Isotopic yield and half-life of spontaneous fission for ${}^{284}\mathrm{Cn}$ and ${}^{284}\mathrm{Fl}$ superheavy isobars using direct calculation and semiempirical formulas

Isotopic yields and half-lives of ${}^{284}\mathrm{Cn}$ and ${}^{284}\mathrm{Fl}$ superheavy nuclei are calculated using nuclear proximity and Coulomb potentials. The energy released in fission, $Q$ value, driving potential $(V-Q)$, the penetrability through barrier, fission decay constant, and relative yield for each possible pair of fission fragments are obtained. According to the fragments mass and charge asymmetry, the most favored binary fragmentation is occurred for the highest $Q$ value and the lowest driving potential. For spontaneous binary fission of ${}^{284}\mathrm{Cn}$ superheavy nuclei, the higher relative yields are belong to production of ${}^{128}\mathrm{Sn}$ and ${}^{134}\mathrm{Te}$ fragments and for ${}^{284}\mathrm{Fl}$ superheavy isotope, the maximum yield were observed for ${}^{136}\mathrm{Xe}$ as one of the fission fragments. The comparison between the obtained isotopic relative yield shows the role of magic and near-magic closed-shell fragments in having the highest isotopic yield. Fission decay constant for each possible fragmentation is calculated and then by summation over them, the total decay constant and fission half-life for ${}^{284}\mathrm{Cn}$ and ${}^{284}\mathrm{Fl}$ superheavy nuclei are estimated. Finally, the calculated half-lives using direct method are compared with the results of semiempirical formulas as well as experimental data. Satisfactory agreement is achieved between the results of this approach and the experimental data than the results of semiempirical formulas.

Figure 1

(a) Diagram of the touching configuration of fission fragments $(s=0)$. (b) Diagram of the separated configuration of fission fragments $\left(s>0\right)$.

Figure 2

Driving potential for binary spontaneous fragmentations of ${}^{284}\mathrm{Fl}$ superheavy nucleus as a function of first fragment mass number, $A_1$.

Figure 3

Driving potential for binary spontaneous fragmentations of ${}^{284}\mathrm{Cn}$ superheavy nucleus as a function of first fragment mass number, $A_1$.

Figure 4

The driving potential for all possible fragmentations of ${}^{284}\mathrm{Fl}$ and ${}^{284}\mathrm{Cn}$ superheavy nuclei as a function of first fragment mass number, $A_1$, are compared. The fragment combinations with the higher yield are labeled.

Figure 5

Relative yields of all possible even fragmentations for ${}^{284}\mathrm{Fl}$ superheavy isotope as a function of fragments mass $\mathrm{number}(A_1$ and $A_2)$. Favored fragment combinations with higher yield are labeled.

Figure 6

Relative yields of all possible even fragmentations for ${}^{284}\mathrm{Cn}$ superheavy isotope as a function of fragments mass number $(A_1$ and $A_2)$. Favored fragment combinations with higher yield are labeled.

Figure 7

Relative yields of all possible even fragmentations for ${}^{284}\mathrm{Fl}$ and ${}^{284}\mathrm{Cn}$ superheavy isobars as a function of fragments mass $\text{number}(A_1$ and $A_2)$ are compared. Favored fragment combinations with the highest yield is labeled.

Figure 8

Bar graph presentation of relative yields for spontaneous even and odd fragmentations of ${}^{284}\mathrm{Fl}$ superheavy nucleus.

Figure 9

Bar graph presentation of relative yields for spontaneous even and odd fragmentations of ${}^{284}\mathrm{Cn}$ superheavy nucleus.