Question

A certain odd-parity shell model state can accommodate up to a maximum of 12 nucleons. What are its j and l values?

Answer 1

A state with quantum number j can accommodate a maximum number of Nj = 2(2_j + 1) nucleons. Now j = l ± 1/2 and for N_j = 12, j = 5/2 and l = 3 or 2. However, because the parity is odd and P = (−1)^l , it follows that l = 3.