Systematic study of shell gaps in nuclei

The nucleon separation energies and shell gaps in nuclei over the whole nuclear chart are systematically studied with eight global nuclear mass models. For unmeasured neutron-rich and superheavy regions, the uncertainty of the predictions from these different mass models is still large. The latest version (WS4) of the Weizsäcker-Skyrme mass formula, in which the isospin dependence of model parameters is introduced into the macroscopic-microscopic approach inspired by the Skyrme energy-density functional, is found to be the most accurate one in the descriptions of nuclear masses, separation energies, and shell gaps. Based on the predicted shell gaps in nuclei, the possible magic numbers in superheavy nuclei region are investigated. In addition to the shell closures at $N=184,Z=114$, the subshell closures at around $N=178,Z=120$ could also play a role for the stability of superheavy nuclei.

Figure 1

Nuclear landscape. The black and green squares denote the stable nuclei and known nuclei in AME2012 [32], respectively. The dark yellow squares denote the theoretical predictions with the WS4 mass formula [16]. The gray solid lines denote the known magic numbers and the dashed lines denote the possible magic numbers in superheavy region.

Figure 2

Two-neutron separation energy $S_{2\mathrm{n}}$ as a function of neutron number $N$. The red and dark cyan curves denote the experimental data and the model predictions, respectively. The dot-dashed lines denote the known neutron magic numbers.

Figure 3

Two-neutron separation energy $S_{2\mathrm{n}}$ from different nuclear mass models. The calculated results for the isotopes with $Z=120$, 110, 100, 90, 80, 70, and 60 are indicated by the thick curves. The value of $\sigma$ (in MeV) denotes the corresponding rms deviations with respect to the 2123 measured $S_{2\mathrm{n}}$.

Figure 4

$S_{2\mathrm{n}}$ of Ra isotopes as a function of neutron number. The black squares denote the experimental data and the curves denote the predictions from five different models.

Figure 5

Contour plot of shell gaps in nuclei scaled by $A^{1/2}$ from the experimental data and model predictions. The dashed lines indicate the possible magic numbers $N=162,184$ and $Z=114,120$. The dot-dashed line indicates the positions of nuclei with $N=Z$.

Figure 6

Shell gaps for nuclei with $N=82$ and 126. The black squares denote the experimental data, and the curves denote the predictions from different models.

Figure 7

The same as Fig. 6, but for nuclei with $N=152$. The dashed lines indicate the positions of $Z=100$ and $Z=108$.

Figure 8

The same as Fig. 7, but for superheavy nuclei with $N=184$.

Figure 9

(a) Shell gaps of superheavy nuclei with the WS4 formula. (b) Corresponding shell corrections for nuclei in (a) with the same mass formula. The dashed lines indicate the positions of $N=152$, 162, 184, and $Z=114$, 120.