Maria Goeppert MayerA Full Floor Is Magic.

The sticker says A Full Floor Is Magic. Inside a nucleus, it is.

Some nuclei are unusually stable: those with 2, 8, 20, 28, 50, 82 or 126 protons or neutrons. They became known as magic numbers, a name said to be Eugene Wigner's, because for years nobody could explain them.

Treat each nucleon as moving in a shared well and the first shells fill at 2, 8 and 20, which is what the three rings of dancers show. Beyond that, the simple picture gives the wrong numbers. In 1949 Maria Goeppert Mayer found the missing ingredient: a strong coupling between each nucleon's spin and its orbit, so that a nucleon spinning the same way it circles sits at a different energy from one spinning the other way. That splitting reshuffles the levels, and the shells close at 28, 50, 82 and 126.

As her daughter later told it, reported by Scientific American, she explained it with a ballroom of waltzers: all the couples go round the floor one way, which is the orbit, while each couple also turns, which is the spin.

Otto Haxel, Hans Jensen and Hans Suess reached the same answer independently that year. In 1963 Goeppert Mayer and Jensen shared half of the Nobel Prize in Physics and the other half went to Wigner. She was the second woman to win the physics prize, sixty years after Marie Curie.

Protons and neutrons fill their shells separately, so our dancers are all one kind. A full floor is magic.