We present a microscopic dynamical study of the reactions involving three ${}^4\mathrm{He}$ clusters. We show that the much discussed triple-$\alpha$ linear chain configuration of ${}^{12}\mathrm{C}$ is formed with a certain lifetime and subsequently makes a transition to a triangular configuration of ${}^{12}\mathrm{C}$ and then to a configuration near the ground state. Time-dependent Hartree-Fock theory coupled with a density constraint is used to study the properties of these configurations.

• Received 24 March 2010

DOI:https://doi.org/10.1103/PhysRevLett.104.212503