Synthesis of the $Z=122$ superheavy nucleus via ${}^{58}\mathrm{Fe}$- and ${}^{64}\mathrm{Ni}$-induced reactions using the dynamical cluster-decay model

Within the framework of the dynamical cluster-decay model (DCM), we have studied the nuclear system with $Z=122$ and mass number $A$ = 306 formed via two “hot” fusion reactions ${}^{58}\mathrm{Fe}+{}^{248}\mathrm{Cm}$ and ${}^{64}\mathrm{Ni}+{}^{242}\mathrm{Pu}$. The up-to-date measured data are available only for the first reaction, and for fusion-fission cross section ${\sigma }_{\mathrm{ff}}$ and quasifission cross section ${\sigma }_{\mathrm{qf}}$, only at one compound nucleus (CN) excitation energy $E^{*}=33\mathrm{MeV}$. In this study, we have included the deformation effects up to quadrupole deformations ${\beta }_{2i}$ and with “optimum” orientations ${\theta }_i^{\mathrm{opt}.}$ for coplanar ($\mathrm{\Phi }=0^0$) configurations. The only parameter of the model is the neck-length parameter $\mathrm{\Delta }R$ whose value, for the nuclear proximity potential used here, remains within its range of validity ($\sim 2\mathrm{fm}$). Using the best fitted $\mathrm{\Delta }R$'s to the observed data for ${\sigma }_{\mathrm{ff}}$, calculated for mass region $A/2\pm 20$, and ${\sigma }_{\mathrm{qf}}$ for the incoming channel of Fe-induced reaction at $E^{*}=33\mathrm{MeV}$, we have extended the DCM calculations to the other Ni-induced reaction, and to $E^{*}$'s in the energy range 25–68 MeV. The interesting result is that the predicted evaporation residue cross section ${\sigma }_{\mathrm{ER}}$ for 1–4 neutrons is largest for 4n decay at $E^{*}=45\mathrm{MeV}$, having the value ${\sigma }_{\mathrm{ER}}\equiv {\sigma }_{4n}\sim {10}^{-5}$ pb for both reactions, and that the $\mathrm{\Delta }R$'s for the three processes (ER, ff, and qf) are different, i.e., they belong to different time scales where ff occurs first, then qf and the ER at the end. Other results of interest are the predictions of the magic $N=82{}^{136}\mathrm{Xe}$ fragment in the ff region of mass $A/2\pm 20$, and the doubly magic ${}^{208}\mathrm{Pb}$ in the qf region, in near close agreement with observed data (the observed fission fragment is of mass 132, instead of the predicted mass 136). The role of the weakly bound neutron-rich intermediate mass fragments and of the nucleus in the neighborhood of deformed magic $Z$ = 108 are also indicated in the DCM calculations, which need experimental verification. For the predicted ${\sigma }_{\mathrm{ER}}$, the largest value of CN fusion probability $P_{\mathrm{CN}}=0.2$, and its survival probability against fission $P_{\mathrm{surv}}\to 0$. Further experiments are called for.

Figure 1

Schematic configuration of two equal or unequal axially symmetric deformed, oriented nuclei, lying in the same plane (azimuthal angle $\mathrm{\Phi }=0^0$) for various ${\theta }_1$ and ${\theta }_2$ values in the range $0^0$–${180}^0$. The ${\theta }_i$ are measured anticlockwise from the colliding axis and angle ${\alpha }_i$ in clockwise from the symmetry axis.

Figure 2

Scattering potential $V(R,\ell )$ for ${}^{306}122\to {}^{302}122$ + 4n at $E^{*}=33\mathrm{MeV}$ ($\mathrm{T}=1.109\mathrm{MeV}$), at two different $\ell$ values ($\ell =50\hslash$ and ${\ell }_{\max }$). The decay path at $R=R_a$, and definition of “barrier lowering” $\mathrm{\Delta }{V}_B\left(\ell \right)=V(R_a,\ell )-V_B\left(\ell \right)$ is also shown for the $\ell =187\hslash$ case.

