Discussion
The nuclear energy levels of mirror nuclei are similar. Using this empirical fact alone, the nuclear force can be said to be independent of which one of the following properties of the nucleons?
Answer: C
The nuclear force is independent of the nucleons' charge.
Mirror nuclei, such as \(^{3}\)H and \(^{3}\)He or \(^{13}\)C and \(^{13}\)N, have their proton and neutron numbers interchanged. Once the Coulomb energy is allowed for, their energy levels are nearly identical, which shows that the nn and pp interactions are the same: the strong force does not distinguish a proton from a neutron. This is charge symmetry, part of the wider idea of charge independence.
Swapping protons and neutrons leaves spins and parities of the nucleons unchanged, so mirror nuclei say nothing about dependence on spin or parity; and the tiny proton-neutron mass difference is not what the comparison tests.
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