Narrow Results

We present Skyrme-force Hartree–Fock calculations of metastable three-α chain-state configurations in ¹²C, ¹⁶C, and ²⁰C. A microscopic dynamical study of reactions involving three ⁴He clusters shows that the triple-α linear chain configuration of ¹²C is formed with a certain lifetime and subsequently decays into a triangular configuration of ¹²C and then to a configuration near the ground state.

The consequences of some symmetries of the three-alpha system are discussed. In particular, the recent description of the low-energy spectrum of the ${}^{12}$C nucleus in terms of the algebraic cluster model (ACM) is compared to that of the multichannel dynamical symmetry (MUSY), which is the intersection of the shell and cluster models. The previous one applies interactions of a $D_{3h}$ geometric symmetry [D. J. Marin-Lambarri et al., Phys. Rev. Lett.113 (2014) 012502], while the latter one has a U(3) dynamical symmetry. The available data is in line with both descriptions.