M2L7i.txt

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Let us summarize.
For the fine structure we have three different terms.
And they all have a different signature.
We have the relativistic kinetic energy correction.
We have the spin-orbit coupling, and we have the Darwin term.
We can now ask which term contributes for an s electron?
Well, relative kinetic energy, of course.
The Darwin term is only for s electrons.
L-S does not contribute because an s electron has L equal zero.

So if you go to p and d states, to states with finite angular
momentum, then we get contribution of L S.
We always get a relativistic kinetic energy contribution,
but for finite angular momentum we don't have the Darwin term.
And finally we can also classify those different contribution
by asking what is the sign?
Thus, do those corrections lower, or increase,
the total energy?
Well the Darwin term reduces the binding energy
because it sort of takes a cusp away
from the Coulomb interaction.
The kinetic energy has the opposite sign.
And spin-orbit coupling is L dot S,
and S can be parallel or anti parallel to L.
So, therefore, the spin-orbit in direction
has plus or minus sign.

Any questions about those three terms?