Can somebody explain me how to derive all term symbols using Young tableaux? Our lecturer showed us but I couldn't quite understand it without any background on group theory. I have some vague algorithm that goes like this:
Given: Configuration $nl^k$
- Construct all possible tables of $k$ with two rows where the first row $\le2l+1$ and the second shorter or equal to the first row.
- Make a symmetrization of rows and antisymmetrization of columns.
- Leave only a linear independent combinations.
- Calculate $S_z$ for all these permutations.
- Gather all $S_z$ to make $S$.
- Transpose the tables to calculate $L$ the same way.
There was a demonstration for $2p^2$ but I still can't understand how to do it for more complicated configurations. Can somebody show how to proceed with $3d^4$ for example?