Bayesian uncertainty quantification for synthesizing superheavy elements

TL;DR

This paper applies Bayesian uncertainty quantification to improve predictions of evaporation residue cross sections for synthesizing superheavy elements, constraining key model parameters with data and analyzing their correlations.

Contribution

It introduces a Bayesian framework to quantify uncertainties in DNS model parameters, enhancing the predictive accuracy for superheavy element synthesis.

Findings

Optimal incident energies are weakly dependent on fission process.

Model parameters are strongly correlated, making independent uncertainty propagation unreasonable.

Predicted ERCS and optimal energies for Z=119 synthesis reactions.

Abstract

To improve the theoretical prediction power for synthesizing superheavy elements beyond Og, a Bayesian uncertainty quantification method is employed to evaluate the uncertainty of the calculated evaporation residue cross sections (ERCS) for the first time. The key parameters of the dinuclear system (DNS) model, such as the diffusion parameter $\textit{a}$, the damping factor $E_\mathrm{d}$, and the level-density parameter ratio $a_\mathrm{f}/a_\mathrm{n}$ are systematically constrained by the Bayesian analysis of recent ERCS data. One intriguing behavior is shown that the optimal incident energies (OIE) corresponding to the largest ERCS weakly depend on the fission process. We also find that these parameters are strongly correlated and the uncertainty propagation considering the parameters independently is not reasonable. The 2$\sigma$ confidence level of posterior distributions for $a = 0.586_{-0.002}^{+0.002}$ fm, $E_\mathrm{d} = 25.65_{-3.41}^{+3.43}$ MeV, and $a_\mathrm{f}/a_\mathrm{n} = 1.081_{-0.021}^{+0.021}$ are obtained. Furthermore, the confidence levels of the ERCS and OIE for synthesizing Z = 119 via the reactions($^{54}\mathrm{Cr}+^{243}\mathrm{Am}$), (${}^{50}\mathrm{Ti}+{}^{249}\mathrm{Bk}$), and (${}^{51}\mathrm{V}+{}^{248}\mathrm{Cm}$) are predicted. This work sets the stage for future analyses to explore the OIE and reaction systems for the synthesis of superheavy elements.