Symmetries in Collisions as Explored through the Harmonic Oscillator

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.