Yesterday I asked this question concerning the existence of terms. This question is on the same topic. I have been looking at some tables (in Yang and Hamilton (2010), pg 199) at the terms that exist for two electrons in the same configuration. I noticed that for example if the state $^1S$ exists the state $^3S$ would not and vice versa. Is this a general rule? I.e. can we say:

For two electrons in the configuration $nl^2$ if the term $^1L$ exists then the term $^3L$ will not and vice versa.

If so can it be proved easily and if not why not?

Yesterday I asked this question concerning the existence of terms. This question is on the same topic. I have been looking at some tables (in Yang and Hamilton (2010), pg 199) at the terms that exist for two electrons in the same configuration. I noticed that for example if the state $^1S$ exists the state $^3S$ would not and vice versa. Is this a general rule? I.e. can we say:

For two electrons in the configuration $nl^2$ if the term $^1L$ exists then the term $^3L$ will not and vice versa.

If so can it be proved easily and if not why not?