$\alpha$-decay chains of recoiled superheavy nuclei: A theoretical study

A systematic theoretical study of $\alpha$-decay half-lives in the superheavy mass region of the periodic table of elements is carried out by extending the quantum-mechanical fragmentation theory based on the preformed cluster model (PCM) to include temperature $\left(T\right)$ dependence in its built-in preformation and penetration probabilities of decay fragments. Earlier, the $\alpha$-decay chains of the isotopes of $Z=115$ were investigated by using the standard PCM for spontaneous decays, with“hot-optimum” orientation effects included, which required a constant scaling factor of ${10}^4$ to approach the available experimental data. In the present approach of the PCM $\left(T\ne 0\right)$, the temperature effects are included via the recoil energy of the residual superheavy nucleus (SHN) left after $x$-neutron emission from the superheavy compound nucleus. The important result is that the $\alpha$-decay half-lives calculated by the PCM $\left(T\ne 0\right)$ match the experimental data nearly exactly, without using any scaling factor of the type used in the PCM. Note that the PCM $\left(T\ne 0\right)$ is an equivalent of the dynamical cluster-decay model for heavy-ion collisions at angular momentum $\ell =0$. The only parameter of model is the neck-length parameter $\Delta R$, which for the calculated half-lives of $\alpha$-decay chains of various isotopes of $Z=113$ to 118 nuclei formed in “hot-fusion” reactions is found to be nearly constant, i.e., $\Delta R\approx 0.95\pm 0.05$ fm for all the $\alpha$-decay chains studied. The use of recoiled residue nucleus as a secondary heavy-ion beam for nuclear reactions has also been suggested in the past.

Figure 1

Schematic of compound nucleus decay via the $\alpha$-decay chain and the compound-nucleus fusion process.

Figure 2

Scattering potential $V\left(R\right)$ for ${}^{293}{117}^{*}\to {}^{289}115+\alpha$ at $T=0.876$ MeV (equivalently, $E_R=13$ MeV) for the $\ell =0$ case. The decay path, defined by $V\left(R_a\right)=Q_{\mathrm{eff}}\left(T\right)$ is shown to begin at $R_a=R_t+\Delta R$ where $R_t=R_1+R_2$.

Figure 3

Mass-fragmentation potential $V\left(A_i\right)(i=1,2)$ for the SHN ${}^{293}{117}^{*}$, formed via a hot-fusion reaction ${}^{249}\mathrm{Bk}+{}^{48}\mathrm{Ca}$ after the $4n$ emission, at $R=R_a=R_t+\Delta R$ and $T=0.876$ MeV (equivalently, ${\mathrm{E}}_R=13$ MeV), calculated for both cases of spherical (open spheres) and deformations ${\beta }_{2i}$ and hot-optimum orientations (solid spheres) for all possible combinations of two nuclei at $\ell =0$. $\Delta R=0.9805$ fm for the best fit to $\alpha$-decay data (see Table 1).

Figure 4

Preformation probability $P_0$ as a function of fragment mass number $A_i,i=1,2$, for the decay of ${}^{293}{117}^{*}$, taking nuclei to be spherical (open spheres) and ${\beta }_2$ deformed with optimum orientations (solid spheres).

Figure 5

The best-fit neck-length parameter $\Delta R$ as a function of mass number of $\alpha$-decay chains at different $E_R$ values for various SHN. For example, in panel (a), the excited SHN ${}^{294}{118}^{*}$ formed via a hot-fusion reaction ${}^{249}\mathrm{Cf}+{}^{48}\mathrm{Ca}$, after $3n$ emission, results in excited superheavy systems ${}^{290}{116}^{*},{}^{286}{114}^{*}$, and ${}^{282}{112}^{*}$ after subsequent $\alpha$ decays. Our calculations refer to PCM $\left(T\ne 0\right)$, and consider in all cases the hot-optimum configuration.

Figure 6

Same as for Fig. 5, but for preformation probability $P_0$.

Figure 7

Same as for Fig. 5, but for penetrability $P$.

Figure 8

Comparison of experimental, PCM $\left(T\ne 0\right)$, and PCM $\left(T=0\right)$ calculated half-lives of $\alpha$-decay chains from (a) $3n$, and (b) $4n$ decay channels of ${}^{291}{115}^{*}$ formed in the ${}^{48}\mathrm{Ca}+{}^{243}\mathrm{Am}$ reaction. The hot-optimum orientations are used in both the PCM $\left(T\ne 0\right)$ and the PCM $\left(T=0\right)$. We refer here to calculations with $\ell =0$ and consider in all cases the hot-optimum configurations.