Spectra of helium and the alkaline earth metal atoms

5 Spectra of helium and the alkaline earth metal atoms 

Derivation of an energy level diagram shows that it consists of two sets of energy levels, one corresponding to the single lines and the other to the double lines, and that no transitions between the two sets of levels are observed. For this reason it was suggested that helium exists in two separate forms. In 1925 it became clear that, when account is taken of electron spin, the two forms are really singlet helium and triplet helium. 

For hydrogen and the alkali metal atoms in their ground configurations, or excited configurations involving promotion of the valence electron, there is only one electron with an unpaired spin. For this electron = - - or — and the corresponding electron spin part 

In helium we need to look more closely at the consequences of electron spin since this is the prototype of all atoms and molecules having easily accessible states with two different multiplicities. 

If the spin-orbit coupling is small, as it is in helium, the total electronic wave function J/ can be factorized into an orbital part J/° and a spin part pl  

The spin part ij/se can be derived by labelling the electrons 1 and 2 and remembering that, in general, each can have an a or ji spin wave function giving four possible combinations a(1)/i(2), /((l)a(2), a(l)a(2) and / (1 )/ (2). Because the first two are neither symmetric nor antisymmetric to the exchange of electrons, which is equivalent to the exchange of the labels 1 and 2, they must be replaced by linear combinations giving 

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