Bayesian model averaging for nuclear symmetry energy from effective proton-neutron chemical potential difference of neutron-rich nuclei

Abstract

The data-driven Bayesian model averaging is a rigorous statistical approach to combining multiple models for a unified prediction. Compared with the individual model, it provides more reliable information, especially for problems involving apparent model dependence. In this work, within both the non-relativistic Skyrme energy density functional and the nonlinear relativistic mean field model, the effective proton-neutron chemical potential difference $\hat{I}”\hat{I}{¼}_{\mathrm{pn}}^{\ast }$ of neutron-rich nuclei is found to be strongly sensitive to the symmetry energy $E_{\mathrm{sym}}(\ddot{I})$ around $2\ddot{I}{}_0/3$, with $\ddot{I}{}_0$ being the nuclear saturation density. Given discrepancies on the $\hat{I}”\hat{I}{¼}_{\mathrm{pn}}^{\ast }$-$E_{\mathrm{sym}}(2\ddot{I}{}_0/3)$ correlations between the two models, we carry out a Bayesian model averaging analysis based on Gaussian process emulators to extract the symmetry energy around $2\ddot{I}{}_0/3$ from the measured $\hat{I}”\hat{I}{¼}_{\mathrm{pn}}^{\ast }$ of 5 doubly magic nuclei ${}^{48}$Ca, ${}^{68}$Ni, ${}^{88}$Sr, ${}^{132}$Sn and ${}^{208}$Pb. Specifically, the $E_{\mathrm{sym}}(2\ddot{I}{}_0/3)$ is inferred to be $E_{\mathrm{sym}}(2\ddot{I}{}_0/3)=25.6_{-1.3}^{+1.4}\mathrm{MeV}$ at $1\ddot{I}ƒ$ confidence level. The obtained constraints on the $E_{\mathrm{sym}}(\ddot{I})$ around $2\ddot{I}{}_0/3$ agree well with microscopic predictions and results from other isovector indicators.

6 pages, 4 figures; published version