The calcium-48 nucleus is like a locked room with 48 nucleons inside. Rearrangements are happening within: a neutron turns into a proton, and the room slowly rebuilds itself into another — titanium-48. The process takes an unimaginably long time: on average, a trillion trillion years, but it does happen.

To describe such a rearrangement, physicists assembled the nuclear wavefunction from pieces. The pieces are states where the numbers of protons and neutrons are fixed, while the shape of the nucleus can vary. Then these pieces were combined with the correct weights, like assembling a puzzle. The method is called generator coordinate projection. They tested it on transitions in calcium and titanium, comparing it with an exact solution — a direct enumeration of all possibilities. The agreement was good: the error in the transition strength is only a few percent.

This calculation matters beyond itself. The same mechanism, but without emitting electrons, could explain why neutrinos have mass. For now, scientists are refining the tool on the slow decay, so they can later apply it to more subtle questions.