ljN | Allowed J values |
---|---|
l1/2 | 1/2 |
l21/2 | 0 |
l3/2 and l3/23 | 3/2 |
l3/22 | 0, 2 |
l3/24 | 0 |
l5/2 and l5/25 |
5/2 |
l5/22 and l5/24 | 0, 2, 4 |
l5/23 | 3/2, 5/2, 9/2 |
l5/26 | 0 |
l7/2 and l7/27 |
7/2 |
l7/22 and l7/26 | 0, 2, 4, 6 |
l7/23 and l7/25 | 3/2, 5/2, 7/2, 9/2, 11/2, 15/2 |
l7/24 | 0, 22, 42, 24, 44, 5, 6, 8 |
l7/28 | 0 |
The allowed levels of the configuration nl N may be obtained by dividing the electrons into sets of two groups $$nl^Q_{l+1/2} ~ nl^R_{l-1/2} ~,$$ Q + R = N. The possible sets run from Q = N - 2l (or zero if N > 2l) up to Q = N or Q = 2l + 2, whichever is smaller. The (degenerate) levels for a set with both Q and R nonzero have wave functions defined by the quantum numbers (αJ1, βJ2) J, with J1 and J2 deriving from the Q and R groups, respectively. The symbols α and β represent any additional quantum numbers required to identify levels. The J values of the allowed levels for each (αJ1, βJ2) subset are obtained by combining J1 and J2 in the usual way.