Global study of beyond-mean-field correlation energies in covariant energy density functional theory using a collective Hamiltonian method

We report the first global study of dynamic correlation energies (DCEs) associated with rotational motion and quadrupole shape vibrational motion in a covariant energy density functional (CEDF) for 575 even-even nuclei with proton numbers ranging from $Z=8$ to $Z=108$ by solving a five-dimensional collective Hamiltonian, the collective parameters of which are determined from triaxial relativistic mean field plus BCS calculation using the PC-PK1 force. After taking into account these beyond mean-field DCEs, the root-mean-square (rms) deviation with respect to nuclear masses is reduced significantly down to 1.14 MeV, which is smaller than those of other successful CEDFs: NL3* (2.96 MeV), DD-ME2 (2.39 MeV), $\mathrm{DD}\text{−}\mathrm{ME}\delta$ (2.29 MeV), and DD-PC1 (2.01 MeV). Moreover, the rms deviation for two-nucleon separation energies is reduced by $\sim 34\%$ in comparison with the cranking prescription.

Figure 1

Contour map of the quadrupole dynamical correlation energies $E_{\mathrm{corr}}$ calculated by the CEDF-based 5DCH model as functions of the neutron and proton numbers.

Figure 2

The quadrupole dynamical correlation energies calculated by 5DCH based on CEDF with PC-PK1 force (open circles) in comparison with those based on HFB using Gogny D1S force (upper triangles).

Figure 3

Discrepancy of the CEDF calculated binding energies by PC-PK1 with the data for 575 even-even nuclei [36]. In panel (a), the CEDF calculated binding energies are given by the binding energies of the lowest mean-field states, while in panel (b) the dynamical correlation energies are taken into account.

Figure 4

Discrepancy of the theoretical two-neutron (a) and two-proton (b) separation energies extracted from the calculated binding energies including the DCEs with respect to the data [36].