Systematic investigation of $\alpha$- and cluster-decay modes in superheavy nuclei

We systematically investigate the $\alpha$-decay and spontaneous fission (SF) half-lives of superheavy nuclei (SHN) $Z=124$ and 126 in the mass number range $292\le A\le 314$. The $\alpha$-decay half-lives $\left({log}_{10}{T}_{1/2}\right)$ have been calculated within the double folding model (DFM), the universal decay law (UDL), the scaling law of Horoi, and the universal curve (UNIV) formula. To identify the mode of decay of these SHN, a competition between SF half-lives and $\alpha$-decay half-lives has been performed. The study reveals that even-mass number isotopes of ${}^{292\text{–}314}124$ and ${}^{292\text{–}314}126$ will survive fission, and $\alpha$ chains can also be predicted from these SHN. The variation of ${log}_{10}{T}_{1/2}$ against parent nucleus mass numbers of $\alpha$-decay chains of each SHN isotope is found to be governed by the presence of magic or semimagic nucleon numbers of the parent nucleus in the sense that ${log}_{10}{T}_{1/2}$ becomes maximum at or near these numbers. The probable heavy cluster radioactivity (CR) in the mass number range $A_c=18\text{–}126$ from ${}^{294\text{–}324}124$ and ${}^{294\text{–}312}126$ is also studied using the same four models of $\alpha$-decay half-lives. Heavy clusters with charge numbers in the range $36\le Z_c\le 46$ are dominant decay modes relative to $\alpha$ decay. Clusters with small $log{T}_c$ values relative to $\alpha$ decay are found to be the six clusters, $\mathrm{Kr}$, $\mathrm{Sr}$, $\mathrm{Zr}$, $\mathrm{Mo}$, $\mathrm{Ru}$, and Pd. The most probable cluster emissions having the smallest $log{T}_c$ values relative to $\alpha$ decay are ${}^{104\text{–}106}\mathrm{Mo}$ and ${}^{106\text{–}110}\mathrm{Ru}$ from ${}^{312}124$; from ${}^{296}126$ the clusters are ${}^{94\text{–}96}\mathrm{Mo},{}^{104\text{–}106}\mathrm{Pd}$; from ${}^{298}126$ the clusters are ${}^{90}\mathrm{Zr}$, ${}^{96}\mathrm{Mo}$; and from the SHN isotope ${}^{300}126$ the most probable clusters are ${}^{100\text{–}102}\mathrm{Ru}$. We found that the most probable cluster emissions occur when the proton and neutron numbers in the emitted clusters and their residual daughter nuclei are magic or near to the magic numbers.

Figure 1

Comparison of the calculated $\alpha$-decay half-lives of the isotopes ${}^{292\text{–}298}124$ and products on their $\alpha$-decay chains.

Figure 2

The the same as Fig. 1 but for ${}^{300\text{–}306}124$ isotopes.

Figure 3

The the same as Fig. 1 but for ${}^{308\text{–}314}124$ isotopes.

Figure 4

Comparison of the calculated $\alpha$-decay half-lives of the isotopes ${}^{292\text{–}298}126$ and products on their $\alpha$-decay chains.

Figure 5

The the same as Fig. 4 but for ${}^{300\text{–}306}126$ isotopes.

Figure 6

The the same as Fig. 4 but for ${}^{308\text{–}314}126$ isotopes.

Figure 7

Comparison of the calculated $\alpha$-decay half-lives of the isotope ${}^{298}124$ and products on their $\alpha$-decay chains using different mass models.

Figure 8

Comparison of the calculated $\alpha$-decay half-lives of the isotope ${}^{306}124$ and products on their $\alpha$-decay chains using different mass models.

Figure 9

Decimal logarithm of the branching ratio of the probable CR relative to $\alpha$ decay versus the mass number of the parent nuclei with $Z=124$.

Figure 10

The same as Fig. 9 but for the isotopes of SHN with $Z=126$.