My task is to assign spin and parities to different nucleus using the shell model and don´t look up the answers in a formula collection (for the ground states). First I have Al-27, it consists of 14 neutrons and 13 protons. So all the six 1d(j=5/2) states are occupied for the neutrons and there is no netron above this level. There will exist one gap in the 1d(j=5/2)-level for protons, so I have a "hole" in this level. Hence; my total spinn for the nucleus will be 5/2. And scince the hole is in the d-shell; L= 2, so the parity will be: (-1)^(2) = postive. (5/2)+ is also the correct answer, Iam doing the right procedure? Second I have K-40, it consists of 19 protons and 21 neutrons. There is one neutron in the 1f(j = 7/2) state and all others are below in filled subshells. There is only three protons in the 1d(j=3/2) state, so there is a "hole" there. NOW how do I get the parity and spin for this nucleus? :uhh: (the correct answer is 4- ) I have tried to add the spins of the proton-"hole" and the "valence-neutron", it does not fit to me, what shall I do?