Theoretical issues for synthesizing new superheavy elements: nuclear masses and fission barriers

Currently, the synthesis of superheavy elements starting from the eighth row of the periodic table has become an important scientific issue in major international nuclear physics laboratories. The cross-section to produce Z=119 superheavy element by experiments is extremely low, and the available combinations of projectiles and targets are limited. Therefore, theoretically, it is essential to accurately estimate the optimal collision energy. The accurate calculation of high-quality nuclear masses is crucial for determining the reaction Q values and obtaining reliable alpha decay energies for identifying new elements and new isotopes. The existing nuclear masses in the heaviest region estimated by different models have large uncertainties about 4 MeV, which is a serious problem. In addition, the height and energy dependence of the fission barriers of highly excited superheavy nuclei are also crucial for calculating the survival probabilities and estimating optimal beam energies. In this respect, we can provide theoretical guidance for the synthesis of superheavy elements based on accurate energy density functional theory calculations. We took into account the experimental values of the alpha decay energy of superheavy nuclei in the fitting of the Sk-SHE1 energy density functional, and obtained a high-quality microscopic superheavy nucleus mass table. The systematic alpha-decay energies in the superheavy region can be well described, with deviations less than 0.3 MeV. The estimated binding energies of superheavy nuclei are surprisingly close to the AME2020 evaluation. The predicted reaction Q-values of 54Cr+243Am and 50Ti+249Bk to synthesize 119 element are –207.79 and –191.78 MeV, respectively. We also calculated energy-dependent fission barriers based on different parameters and studied the production cross-sections of Z=115 and 119 superheavy nuclei. The energy-dependent (or temperature-dependent) fission barriers are calculated using the HFODD code, which has taken into account the triaxial deformation and octupole deformation in finite-temperature Hartree-Fock+BCS calculations. The residual cross sections are obtained by combining fusion probabilities from dinuclear system models and our results of survival probabilities. We find that fission barriers with UNEDF1 and Sk-SHE1 lead to very different cross sections and optimal beam energies. The different fission barriers could result in ~4 MeV differences in the optimal beam energies. The fission barriers by UNEDF1 force decrease faster with increasing excitation energies compared to Sk-SHE1. The 3n channel can be well described by UNEDF1, and the 4n channel can be well described by Sk-SHE1. In this respect, further systematic studies on microscopic fission barriers and uncertainties are still needed. In addition, the dependence on level densities has also studied. The results with a complex level density parameter formula, including shell effects, are not very different from those using a simple level density parameter formula. The cross sections are not sensitive to the forms of level densities. In the future, both large-scale microscopic calculations and more experiments on other reactions are needed for better estimations of reaction beam energies.