- #1
Yuli
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- TL;DR
- Deducing total spin from atomic spectra with unusual term symbols, like in Ne. What do these term symbols specify, and do they have a well-defined total spin, S^2?
I'm interested in deducing spin-flip energies of various atoms from the NIST atomic spectra database:
https://physics.nist.gov/PhysRefData/ASD/levels_form.html
These are the minimal energies required to go from the ground state to a state with some given total spin [tex]S[/tex] (such that the eigenvalue of the spin operator [tex]\hat{S}^2[/tex] is [tex]S(S+1)[/tex]).
This entails interpreting term symbols of excited states. For example, these are the excited levels of B⁺:
https://physics.nist.gov/cgi-bin/AS...t=on&lande_out=on&perc_out=on&biblio=on&temp=
In [tex]LS[/tex] coupling, terms like all those in the link above give [tex]S[/tex] explicitly (as well as [tex]L[/tex] and [tex]J[/tex]). For [tex]jj[/tex] coupling terms, my understanding is that these arise in large atoms where relativistic effects become significant, and [tex]S[/tex] is no longer a good quantum number, so the spin-flip energy is ill-defined.
My question is about other terms, like these in the excited levels of neutral neon:
https://physics.nist.gov/cgi-bin/AS...t=on&lande_out=on&perc_out=on&biblio=on&temp=
I believe these might be [tex]J_1 L_2[/tex] coupling terms, which separate the outermost electron from the rest and specify quantities like [tex]L_2[/tex] (orbital angular momentum of the outer electron) and [tex]J_1[/tex] (angular momentum of the other electrons). However, this seems strange, because properties of a single electron in a many-electron system, like [tex]L_2[/tex], are typically bad quantum numbers. So,
- Which quantum numbers *are* specified by term symbols like those in the excited states of Ne?
- If [tex]L_1, L_2, J_1[/tex] or [tex]J_2[/tex] are specified, aren't these bad quantum numbers? How is this reconciled?
- Do the excited states of Ne have well-defined values of [tex]S[/tex]? If so, how is it deduced? That is, how are the spin-flip energies of Ne obtained from the NIST data?
https://physics.nist.gov/PhysRefData/ASD/levels_form.html
These are the minimal energies required to go from the ground state to a state with some given total spin [tex]S[/tex] (such that the eigenvalue of the spin operator [tex]\hat{S}^2[/tex] is [tex]S(S+1)[/tex]).
This entails interpreting term symbols of excited states. For example, these are the excited levels of B⁺:
https://physics.nist.gov/cgi-bin/AS...t=on&lande_out=on&perc_out=on&biblio=on&temp=
In [tex]LS[/tex] coupling, terms like all those in the link above give [tex]S[/tex] explicitly (as well as [tex]L[/tex] and [tex]J[/tex]). For [tex]jj[/tex] coupling terms, my understanding is that these arise in large atoms where relativistic effects become significant, and [tex]S[/tex] is no longer a good quantum number, so the spin-flip energy is ill-defined.
My question is about other terms, like these in the excited levels of neutral neon:
https://physics.nist.gov/cgi-bin/AS...t=on&lande_out=on&perc_out=on&biblio=on&temp=
I believe these might be [tex]J_1 L_2[/tex] coupling terms, which separate the outermost electron from the rest and specify quantities like [tex]L_2[/tex] (orbital angular momentum of the outer electron) and [tex]J_1[/tex] (angular momentum of the other electrons). However, this seems strange, because properties of a single electron in a many-electron system, like [tex]L_2[/tex], are typically bad quantum numbers. So,
- Which quantum numbers *are* specified by term symbols like those in the excited states of Ne?
- If [tex]L_1, L_2, J_1[/tex] or [tex]J_2[/tex] are specified, aren't these bad quantum numbers? How is this reconciled?
- Do the excited states of Ne have well-defined values of [tex]S[/tex]? If so, how is it deduced? That is, how are the spin-flip energies of Ne obtained from the NIST data?