I’m confounded by magic.

Radioactive isotope of tin confirmed to have doubly magic nucleus

Magic proton or neutron numbers give the nucleus greater stability and stronger binding, and are therefore usually more common than nuclei with unfilled orbital shells. In doubly magic nuclei both proton and neutron shells are filled, leading to even stronger binding and stability. The outer shells of doubly magic nuclei are rigidly spherical.

OK, here’s an instance where someone is using inconsistent and/or confusing terminology. If magic numbers refer to filled shells, then Sn-132, having 50 protons and 82 neutrons, is doubly-magic by definition. The only thing you have to confirm is that it’s Sn-132. The Tin isotope whips out its ID card, and you’re done.

But no, apparently that’s not enough.

Other confirmed doubly magic nuclei include helium-4, oxygen-16, lead-208, calcium-49, and nickel-48, which are abundant and stable, and nickel-56, which was discovered in 1998 and is less stable than the others, having a half-life of just 5.9 days. Tin-132 is even more unstable with a half-life of only four seconds, which has made confirmation of its doubly magic nature difficult. It has 50 protons and 82 neutrons, and is the first confirmed doubly magic isotope that is both neutron-rich and radioactive.

The scientists investigating this seem to already know it has magic numbers of both, but that doesn’t confirm the doubly-magic nature of the isotope. They had to verify that it is spherical as well, by looking at Sn-133 and saw that it behaved as expected of having a single excess neutron (I assume in terms of a quadrupole moment). But if it hadn’t, would the nucleus still be doubly-magic? Or would it be that the model of doubly-magic nuclei was wrong? I think it’s the latter; magic numbers refer to the numbers (hence the name), and models of nuclear shape are something separate.

On a related note, I wonder if anyone is looking at Sn-100, which is also doubly-magic (using my definition). It’s listed on the table of nuclides as having a half-life of 0.94 seconds, which implies it’s been made in the lab and studied to some extent. Then again, the table of nuclides lists Sn-132 has having a half-life of 39.7 seconds, which is an order of magnitude longer than what’s given in the article. So I’m thoroughly confused. But as a Gemini, I never know what to expect.