Goeppert Mayer and her contemporaries explained these numbers by proposing that protons and neutrons occupy discrete energy levels, or shells. This model, which is still used to interpret many nuclear physics experiments, treats each particle in the nucleus as independent, but our best quantum theories assert that particles within nuclei actually interact strongly.
Jiangming Yao at Sun Yat-sen University in China and his colleagues have now resolved this contradiction and, in the process, elucidated how magic numbers emerge from these interactions.
Yao says the shell model relies on input from experiments and doesn’t encode details of interactions between each particle. Instead, he and his team started their calculations from first principles, which means they mathematically described how particles interact with each other, how they stick together and how much energy is needed to move them apart in more detail.
Takes the 'shell model', which is exceedingly dodgy theoretically but gives good results, and reinterprets it in terms of quantum mechanics, which are pretty solid theoretically. So just need to validate it against what we already know - sounds like they did most of their work against a single isotope of tin.
(We don't have a theory of quantum gravity, so even though quantum mechanics and general relativity are both well-studied and tested theories with enormous predictive power, they can't quite be right. If this new result gives us a better understanding of the strong nuclear force, which it might, then it might also give us a better understanding of all forces. Getting some 'island of stability' larger isotopes might help with packing a lot of power into a small space; elerium-115 style, too.)