetic resonance spectroscopy based on $m_l$? When an external magnetic field is applied, won't the energy of electron also split according to $m_l$? But I do not recall any spectroscopic method based on $m_l$.

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    $\begingroup$ You might look into the Zeeman and Paschen-Back effects en.wikipedia.org/wiki/Zeeman_effect $\endgroup$
    – Ian Bush
    Commented Oct 4, 2021 at 19:02
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    $\begingroup$ I think Zeeman effect cannot be considered as "pure" $m_l$, because Zeeman effect led to the concept of electron spin. $\endgroup$
    – ACR
    Commented Oct 4, 2021 at 19:39
  • $\begingroup$ @M.Farooq Indeed! These were just the first things that came to mind, and I hoped they might nudge someone towards what might be an answer $\endgroup$
    – Ian Bush
    Commented Oct 4, 2021 at 19:43
  • $\begingroup$ @Ian Bush, What about Stark effect? Basically, I think the OP wanted to see how $m_l$ is experimentally detected. Interesting question. $\endgroup$
    – ACR
    Commented Oct 4, 2021 at 20:22
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    $\begingroup$ @TheLearner, I may be wrrong but there is no magnetic moment associated with orbital motion. The $m_l$ values become observable in Stark experiments. I will try to modify your question properly and ask it in SE physics. $\endgroup$
    – ACR
    Commented Oct 8, 2021 at 13:39

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