Superheavy nuclei in a microscopic collective Hamiltonian approach: The impact of beyond-mean-field correlations on ground state and fission properties

The impact of beyond-mean-field effects on the ground state and fission properties of superheavy nuclei has been investigated in a five-dimensional collective Hamiltonian based on covariant density functional theory. The inclusion of dynamical correlations reduces the impact of the $Z=120$ shell closure and induces substantial collectivity for the majority of the $Z=120$ nuclei which otherwise are spherical at the mean-field level (as seen in the calculations with the PC-PK1 functional). Thus, they lead to a substantial convergence of the predictions of the functionals DD-PC1 and PC-PK1 which are different at the mean-field level. On the contrary, the predictions of these two functionals remain distinctly different for the $N=184$ nuclei even when dynamical correlations are included. These nuclei are mostly spherical (oblate) in the calculations with PC-PK1 (DD-PC1). Our calculations for the first time reveal significant impact of dynamical correlations on the heights of inner fission barriers of superheavy nuclei with soft potential energy surfaces, the minimum of which at the mean-field level is located at spherical shape. These correlations affect the fission barriers of the nuclei, which are deformed in the ground state at the mean-field level, to a lesser degree.

Figure 1

Potential energy surfaces (top panels), collective energy surfaces (CES) with zero-point-energy (ZPE) taken into account (middle panels), and probability density distributions (in arbitrary units) in the $\beta -\gamma$ plane for the $0_1^{+}$ states (bottom panels) of selected nuclei in $Z=120$ isotopic chain. The results are obtained with PC-PK1 CEDF. The energy difference between two neighboring equipotential lines is equal to 0.5 MeV. The minima and saddles in top and middle panels are shown by circles and squares, respectively.

Figure 2

The quadrupole deformations of the minima in potential and collective energy surfaces obtained in the RMF+BCS and RMF+BCS+ZPE calculations, respectively. The results obtained with DD-PC1 and PC-PK1 CEDFs are presented for the $N=174$ (a) and $N=184$ (c) isotonic chains as well as for the $Z=120$ isotopic chain (b).

Figure 3

Excitation energies of the $2_1^{+}$ states a function of proton number in the $N=174$ and 184 isotonic chains and as a function of neutron number in the $Z=120$ isotopic chain.

Figure 4

The $B(E2;2_1^{+}\to 0_1^{+})$ values as a function of proton number in the $N=174$ and 184 isotonic chains and as a function of neutron number in the $Z=120$ isotopic chain.

Figure 5

The heights of inner fission barriers in the mean-field calculations (labeled as “RMF+BCS”) and in the calculations with dynamical correlations included (labeled as “RMF+BCS+ZPE”).

Figure 6

The same as Fig. 2 but for the impact of dynamical correlations on the height of inner fission barrier. Negative (positive) value of ${\mathrm{E}}_{\mathrm{B}}$(RMF+BCS)-${\mathrm{E}}_{\mathrm{B}}$(RMF+BCS+ZPE) means higher (lower) fission barrier in the calculations with dynamical correlations included.

Figure 7

Dynamical correlations energies at the ground states and the saddles of inner fission barriers of the nuclei under study.

Figure 8

The energy difference $V_{\text{coll}}\left(\text{saddle}\right)-V_{\text{coll}}\left(\text{min}\right)$ between the saddle point and the minimum of collective energy surface compared with the energy difference $V_{\text{coll}}-E\left(0_1^{+}\right)$. The energy $E\left(0_1^{+}\right)-V_{\text{coll}}\left(\text{min}\right)$ (shown in bottom panels) is the ground-state energy (relatively to the energy of the minimum of CES) in the 5DCH calculations.