A heavy atomic nucleus of californium-252 can spontaneously split into two large fragments — much like a water droplet bursting apart. But inside such a droplet, quantum laws are at play, and each fragment acquires its own rotation — a spin. Physicists have long suspected that fragment spins are not random but are linked to each other, like dance partners who must move in sync.

In the new study, the researchers calculated how exactly the nucleus's shape at the moment of scission affects this dance. If the nucleus remains symmetric, like a perfect rugby ball, the fragment spins are tightly correlated: along the fission axis they rotate in opposite directions, like two gears meshing together, while perpendicular to the axis they can bend or wiggle with equal probability. But if the nucleus loses symmetry (say, becoming slightly flattened on one side) the rules change. Along the fission axis, the spin correlation weakens, but new, previously forbidden types of collective rotation emerge.

To measure the degree of correlation, the authors used mutual information analysis — a method that estimates how much knowing the spin of one fragment reduces the uncertainty of the other's spin. It turned out that correlations perpendicular to the fission axis are surprisingly robust to symmetry breaking, while those along the axis quickly fade away. This paves the way for understanding how quantum entanglement manifests in one of the most energetic processes in nature.