For nuclei farther from the magic quantum numbers one must add the assumption that due to the relation between the strong nuclear force and total angular momentum, protons or neutrons with the same n tend to form pairs of opposite angular momentum. Therefore, a nucleus with an even number of protons and an even number of neutrons has 0 spin and positive parity. A nucleus with an even number of protons and an odd number of neutrons (or vice versa) has the parity of the last neutron (or proton), and the spin equal to the total angular momentum of this neutron (or proton). By "last" we mean the properties coming from the highest energy level.
For nuclei farther from the magic quantum numbers one must add the assumption that due to the relation between the strong nuclear force and total angular momentum protons or neutrons with the same n tend to form pairs of opposite angular momentum Therefore a nucleus with an even number of protons and an even number of neutrons has 0 spin and positive parity A nucleus with an even number of protons and an odd number of neutrons (or vice versa) has the parity of the last neutron (or proton) and the spin equal to the total angular momentum of this neutron (or proton) By "last" we mean the properties coming from the highest energy level