[Paper Review] Nuclear landscape in a mapped collective Hamiltonian from covariant density functional theory

Yilong Yang, Y. K. Wang+2 more|arXiv (Cornell University)|Aug 30, 2021

Nuclear physics research studies58 references64 citations

TL;DR

This study presents a microscopic, parameter-free mapping of a five-dimensional collective Hamiltonian (5DCH) onto triaxial relativistic Hartree-Bogoliubov (RHB) calculations using the PC-PK1 density functional to include beyond-mean-field dynamical correlation energies (DCEs). The inclusion of triaxiality and DCEs significantly improves the description of experimental binding energies—particularly in medium-to-heavy nuclei—and extends the predicted nuclear landscape, especially the neutron drip line, beyond previous covariant density functionals like DD-PC1 and TMA due to PC-PK1's distinct isovector properties.

ABSTRACT

The nuclear landscape has been investigated within the triaxial relativistic Hartree-Bogoliubov theory with the PC-PK1 density functional, and the beyond-mean-field dynamical correlation energies are taken into account by a microscopically mapped five-dimensional collective Hamiltonian without additional free parameters. The effects of triaxial deformation and dynamical correlations on the nuclear landscape are analyzed. The present results provide the best description of the experimental binding energies, in particular for medium and heavy mass regions, in comparison with the results obtained previously with other state-of-the-art covariant density functionals. The inclusion of the dynamical correlation energies plays an important role in the PC-PK1 results. It is emphasized that the nuclear landscape is considerably extended by the PC-PK1 functional in comparison with the previous results with other density functionals, which may be due to the different isovector properties in the density functionals.

Motivation & Objective

• To systematically investigate the limits of nuclear stability (two-proton and two-neutron drip lines) using triaxial RHB with the PC-PK1 density functional.
• To analyze the impact of triaxial deformation and beyond-mean-field dynamical correlation energies (DCEs) on the nuclear landscape.
• To compare the predicted nuclear drip lines and binding energy accuracy using PC-PK1 against previous covariant density functionals (DD-PC1 and TMA).
• To validate the role of DCEs in improving the description of experimental nuclear masses across the nuclear chart.

Proposed method

• The triaxial RHB theory is used to compute mean-field solutions across the full β-γ deformation plane (0° ≤ γ ≤ 60°) for even-even nuclei with 8 ≤ Z ≤ 104.
• The PC-PK1 density functional is employed for the energy functional, with a finite-range separable pairing interaction (G = 728 MeV·fm³) to describe pairing correlations.
• A microscopically mapped five-dimensional collective Hamiltonian (5DCH) is applied to compute beyond-mean-field dynamical correlation energies (DCEs) without additional parameters.
• The DCE is defined as the energy difference between the mean-field ground state and the collective 0⁺₁ state obtained by diagonalizing the 5DCH.
• Adiabatic deformation constraints are applied to ensure convergence across the β-γ plane, with maximum β values set at 1.20 for Z < 20 and 0.72 for heavier nuclei.
• Only nuclei with negative chemical potentials across the full β-γ plane are considered; for closed-shell nuclei, DCE is set to zero to avoid unphysical correlations.

Experimental results

Research questions

• RQ1 How do triaxial deformation and beyond-mean-field dynamical correlation energies affect the predicted location of the two-proton and two-neutron drip lines?
• RQ2 How does the PC-PK1 density functional compare to DD-PC1 and TMA in predicting nuclear binding energies across the nuclear chart?
• RQ3 To what extent do DCEs improve the agreement between theoretical binding energies and experimental data, especially in medium- and heavy-mass nuclei?
• RQ4 Why is the nuclear landscape predicted to be more extended with PC-PK1 compared to other covariant density functionals?

Key findings

• The inclusion of dynamical correlation energies via the 5DCH reduces the root-mean-square (rms) deviation from experimental binding energies to 1.14 MeV for even-even nuclei, matching the accuracy of functionals like DD-MEB1 and DD-MEB2.
• The description of experimental binding energies is significantly improved, particularly in the medium- and heavy-mass regions, due to the inclusion of DCEs.
• The two-neutron drip line predicted with PC-PK1 is more extended than those from DD-PC1 and TMA, primarily due to differences in the isovector properties of the density functionals.
• Triaxial deformation has a minor effect on the mean-field energy but plays a crucial role in determining the DCEs, which are essential for accurate binding energy predictions.
• The nuclear landscape is substantially extended with PC-PK1 compared to previous results with DD-PC1 and TMA, indicating a more realistic extrapolation of nuclear stability.
• The results demonstrate that the 5DCH mapping provides a reliable, parameter-free method to include beyond-mean-field effects in large-scale nuclear structure calculations.