$\alpha$ decay and spontaneous fission half-lives of nuclei around ${}^{270}\mathrm{Hs}$

$\alpha$ decay and spontaneous fission half-lives of 81 superheavy nuclei with $Z=104–112$ and $N=158–166$ have been calculated with simple formulas extracted from the systematics of measured and calculated half-lives. Half-life calculations are performed within the shell model and one-body rate theories for $\alpha$ decay and a dynamical approach for spontaneous fission defined essentially by the shape, the height of fission barrier, the fissility, and the nuclear deformations. We obtained a rather good accordance between calculated and experimental half-lives for 30 nuclei with measured $Q_{\alpha }$ values. We predicted with different fitting formulas the most probable half-lives for 51 nuclides at which there are no experimental data. The rms values for experimental and theoretical half-lives are evaluated and discussed. The comparison of theoretical calculations with experimental data allows us to draw conclusions on the role of the nuclear structure and shell effects in low-energy decay processes.

Figure 1

The measured [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] (for 30 nuclei) and the calculated [46] from Eq. (11) (for 51 nuclei), $Q_{\alpha }$ values of the nuclei with Z=104–112 and N=158–166 as a function of Z and N.

Figure 2

The $\alpha$-decay half-lives, $T_{\alpha }^{f\mathrm{SM}}$ given by Eq. (8), with the SM parameters resulted from the fit of the SM $\alpha$ half-lives, as a function of Z and N.

Figure 3

The total experimental (triangle) and calculated from $T_{\alpha }^{f\mathrm{SM}}$ and $T_{\mathrm{SF}}$ values (sphere) half-lives of nuclei with $Z=104–112$ and $N=158–166$, as a function of $Z$ and $N$. The values of $T_{\alpha }^{f\mathrm{SM}}$ are shown in Fig. 2 and Table 2, while those of $T_{\mathrm{SF}}$ are given by Eq. (10).

Figure 4

The total half-lives of SHN with $Z=104–112$ and $N=158–166$ calculated from $T_{\alpha }^{f\mathrm{SM}}$ and $T_{\mathrm{SF}}$ values as a function of the numbers of valence nucleons (holes) of the doubly magic core ${}^{270}\mathrm{Hs}$. The AD channels starting from parent nuclei with valence nucleons are always terminating at spontaneously fissioning nuclei with nucleon holes.

Figure 5

The summary of predicted decay properties of 81 SHN with $Z=104–112$ and $N=158–166$. For each nuclide the mass number $A=Z+N, Q_{\alpha }$ value for the ground-state–ground-state decay, the total half-life $T_t$ (resulted from $T_{\alpha }^{f\mathrm{SM}}$ and $T_{\mathrm{SF}}$ values), and the branching ratios $b_{\alpha }$ and $b_{\mathrm{SF}}$ for $\alpha$ decay and SF are shown. The nuclei colored in yellow are prominent $\alpha$ emitters ($b_{\alpha }>b_{\mathrm{SF}}$), while the spontaneously fissioning nuclei are colored in green ($b_{\alpha }<b_{\mathrm{SF}}$).

Figure 6

Experimental [17, 67] and presently calculated $T_{\alpha }^{f\mathrm{SM}}$ AD half-lives for transitions from the ground to excited states in the $\alpha$ chain starting from ${}^{269}\mathrm{Hs}$.