Microscopic Study of the triple-$\alpha$ Reaction

TL;DR

This paper uses a microscopic dynamical approach to study the formation and decay of $^{12}$C configurations from three $^{4}$He clusters, revealing a sequence of transitions relevant to astrophysical processes.

Contribution

It introduces a time-dependent Hartree-Fock method with density constraints to analyze the formation and decay of triple-$ ext{alpha}$ configurations in $^{12}$C.

Findings

Identification of a linear chain configuration with a finite lifetime

Observation of a transition to a triangular configuration of $^{12}$C

Sequence of dynamical transitions relevant to astrophysical nucleosynthesis

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.