Cluster-liquid phase separation in cluster decay

In cluster decay, a heavy nucleus spontaneously emits a light nucleus, leaving a daughter nucleus in the neighborhood of the double-magic 208 Pb. The two fragments exhibit extreme mass asymmetry and possess completely distinct properties, including different phase structures such as clustering patterns. We investigate the phase structure of cluster decay via 14 C emission from 222 Ra using energy density functional theory. Systematic analysis reveals that post-scission, the emitted 14 C retains a triangular 3 α cluster structure while 208 Pb rapidly rebounds to sphericity due to its double-magic nature. The fragments manifest distinct quantum phases: a cluster phase in the emitted 14 C and a quantum liquid phase in 208 Pb. This coexistence provides direct evidence for cluster-liquid quantum phase separation in cluster decay processes. Furthermore, it resolves a longstanding puzzle: why the neutron-rich 14 C emission experimentally observed instead of more strongly bound 12 C, the excess neutrons act as “glue” to stabilize the cluster phase.