Fusion cross section of the superheavy Z=120 nuclei within the relativistic mean-field formalism

Abstract

Background: Isotopes of $Z=107\text{--}118$ have been synthesized using cold fusion at GSI, Darmstadt, and hot fusion reactions at JINR, Dubna. Recently theoretical models have predicted $Z=120$ with $N=184$ as an island of stability in the superheavy valley. Hence it is crucial and exciting to predict theoretically the possible combination of projectiles and targets for the synthesis of $Z=120$, which can be informative for upcoming experiments.Purpose: Present theoretical investigations aim to explore the fusion characteristics of various isotopes of $Z=120$ within the relativistic mean-field formalism. We predict the most suitable projectile-target combination for the synthesis of element $Z=120$. The increase in fusion cross section of nuclei in the superheavy island directly signals the nuclear shell effects. Besides these, the analysis will be crucial and relevant for future experiments to synthesize superheavy nuclei.Methods: The microscopic nucleon-nucleon R3Y interaction and the density distributions for targets and projectiles are calculated using a relativistic mean-field formalism with the ${\mathrm{NL3}}^{*}$ parameter set. These densities and R3Y nucleon-nucleon (NN) interaction are then used to calculate the nuclear interaction potential using the double folding approach. Seventeen different projectile-target combinations that allow a high $N$/$Z$ ratio are considered in the present analysis to calculate the capture and/or fusion cross sections of various isotopes of $Z=120$ within the $\ensuremath{\ell}$-summed Wong formula.Results: The nuclear density distributions for the interacting projectile and target nuclei are obtained from relativistic mean-field Lagrangian for the ${\mathrm{NL3}}^{*}$ parameter set. The nucleus-nucleus interaction potential is estimated for seventeen possible projectile-target combinations using the mean-field density and the R3Y NN potential via a double folding approach. The fusion barriers are obtained by adding the Coulomb potential to the nucleus-nucleus interaction potential. Finally, the fusion and/or capture cross section is calculated for all the systems within the $\ensuremath{\ell}$-summed Wong formula. Further, the equivalent surface diffusion parameter is estimated to correlate the surface properties of interacting nuclei with the fusion cross section.Conclusions: The four Ti-based reactions with the heaviest available target $^{\mathrm{x}}\mathrm{Cf}$, namely, $^{46}\mathrm{Ti}+^{248}\mathrm{Cf}$, $^{46}\mathrm{Ti}+^{249}\mathrm{Cf}$, $^{50}\mathrm{Ti}+^{249}\mathrm{Cf}$, and $^{50}\mathrm{Ti}+^{252}\mathrm{Cf}$, and also $^{54}\mathrm{Cr}+^{250}\mathrm{Cm}$ are found to have the most suitable target-projectile combinations for the synthesis of various isotopes $Z=120$. We also notice that $^{48}\mathrm{Ca}$ beams merely provide the required number of protons to synthesize the element with $Z=120$. We established a correlation among the surface properties of interacting nuclei with the fusion characteristics in terms of the equivalent surface diffusion parameter.