Synthesis of the Z=122 superheavy nucleus via Fe58 - and Ni64 -induced reactions using the dynamical cluster-decay model

Abstract

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 $^{58}\mathrm{Fe}+\phantom{\rule{0.16em}{0ex}}^{248}\mathrm{Cm}$ and $^{64}\mathrm{Ni}+\phantom{\rule{0.16em}{0ex}}^{242}\mathrm{Pu}$. The up-to-date measured data are available only for the first reaction, and for fusion-fission cross section ${\ensuremath{\sigma}}_{\mathrm{ff}}$ and quasifission cross section ${\ensuremath{\sigma}}_{\mathrm{qf}}$, only at one compound nucleus (CN) excitation energy ${E}^{*}=33\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$. In this study, we have included the deformation effects up to quadrupole deformations ${\ensuremath{\beta}}_{2i}$ and with ``optimum'' orientations ${\ensuremath{\theta}}_{i}^{\mathrm{opt}.}$ for coplanar ($\mathrm{\ensuremath{\Phi}}={0}^{0}$) configurations. The only parameter of the model is the neck-length parameter $\mathrm{\ensuremath{\Delta}}R$ whose value, for the nuclear proximity potential used here, remains within its range of validity ($\ensuremath{\sim}2\phantom{\rule{0.28em}{0ex}}\mathrm{fm}$). Using the best fitted $\mathrm{\ensuremath{\Delta}}R$'s to the observed data for ${\ensuremath{\sigma}}_{\mathrm{ff}}$, calculated for mass region $A/2\ifmmode\pm\else\textpm\fi{}20$, and ${\ensuremath{\sigma}}_{\mathrm{qf}}$ for the incoming channel of Fe-induced reaction at ${E}^{*}=33\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, 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 ${\ensuremath{\sigma}}_{\mathrm{ER}}$ for 1--4 neutrons is largest for 4n decay at ${E}^{*}=45\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$, having the value ${\ensuremath{\sigma}}_{\mathrm{ER}}\ensuremath{\equiv}{\ensuremath{\sigma}}_{4n}\ensuremath{\sim}{10}^{\ensuremath{-}5}$ pb for both reactions, and that the $\mathrm{\ensuremath{\Delta}}R$'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 $N=82\phantom{\rule{4pt}{0ex}}^{136}\mathrm{Xe}$ fragment in the ff region of mass $A/2\ifmmode\pm\else\textpm\fi{}20$, 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 ${\ensuremath{\sigma}}_{\mathrm{ER}}$, the largest value of CN fusion probability ${P}_{\mathrm{CN}}=0.2$, and its survival probability against fission ${P}_{\mathrm{surv}}\ensuremath{\rightarrow}0$. Further experiments are called for.