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

Abstract

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.

arXiv comment14 pages, 7 figures, 8 tables

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Cited by in corpus (6)

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• Nuclear Quantum Many-Body Dynamics: From Collective Vibrations to Heavy-Ion Collisions (2nd edition)
• A Quantum Simulation Approach to Implementing Nuclear Density Functional Theory via Imaginary Time Evolution
• Revisiting the variational two-particle reduced density matrix for nuclear systems
• Role of two-body dissipation on the mean-field dynamics validity
• Bulk and spectroscopic nuclear properties within an ab initio renormalized random-phase approximation framework