Machine learning study of fission barriers in superheavy nuclei

The synthesis of superheavy elements represents the forefront of exploring the properties of unknown nuclear matter. Theoretically, significant uncertainties in predicting the fission barriers of superheavy nuclei make accurate calculations of the survival probabilities of compound nuclei extremely challenging. This study utilizes a machine learning methodology to predict the fission barriers of nuclides with $93<Z\le 120$ and $135<N\le 184$. We have estimated the fission barriers for a total of 660 nuclides, and leveraged these fission barriers to calculate the crucial survival probabilities in the synthesis of superheavy elements. Based on this, we calculated the reaction cross sections for the ${}^{48}\mathrm{Ca}+{}^{243}\mathrm{Am}$ reaction within the framework of the dinuclear system model, and compared the results with experimental data measured using the new gas-filled separator DGFRS-2. The calculations successfully reproduced the experimental data within an acceptable range of error. Additionally, we explored the optimal synthesis conditions for synthesizing the new elements $Z=119$ and $Z=120$, including projectile-target combinations, incident energies, and maximum reaction cross sections.