a term symbol
When a configuration splits into several energy levels, spectroscopists need a compact name for each. A term symbol is that name: a small piece of notation, like ^3P_0 or ^2S_(1/2), that encodes the total spin, total orbital angular momentum, and total angular momentum of an atomic level in one glance.
The form is ^(2S+1)L_J. The left superscript 2S+1 is the spin multiplicity (1 = singlet, 2 = doublet, 3 = triplet, telling you the total spin S). The central letter encodes the total orbital angular momentum L using S, P, D, F, G for L = 0, 1, 2, 3, 4. The right subscript J is the total angular momentum, the vector sum of L and S, running over J = |L - S|, ..., L + S. Each J level has a degeneracy of 2J+1 (its m_J states). An optional superscript 'o' marks odd parity. The scheme presumes LS (Russell-Saunders) coupling, where the individual orbital angular momenta first add to a good L and the spins to a good S, and only then do L and S couple weakly to J.
Term symbols are the vocabulary of atomic spectroscopy: selection rules, Zeeman patterns, and transition tables are all written in them. The important caveat is that S and L are only approximate ('good') quantum numbers in the LS regime of light atoms. In heavy atoms spin-orbit coupling is strong and jj coupling takes over, so S and L blur; J and parity remain exactly good, so the J subscript and parity stay meaningful even when the ^(2S+1)L label is only nominal.
The hydrogen and alkali ground states are ^2S_(1/2): a single valence s-electron gives S = 1/2 (multiplicity 2), L = 0 (an S term), and J = 1/2. Sodium's yellow D-lines are the ^2S_(1/2) to ^2P_(1/2) and ^2P_(3/2) transitions, the pair split by spin-orbit coupling.
One configuration, several term symbols; the J subscript labels the fine-structure sublevels.
Read the notation as three separate facts (spin, orbital, total), not a single number — the superscript is 2S+1, not S, so a '3' means S = 1, not S = 3.