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## Main Question or Discussion Point

Consider the pairing term in Weizsäcker formula. Here https://en.wikipedia.org/wiki/Semi-empirical_mass_formula#Pairing_term it is claimed that:

I don't understand how Pauli exclusion principle should be the cause of this. This term comes from spin-spin interaction (or "coupling"), but I do not see the link with the fact that protons (or neutrons) with the same quantum numbers cannot occupy the same quantum state within a quantum system simultaneously

Due to the Pauli exclusion principle the nucleus would have a lower

energy if the number of protons with spin up were equal to the number

of protons with spin down.

I don't understand how Pauli exclusion principle should be the cause of this. This term comes from spin-spin interaction (or "coupling"), but I do not see the link with the fact that protons (or neutrons) with the same quantum numbers cannot occupy the same quantum state within a quantum system simultaneously