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The present study explores the symmetries associated with the cluster structure of light nuclei and draws the connection between solutions of the Schrödinger equation for the harmonic oscillator and the quasi-crystalline arrangements of α-particles, which gives rise to a series of collective behaviors. The double-center harmonic oscillator is used to formulate the collisions of two nuclei described by harmonic oscillator solutions and traces out the evolution of the cluster structure in the dynamics of the collision process and demonstrates that the symmetries are preserved in this process. The connection between this study and stellar nucleosynthesis is described.

An experimental study of the helium-cluster decays of the 12Be excited states has been performed using the 9Li + 7Li → α + α + 8He and 9Li + 7Li → α + 6He + 6He reactions at the 9Li beam energy of 74.8 MeV. At excitation energies between 10 and 25 MeV, the 12Be excited states decaying into the 4He + 8He, 6He + 6He, and 6He + 6He*(1.8 MeV, Jπ = 2+) have been observed. Most of the observed states decaying into the 4He + 8He and 6He + 6He correspond to previously reported states. The decay to the 6He + 6He*(1.8 MeV, Jπ = 2+) channel has been observed for the first time. Two of the five states observed in this new decay channel are also observed in the ground state channel 6He + 6He, while two may correspond to the 4He + 8He decaying states. The states around 13.5 and 20.0 MeV decay to the 6He + 6He and 4He + 8He channels, while the state around 22.3 MeV decays into all three decay channels examined. This experiment is complementary to all previous studies of the 12Be cluster states because of the different reaction mechanisms used for the population of the 12Be cluster states. The observation of the states at high excitations with these exotic decay properties strongly supports the molecular structure of the 12Be excited states.