Spontaneous fission and competing ground state decay modes of actinide and transactinide nuclei

Based on the preformed cluster model, we have carried out a comprehensive theoretical study on the decay paths of ground state actinide and transactinide nuclei, specifically from ${}^{232}\mathrm{U}$ to ${}^{264}\mathrm{Hs}$ exhibiting the phenomenon of spontaneous fission (SF). This is an extension of our earlier studies on $\alpha$ decay, exotic cluster emission, and heavy particle radioactivity, where an effort is made to identify the most probable fragments in the SF process. These observations in turn, could provide a testing ground for future SF half-life measurements. To obtain a clear picture of the dynamics involved, the variations of fragmentation potential, preformation factor, and decay barrier height have been examined. The calculated potential energy surfaces show a change from a predominantly asymmetric fission to a symmetric fragmentation with the increase in the N/Z ratio of parent nuclei. In addition, an exclusive analysis of SF with $\alpha$ and other possible cluster emissions for the ${}^{232,234,236,238}\mathrm{U}$ parents was made to have better insight of nuclear structure information. In other words, the comparative nature of $\alpha$, cluster, heavy fragment, and SF decay paths is analyzed in view of shell closure property of the decay fragments. Interestingly, the calculated decay half-lives for the ${}^{82}\mathrm{Ge}$ heavy cluster are in fact shown to lie within the limits of experiments, thereby presenting themselves as exciting new possibilities which may be validated via future experiments.

Figure 1

The variation of hydrodynamical masses $B_{\eta \eta }$ with the (a) different decay modes and (b) neck length parameter $\mathrm{\Delta }R$.

Figure 2

Fragmentation potential $V\left(A_2\right)$ plotted for various ground state parent nuclei, taking the two emitting fragments as spheres only.

Figure 3

(a) The variation of fragmentation potential as a function of fragment mass $A_2$ for the decay of ${}^{238}U$ using two different radius (effective sharp radius $R_t$ and $\mathrm{S}\ddot{u}$ssmann's central radius $C_t$) approaches. (b) Same as panel (a) but for the fragment preformation probability. (c) Scattering potentials for the spontaneous decay of ${}^{238}\mathrm{U}\to {}^{106}M\mathrm{o}+{}^{132}Sn$ using $R_t$ and $C_t$, showing the three steps of barrier penetration used in PCM.

Figure 4

Variation of barrier lowering parameter $\mathrm{\Delta }{V}_B$ (MeV) with the mass of fission fragments on the $x$ axis for (a) even ${}^{250-256}\mathrm{Fm}$ isotopes and (b) ${}^{255-260}\mathrm{Rf}$ isotopes.

Figure 5

The best fit neck-length parameter $\mathrm{\Delta }R$ in fm (left Y axis) and preformation probability $P_0$ (right Y axis), plotted as a function of parent nuclei mass number A calculated on the basis of PCM for the most favored decays of the parents with Z=92, 94, 96, 100, 101, 102, 103, 104, and 106.

Figure 6

Deviations between the logarithms of the PCM calculated half-lives and the experimental ones corresponding to different cases of spontaneous fissioning nuclei, mentioned in Table 1.

Figure 7

Comparative behavior of fragmentation potential for even ${}^{232-238}\mathrm{U}$ parents for different decay paths namely (a) $\alpha$ radioactivity, (b) cluster emission, (c) heavy particle decay, and (d) spontaneous fission. The choice of most preferred fragments is identified by solid arrows.

Figure 8

The scattering potential for the four possible decay modes occurring in ${}^{232}\mathrm{U}$ showing steps of barrier penetration with both the daughter and cluster taken as spherical only. The path of barrier tunneling is also shown.

Figure 9

Variation of Q value (MeV) (left Y axis) and penetrability P (right Y axis) with the mass asymmetry of the emitted fragments for the parent nucleus ${}^{232}\mathrm{U}$.

Figure 10

Histogram representation of (a) preformation probability, (b) penetrability, and (c) logarithm of decay half-lives for the four different decay modes ($\alpha$, cluster, heavy particle, and SF) of ground state parent nuclei ${}^{232}\mathrm{U}$, ${}^{234}\mathrm{U}$, ${}^{236}\mathrm{U}$, and ${}^{238}\mathrm{U}$.

Figure 11

Geiger-Nuttal plots of ${\log }_{10}{T}_{1/2}^{\mathrm{PCM}}$ (s) vs $Q^{-1/2}$ for various clusters emitted from ${}^{232-238}\mathrm{U}$.