Cluster preformation law for heavy and superheavy nuclei

The concept of cluster radioactivity has been extended to allow emitted particles with $Z_C>28$ for superheavy nuclei by nuclear theory [Poenaru et al., Phys. Rev. Lett. 107, 062503 (2011)]. The preformation and emission mechanics of heavy-ion particles must be examined again before the fascinating radioactivity is observed for superheavy nuclei in laboratory. We extract the cluster preformation factor for heavy and superheavy nuclei within a preformed cluster model, in which the decay constant is the product of the preformation factor, assault frequency, and penetration probability. The calculated results show that the cluster penetration probability for superheavy nuclei is larger than that for actinide elements. The preformation factor depends on the nuclear structures of the emitted cluster and mother nucleus, and the well-known cluster preformation law $S\left(A_C\right)=S{\left(\alpha \right)}^{\left(A_C-1\right)/3}$ [Blendowske and Walliser, Phys. Rev. Lett. 61, 1930 (1988)] will break down when the mass number of the emitted cluster $A_c>28$, and new preformation formulas are proposed to estimate the preformation factor for heavy and superheavy nuclei.

Figure 1

Potential barriers for ${}_{88}^{222}\mathrm{Ra}⟶{}_6{}^{14}\mathrm{C}+{}_{82}{}^{208}\mathrm{Pb}$ and ${}_{110}{}^{276}\mathrm{Ds}⟶{}_{28}{}^{68}\mathrm{Ni}+{}_{82}{}^{208}\mathrm{Pb}$ cluster radioactivity.

Figure 2

Negative logarithm of the preformation factors $S\left(A_C\right)$ as a function of the cluster mass number $A_C$, charge number $Z_C$, and neutron number $N_C$ for the cluster radioactivity.

Figure 3

Negative logarithm of the preformation factor vs mass, charge, and neutron number of daughter nuclei for heavy and superheavy nuclei cluster radioactivity.

Figure 4

Negative logarithm of the preformation factor vs mass, charge, and neutron number of mother nuclei for cluster radioactivity of heavy and superheavy nuclei.