$^{17}_8 O$ quoted here has a spin of 5/2 and parity of +1 for the ground state, I agree with this, the unpaired neutron is in the $1d_{1/2}$ state so l = 2, spin = 5/2.

Now I want to figure out the spin an parity of the first two excited states, but how do I know which proton and which neutron move up.

I am thinking that the first excited state is where the unpaired neutron moves to the $2s_{1/2}$ state, so that l = 2, and spin = 1/2, thus the parity remains 1.

But how do I figure out the configuration for the second excited state.

  • $\begingroup$ On the same LBL site there is a full set of level drawings. Now all I have to do is recall how to read them. Here's the one for A=17 (PDF link). $\endgroup$ Feb 21, 2013 at 0:32
  • $\begingroup$ For any future visitors, the $2s_{1/2}$ is the next excited state only by some authors (e.g. dommelen.net/quantum2/style_a/ntsm.html)... Other authors might have the $1d_{5/2}$ as above the $1d_{3/2}$ which would predict a different first excited state (namely $J^P={\frac32}^−$). This shows the deficiencies in the nuclear shell model. I believe the different orderings are due to to the strength of the spin-orbit coupling used. $\endgroup$
    – Joe Iddon
    May 12, 2023 at 8:56

2 Answers 2


A better reference for determining these nuclear states from experiment is NuDat at Brookhaven. Figuring out the interaction energy of a neutron in any particular energy level with a $^{16}O$ core is extremely difficult. There is some model intuition that can help you, as you used for the first excited state. In this case, the second excited state $1/2^-$ must be more complicated. I would guess that it results from a neutron from the closed core joining the extra neutron in the d-shell, leaving a hole in the p-shell that gives the quantum numbers here. As you can see, there's a huge extra energy needed to make this configuration.


As answered by others, you can check the experimental spin in NuDat database. However, if you would like to figure out the spin using the single-particle configuration, the results are generally not very reliable for excited state at higher energies. Usually, using a shell model code would provide a more accuracy and realistic result as I mention in this answer


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