Systematic study of $\alpha$-decay energies and half-lives of superheavy nuclei

Systematic calculations on the $\alpha$-decay energies $\left(Q_{\alpha }\right)$ and $\alpha$-decay half-lives of the superheavy nuclei (SHN) with $Z\ge 100$ are performed by using 20 models and 18 empirical formulas, respectively. According to the comparisons between the calculated results and experimental data, it is shown that the WS4 mass model is the most accurate one to reproduce the experimental $Q_{\alpha }$ values of the SHN. Meanwhile it is found that the SemFIS2 formula is the best one to predict the $\alpha$-decay half-lives of the SHN because the parameters in this formula are from the experimental $\alpha$ emitter data of transuranium nuclei including SHN $\left(Z=92\text{–}118\right)$. In addition, the UNIV2 formula with fewest parameters and the VSS, SP and NRDX formulas with fewer parameters work well in prediction on the SHN $\alpha$-decay half-lives. Finally, the $\alpha$-decay half-lives of $Z=110\text{–}120$ isotopes are predicted within the above mentioned five formulas by inputting the $\mathrm{WS}4 Q_{\alpha }$ values. By analyzing the $Q_{\alpha }$ values and the $\alpha$-decay half-lives of this region, it is found that for $Z=110\text{–}114$ isotopes $N=162$ and $N=184$ are the submagic number and magic number, respectively. However, for the isotopes of $Z=116\text{–}120$ the submagic number is $N=178$.

Figure 1

The deviations between experimental and calculated $Q_{\alpha }$ values as functions of the neutron number $N$ for 20 different models.

Figure 2

The $Q_{\alpha }$ values of $Z=110\text{–}120$ isotopes as a function of $N$ for WS4 model.

Figure 3

The values of ${log}_{10}R$ as functions of $N$ for 18 different analytic formulas.

Figure 4

The predicted decimal logarithm of $\alpha$-decay half-lives of the $Z=110\text{–}120$ isotopes as functions of $N$ for the SemFIS2, VSS, SP, NRDX, and UNIV2 formulas.