Background: The synthesis of new elements, extending the periodic table, remains one of the central challenges in modern science and requires the production of superheavy nuclei in nuclear reactions. However, the production of superheavy nuclei involves highly complex reaction mechanisms, and theoretical predictions remain subject to substantial uncertainties in nuclear-physics inputs and models.

Purpose: Fusion reactions with ${}^{48}\mathrm{Ca}$ beams, which have been used for synthesis of $Z\le 118$ nuclei, face practical limitations for the synthesis of nuclei with $Z\ge 119$ because of the short half-lives and limited availability of suitable target nuclei. We estimate evaporation-residue cross sections ${\sigma }_{\mathrm{ER}}$ for the reactions ${}^{48}\mathrm{Ca}+{}^{254}\mathrm{Es}, {}^{50}\mathrm{Ti}+{}^{249}\mathrm{Bk}, {}^{51}\mathrm{V}+{}^{248}\mathrm{Cm}$, and ${}^{54}\mathrm{Cr}+{}^{243}\mathrm{Am}$, and examine the role of nuclear-mass-model uncertainties.

Methods: We employ a hybrid framework for the three stages of the fusion reaction. The capture stage is described by the coupled-channels method, the competition between fusion and quasifission by a multidimensional Langevin approach, and the de-excitation stage by a statistical model. ${\sigma }_{\mathrm{ER}}$ is evaluated by combining the corresponding capture, compound-nucleus formation, and survival probabilities.

Results: Using the nuclear properties from the FRDM2012 mass model, the maximum values of ${\sigma }_{\mathrm{ER}}$ summed over all $xn$ channels are calculated to be 233, 206, 33, and $38\mathrm{fb}$ for the ${}^{48}\mathrm{Ca}+{}^{254}\mathrm{Es}, {}^{50}\mathrm{Ti}+{}^{249}\mathrm{Bk}, {}^{51}\mathrm{V}+{}^{248}\mathrm{Cm}$, and ${}^{54}\mathrm{Cr}+{}^{243}\mathrm{Am}$ reactions, respectively. The relative relationship between the reaction $Q$ value and the Coulomb-barrier height is found to be a key factor in comparing reactions leading to the same atomic number. In particular, the relatively small $Q$ value magnitude of the ${}^{51}\mathrm{V}+{}^{248}\mathrm{Cm}$ reaction leads to a higher excitation energy and a reduced survival probability, giving the smallest ${\sigma }_{\mathrm{ER}}$ among the reactions considered. We also find a significant mass-model dependence on the survival probability. Using the nuclear properties predicted by several mass tables (FRDM2012, FRDM1995, WS4, and KTUY05) yields differences in the survival probability ranging from about one to several orders of magnitude. This difference mainly originates from the neutron binding energy and shell-correction energy predicted by the nuclear mass models.

Conclusions: The cross sections ${\sigma }_{\mathrm{ER}}$ for the synthesis of $Z=119$ nuclei are governed by both the relative relationship between the reaction $Q$ value and the Coulomb-barrier height and nuclear-mass-model uncertainties that strongly affect the survival probability. Both effects must be taken into account in theoretical predictions and in the planning of future experiments.

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• Binding energy & masses
• Fusion evaporation reactions
• Low & intermediate energy heavy-ion reactions
• Nuclear reactions
• Synthesis of new superheavy elements
• A ≥ 220
• Langevin algorithm
• Nuclear many-body theory