The atomic nucleus is not just a jumble of protons and neutrons. The particles inside arrange themselves in layers, like spectators in a stadium: the lower rows are filled, and each new proton or neutron looks for a spot on a higher tier. When a row is completely filled, the nucleus becomes especially stable — physicists call this a magic number.

Of particular interest is the tin-140 nucleus: it has 8 more neutrons than the doubly magic tin-132. Theorists have long debated whether a closed neutron subshell forms there. The authors performed a first-principles calculation, that is, starting from the very basics of particle interactions, without adjustable parameters. They took an interaction that has already proven itself on other magic nuclei and tested it on tin-133—everything matched.

Then the scientists made a bold assumption: let the neutron subshell in tin-140 be closed. Based on this, they calculated the energy of the first excited state of the nucleus — the moment when the nucleus receives a burst of energy and one neutron jumps to a higher level. If the shell is indeed closed, this jump requires a lot of energy, like leaping over a wide step. But the calculation showed the opposite: the energy came out small. The step turned out to be narrow, meaning there is no closed subshell. The debate is settled: tin-140 does not hide a magic framework inside.