Notation for nuclear energy states

Somewhat parallel to the labeling of atomic energy states, the labels of nuclear states are determined by their angular momenta. For single particle states you know that the spin part is S=1/2 and then the orbital angular momentum is used to determine a letter designation according to the spectroscopic notation. If L=2, then the state is represented by "d" and then the total angular momentum could be either L+S=3/2 or L+S=5/2. The two states would then be labeled:

The number n preceding the letter designation is analogous to the principal quantum number in the hydrogen atom in that it indicates the order of the energy states. But this number n is not subject to the same limitations as in the atomic case - it is just an indexing parameter. So the lowest energies with L=2 are labeled 1d (1d_3/2,1d_5/2), but there are higher levels with L=2 with would be labeled 2d_3/2,2d_5/2,3d_3/2,3d_5/2, etc.

For light nuclei it is presumed that the nucleons will fill levels according to the sequence of the shell model. Those nucleons in closed shells will be presumed not to contribute to the total nuclear spin, so the configuration of the nucleus will be indicated by the symbols for the nucleons outside closed shells. For example, ¹⁷O has one neutron outside a closed shell and its ground state would be designated (1d_5/2)¹.