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Furthermore,

a) Why is the order of domination in $L$-$S$ coupling:

  1. Spin-Spin correlation

  2. Residual Interaction

  3. Spin-Orbit Interaction

b) While the order in $J$-$J$ coupling is:

  1. Spin-orbit interaction

  2. Residual Interaction

  3. Spin-spin correlation

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I found some Q&A which maybe quite helpful if someone else has similar queries.

1.Why is spin-orbit splitting larger in heavier atoms?

2.Why do you need weak spin-orbit interaction for LS coupling?

3.LS-coupling, residual electrostatic interaction and interval rule

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