The variational approach to the density matrix for light nuclei

Abstract

A previously introduced variational method for density matrices is adapted for applications in light nuclei. In this method the energy E = ∑ H ijklϱijkl is minimized using the two-body density matrix elements ϱijkl = 〈 Ψ‖ a j + a i + a k a l ‖ Ψ〉 as variational parameters. As the approximation, a subset of necessary conditions on the two-body density matrix is satisfied: the non-negativity of the two-body density matrix, the non-negativity of the two-hole density matrix Q ijkl = ϱijkl− δ ikϱjl + δ ilϱjk − δ jlϱik + δ jkϱil + δ ik δ jl − δ il δ jk and the non-negativity of the particle-hole matrix G ijkl = − ϱkjil+ δ ikϱjl . The method is applied to the ground states of the nuclei 15O, 16O, 17O and 18O using the model space spanned by the 1 p 1 2 , 1 d 5 2 , 2 s 1 2 subshells and of the nuclei 20Ne, 24Mg and 28Si using the model space spanned by the 1d, 2s shell. The comparison of the ground state energy with the results of the complete diagonalization in the same model space is encouraging.