Spin-Orbit Interaction

Sleeker

1. The problem statement, all variables and given/known data
List all of the elements through calcium that you would expect not to have a spin-orbit interaction that splits the ground state energy. Explain.


2. Relevant equations
Not quite sure, but I'll list a few.
If there are two electrons:
L=|l₁-l₂| to |l₁+l₂|
S=|s₁-s₂| to |s₁+s₂|
J=|L-S| to |L+S|
j=l +\- s

3. The attempt at a solution
The book barely ever mentions the "ground state" and instead just picks out random scenarios with an electron in this particular subshell and another in this other particular subshell. One of my guesses is to just pick out the elements that have filled outer subshells (noble gases and alkalines), but I don't really have a specific reason to do so except that they seem to be a plausible guess.

The book's example to find the spectroscopic notation for the ground state of helium finds L₁=0, L₂=2, and so L=0, but I don't quite see how they did that. My guess is that both of them are in a l=0 subshell (but then how do I do this for atoms with much more electrons?). The spins must be anti-aligned due to the exclusionary principle, so S=0. I understand how that is calculated. Therefore, J=0. They then say that the ground state spectroscopic symbol for Helium is 1¹S₀, but I don't know what that means, including whether or not it means the ground state doesn't split.