Production probability of super-heavy nuclei in fusion

Abstract

The synthesis of super-heavy nuclei (SHN) through fusion reactions is a critical area of nuclear physics, offering insights into nuclear stability and the limits of the periodic table. However, theoretical predictions of evaporation residue cross sections ${\sigma }_{\mathrm{ER}}$ remain challenging due to large uncertainties arising from complex reaction mechanisms and sensitive model parameters. In this work, the average production probabilities of SHN with atomic number $Z\ge 110$ are systematically analyzed, based on barrier tunneling concept. Together with the empirical barrier distribution method for describing capture, a phenomenological formula, EBD3, is proposed, which reproduces 58 measured ${\sigma }_{\mathrm{ER}}$ within one order of magnitude, with a root-mean-square deviation of 0.369. The formula successfully captures key quantities in fission-like process, including fission barrier height, mass asymmetry, depth of capture pocket and the effective fusion barrier height. Predictions for the synthesis of element 119 are presented, identifying promising projectile-target combinations such as ${}^{50}$Ti + ${}^{249}$Bk with a maximum cross section of $54.9_{-29.0}^{+61.3}$ fb at excitation energy of 36.5 MeV. The maximum cross section falls to $3.2_{-1.7}^{+3.6}$ fb for ${}^{54}$Cr + ${}^{243}$Am at the optimal incident energy of 244 MeV.

9 figures, 1 table, accepted for publication in Phys. Rev. C