Nuclear ground states in a consistent implementation of the time-dependent density matrix approach

Background: Time-dependent techniques in nuclear theory often rely on mean-field or Hartree-Fock descriptions. Beyond mean-field dynamical calculations within the time-dependent density matrix (TDDM) theory have often invoked symmetry restrictions and ignored the connection between the mean-field and the induced interaction. Purpose: We study the ground states obtained in a TDDM approach for nuclei from $A=12$ to $A=24$, including examples of even and odd-even nuclei with and without intrinsic deformation. We overcome previous limitations using three-dimensional simulations and employ density-independent Skyrme interactions self-consistently. Methods: The correlated ground states are found starting from the Hartree-Fock solution, by adiabatically including the beyond-mean-field terms in real time. Results: We find that, within this approach, correlations are responsible for $\approx 4-5 \%$ of the total energy. Radii are generally unaffected by the introduction of beyond mean-field correlations. Large nuclear correlation entropies are associated to large correlation energies. By all measures, $^{12}$C is the most correlated isotope in the mass region considered. Conclusions: Our work is the starting point of a consistent implementation of the TDDM technique for applications into nuclear reactions. Our results indicate that correlation effects in structure are small, but beyond-mean-field dynamical simulations could provide new insight into several issues of interest.