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.
as written by the authors arXiv:2607.09897
There are conflicting theoretical results about the presence of a shell closure in the neutron-rich nucleus $$^{140}$$Sn. We address this controversy by performing ab initio computations, using a nuclear interaction from chiral effective field theory that accurately reproduced and predicted low-lying states in doubly magic nuclei. We verify that this interaction accurately reproduces low-lying states in $$^{133}$$Sn. We assume that $$^{140}$$Sn exhibits a closed $$7/2^-$$ neutron subshell beyond $$^{132}$$Sn and compute its first excited $$2^+$$ state. The resulting energy is small and this contradicts the assumption.
Tin holds the record for the number of stable isotopes: it has ten of them, from tin-112 to tin-124.