Cluster model of C 12 in the density functional theory framework

We employ the constrained density functional theory to investigate cluster phenomena for the C12 nucleus. The proton and neutron densities are generated from the placement of three He4 nuclei (α 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 C12 as an equilateral triangular configuration of three αs 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 α particle condensate. This development could facilitate density functional theory based fusion calculations with a more realistic C12 ground state.