Correlations between neutrons and protons near the Fermi surface and $Q_{\alpha }$ of superheavy nuclei

The shell corrections and shell gaps in nuclei are systematically studied with the latest Weizsäcker-Skyrme (WS4) mass model. We find that most of asymmetric nuclei with (sub)shell closures locate along the shell stability line (SSL), $N=1.37Z+13.5$, which might be due to a strong correlation between neutrons and protons near the Fermi surface. The double magicity of nuclei ${}^{46}\mathrm{Si}$ and ${}^{78}\mathrm{Ni}$ is predicted according to the corresponding shell gaps, shell corrections, and nuclear deformations. The unmeasured superheavy nuclei, ${}^{296}118$ and ${}^{298}120$, with relatively large shell gaps and shell corrections, also locate along the SSL, whereas the traditional magic nucleus ${}^{298}\mathrm{Fl}$ evidently deviates from the line. The $\alpha$-decay energies of superheavy nuclei with $Z=113\text{–}126$ are simultaneously investigated by using the WS4 model together with the radial basis function corrections. For superheavy nuclei with large shell corrections, the smallest $\alpha$-decay energy for elements $Z=116$, 117, and 118 in their isotope chains locates at $N=178$ rather than 184.

Figure 1

Shell corrections of nuclei from the WS4 calculations. The solid and open squares denote the positions of nuclei with (sub)shell closure according to the predicted shell gaps.

Figure 2

Neutron separation energy of silicon and nickel isotopes. The squares and circles denote the measured neutron $\left(S_n\right)$ and two-neutron $\left(S_{2n}\right)$ separation energies, respectively. The curves denote the predictions of the ${\text{WS4}}^{\mathrm{RBF}}$ model.

Figure 3

Scaled shell gaps of nuclei along the shell stability line. The squares and solid curve denote the experimental data and ${\text{WS4}}^{\mathrm{RBF}}$ predictions, respectively. The dashed line denotes the mean value of measured shell gaps for all known nuclei.

Figure 4

$\alpha$-decay energies of odd-$Z$ super-heavy nuclei (a) and those of even-$Z$ nuclei (b) from the ${\text{WS4}}^{\mathrm{RBF}}$ predictions.