Hund's rule and strong spin-orbit interacion

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SUMMARY

Hund's rules, particularly the first and second, are applicable to heavy atoms with significant spin-orbit interaction, but their utility diminishes due to the lack of good quantum numbers for total orbital angular momentum (L) and total spin (S) in such cases. The third Hund's rule, which relies on Russell-Saunders coupling, is not directly applicable in the presence of strong spin-orbit coupling. To determine the ground state of an atom with large spin-orbit interaction, one should refer to term symbols and their derivation under jj-coupling.

PREREQUISITES
  • Understanding of Hund's rules and their application in atomic physics
  • Familiarity with Russell-Saunders coupling and jj-coupling
  • Knowledge of quantum numbers and their significance in atomic structure
  • Basic grasp of term symbols and their role in determining atomic states
NEXT STEPS
  • Research the derivation and application of term symbols in jj-coupling
  • Study the effects of spin-orbit coupling on atomic states
  • Explore advanced quantum mechanics concepts related to angular momentum
  • Investigate the implications of Hund's rules in heavy-element chemistry
USEFUL FOR

Physicists, chemists, and students studying atomic structure and quantum mechanics, particularly those focusing on heavy atoms and spin-orbit interactions.

Abigale
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Hi,
I have read that Hund's rules are valid for Atoms with low z.
Because the third Hund's rule is build of Russell-Saunders coupling.

Can I still use the first and second Hund's rule for heavy atoms and jj-coupling( for the third rule)?
Or how can I know the groundstate for an atom with large spin-orbit interaction?

Thank you
Abby
 
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Abigale said:
Can I still use the first and second Hund's rule for heavy atoms and jj-coupling( for the third rule)?
I suppose you could, but it'll be meaningless, because ##\textbf{L}## and ##\textbf{S}## are not good quantum numbers in the presence of large spin-orbit coupling. You might take a look at the Wikipedia entry for term symbols:
https://en.m.wikipedia.org/wiki/Term_symbol
It has a good overview for how we determine term symbols for jj coupling.
 

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