The term term is often used to denote energy levels of an atom. I dont know what the rational justificiation behind this is but it seems to be a hangover from the work of Rydberg and Ritz.

A notation has been invented for describing terms and this is what this WU tries to describe.

Lighter atoms follow a scheme called LS coupling (Please follow the link if you dont know what this is). L denotes the total orbital angular momentum of the electrons and S the total spin angular momentum. Under LS coupling the stationary states of the atom(at 0 order of perturbation theory) are states of constant L and S. At the 1^{st} order some spin orbit coupling is introduced and each LS state gets split into *multiplets* of constant J where J=L+S is the total angular momentum. Please also look at this link on addition of angular momenta.

Now the inner complete shells contribute neither to L nor to S so we must look only at the outer valence electrons, and to describe a stationary state we need to specify the total L,S and J.

This is done as follows:

First a letter is used for denoting L.

S - L=0

P - L=1

D - L=2

F - L=3

G - L=4

and so on except that you must skip J when you come to it.

The reason for these mysterious letters is also rather interesting. S stands for *Sharp* after the sharp lines which were seen in an alkali spectrum due to transitions from S states to P states. P stands for *Principal* after the most prominent lines in an alkali spectrum due to transitions from P states to S states. D stands for diffuse after the *diffuse* lines due to transitions from D states to P states. F stands for the *fundamental* lines from F states to D states. Later people got tired and decided to continue down the alphabet skipping J to avoid confusion with the total angular momentum.

Now (2S+1) is written as a superscript to the left of this letter. Why 2S+1 why not S? Primarily because 2S+1 often(but not always) gives the multiplicity of the state i.e how many multiplets each state is split into. If S > L then 2S+1 does not specify the multiplicity but we put it there anyway. So now we have reached a stage where we could write something like

^{2}S

Finally each multiplet has a certain J because of the way L and S add up. So we write the total J as a subscript to the right of this letter. Thats it! So a final term symbol would like

^{3}S_{1}

Of course J cannot take arbitary values. It can only range from |L-S| to |L+S| if L > S and from |S-L| to |S+L| if S > L.