Microscopic Study of the triple-$\alpha$ Reaction

We present a microscopic dynamical study of the reactions involving three $^{4}$He clusters. We show that the much discussed triple-$\alpha$ linear chain configuration of $^{12}$C is formed with a certain lifetime and subsequently decays into a triangular configuration of $^{12}$C and then to a configuration near the ground state. Time-dependent Hartree-Fock (TDHF) theory coupled with a density constraint is used to study the properties of these configurations. We find a sequence of dynamical transitions analogous to the suggested astrophysical mechanism for the formation of $^{12}$C nuclei.
Comment: 4 pages, 5 figures