Synthesis of the superheavy elements beyond Og: extrapolating from ${}^{48}\mathrm{Ca}$ to ${}^{54}\mathrm{Cr}$

Abstract

Theoretical predictions on the optimal reaction energies are essential for producing superheavy elements (SHEs) beyond Og. Due to the limitation of the targets, synthesizing elements 119 and 120 will require beams of ${}^{50}\mathrm{Ti}$ and/or ${}^{54}\mathrm{Cr}$ ions. However, is it reliable to theoretically extrapolate from the well-investigated ${}^{48}\mathrm{Ca}$ induced reactions to those with heavier projectiles? In this work, we apply the Fusion-by-Diffusion (FBD) concept to answer this question from two perspectives: radial and mass asymmetry degrees of freedom. The FBD concept is employed in the mass asymmetry degree of freedom for the first time, in which by fitting the calculations to experimental evaporation residue cross sections (ERCS) for the reactions of ${}^{48}\mathrm{Ca}$ as projectiles with the actinide targets, a strong linear correlation between the contact distance ($D_\mathrm{cont}$) and center-of-mass energy excess above the Coulomb barrier ($E_\mathrm{c.m.}-B_0$) is found and a parametrization of the $D_\mathrm{cont}$ is introduced. Using the result of parametrization, the calculations satisfactorily reproduce the shapes of all hot fusion excitation functions and values of the ERCS. Furthermore, thanks to the recent experimental data, we extrapolate the calculation in the reactions \({}^{50}\mathrm{Ti}+{}^{242}\mathrm{Pu}\), \({}^{50}\mathrm{Ti}+{}^{244}\mathrm{Pu}\), and \({}^{54}\mathrm{Cr}+{}^{238}\mathrm{U}\). The calculations reproduce the experimental data rather well within the experimental errors in both perspectives. Our results demonstrate that there is no non-negligible systematic deviation in extrapolating the projectiles from $^{48}\text{Ca}$ to $^{50}\text{Ti}$ and $^{54}\text{Cr}$ for synthesizing SHEs beyond Og.