Figure 3

Scattering potentials $V$($R$) for the ${}^{58}\mathrm{Fe}+{}^{248}\mathrm{Cm}\to {}^{306}122^{*}$ reaction at various illustrative orientations, for quadrupole (${\beta }_{2i}$) deformatted and spherical nuclei. The barrier positions $R_{\max }$ and $R_{\min }$ referring, respectively, to the lowest (cold) and highest (hot) barriers are also shown.

Figure 4

(a) Fragmentation potential $V\left(A_2\right)$ for the compound system ${}^{306}122$ formed via ${}^{58}\mathrm{Fe}+{}^{248}\mathrm{Cm}$ reaction at $E^{*}=33\mathrm{MeV}$ for “hot compact” configurations, using the best fitted $\mathrm{\Delta }R$'s, plotted for the extreme $\ell$ values ($\ell =0$ and ${\ell }_{\max }=187\hslash$). For the light fragment mass region ($A_2=1$–4) $\mathrm{\Delta }{R}_{\mathrm{ER}}=1.242\mathrm{fm}$ and for the fission region ($A/2\pm 20=133$–173) and the remaining fragments ($A_2=5$–132) $\mathrm{\Delta }{R}_{\mathrm{ff}}=-0.1421\mathrm{fm}$. Note that some charge minimized intermediate mass fragments are the very weakly bound neutron-rich nuclei, such as ${}^{16-18}\mathrm{C}, {}^{34}\mathrm{Mg}, {}^{50-52}\mathrm{Ar}, {}^{54}\mathrm{K}$, etc., which enter the calculations because of their lower binding energies. (b) Same as above, but for “cold elongated” configurations, and at $\ell =0$ and ${\ell }_{\max }=108\hslash$ values fixed in the same way as for above, and (c) spherical considerations of nuclei, for the same parameter set as above but ${\ell }_{\max }=82\hslash$.

Figure 5

Variation of $P_0$ with angular momentum $\ell$ for light particles 1n-4n and ff decays of ${}^{306}122$, for the case of “hot compact” configurations.

Figure 6

Variation of $P$ with angular momentum $\ell$ for light particles 1n-4n decays of ${}^{306}122$, for the case of “hot compact” configurations.

Figure 7

(a) Preformation probability $P_0$ as a function of fragment mass $A_i, i=1,2$, for the fragmentation potential in Fig. 4, i.e., for the case of “hot compact” configurations, and at only ${\ell }_{\max }=187\hslash$. (b) Same as above, but for the fragmentation potential in Fig. 4, i.e., for the case of “cold elongated” configurations, and at only ${\ell }_{\max }=108\hslash$, and (c) same as above, but for spherical considerations of nuclei, i.e., for the fragmentation potential in Fig. 4, at only ${\ell }_{\max }=82\hslash$.

Figure 8

Variation of DCM-calculated ${\sigma }_{\mathrm{ER}}, {\sigma }_{\mathrm{ff}}$, and ${\sigma }_{\mathrm{qf}}$ with $E^{*}$ for best fitted ${\sigma }_{\mathrm{ff}}$ and ${\sigma }_{\mathrm{qf}}$ cross sections measured at $E^{*}=33\mathrm{MeV}$ in the reaction ${}^{58}\mathrm{Fe}+{}^{248}\mathrm{Cm}\to {}^{306}122^{*}$, and for the same best fitted $\mathrm{\Delta }{R}_{\mathrm{ER}}=1.242, \mathrm{\Delta }{R}_{\mathrm{ff}}=-0.1421$, and $\mathrm{\Delta }{R}_{\mathrm{qf}}=1.007\mathrm{fm}$, for the other reaction ${}^{64}\mathrm{Ni}+{}^{242}\mathrm{Pu}\to {}^{306}122^{*}$ and at other $E^{*}$'s in the range 25–68 MeV, using “hot compact” configurations.