Microscopic Study of the triple-$\alpha$ Reaction

Abstract

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.

4 pages, 5 figures

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• 3-D unrestricted TDHF fusion calculations using the full Skyrme interaction
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• Density-constrained time-dependent Hartree-Fock calculation of ${}^{16}$O+${}^{208}$Pb fusion cross sections
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