Cluster model of C12 in the density functional theory framework

Abstract

We employ the constrained density functional theory to investigate cluster phenomena for the $^{12}\mathrm{C}$ nucleus. The proton and neutron densities are generated from the placement of three $^{4}\mathrm{He}$ nuclei ($\ensuremath{\alpha}$ particles) geometrically. These densities are then used in a density constrained Hartree-Fock calculation that produces an antisymmetrized state with the same densities through energy minimization. In the calculations no a priori analytic form for the single-particle states is assumed and the full energy density functional is utilized. The geometrical scan of the energy landscape provides the ground state of $^{12}\mathrm{C}$ as an equilateral triangular configuration of three $\ensuremath{\alpha}\mathrm{s}$ with molecular bond like structures. The use of the nucleon localization function provides further insight to these configurations. One can conclude that these configurations are a hybrid between a pure mean-field and a pure $\ensuremath{\alpha}$ particle condensate. This development could facilitate density functional theory based fusion calculations with a more realistic $^{12}\mathrm{C}$ ground state.