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

• Published in: arXiv.org
• Main Authors: Qiu, Mengying, Bao-Jun, Cai, Lie-Wen, Chen, Cen-Xi Yuan, Zhang, Zhen
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 18.01.2024
• Subjects: Bayesian analysis; Chemical potential; Confidence intervals; Gaussian process; Lead; Nuclei (nuclear physics); Physics - Nuclear Theory; Protons; Relativistic effects; Statistical analysis; Symmetry; Tin
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2312.07031

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 \(\Delta \mu^*_{\rm{pn}}\) of neutron-rich nuclei is found to be strongly sensitive to the symmetry energy \(E_{\rm{sym}}(\rho)\) around \(2\rho_0/3\), with \(\rho_0\) being the nuclear saturation density. Given discrepancies on the \(\Delta \mu^*_{\rm{pn}}\)-\(E_{\rm{sym}}(2\rho_0/3)\) correlations between the two models, we carry out a Bayesian model averaging analysis based on Gaussian process emulators to extract the symmetry energy around \(2\rho_0/3\) from the measured \(\Delta \mu^*_{\rm{pn}}\) of 5 doubly magic nuclei \(^{48}\)Ca, \(^{68}\)Ni, \(^{88}\)Sr, \(^{132}\)Sn and \(^{208}\)Pb. Specifically, the \(E_{\mathrm{sym}}(2\rho_0/3)\) is inferred to be \(E_{\mathrm{sym}}(2\rho_0/3) = 25.6_{-1.3}^{+1.4}\,\mathrm{MeV}\) at \(1\sigma\) confidence level. The obtained constraints on the \(E_{\mathrm{sym}}(\rho)\) around \(2\rho_0/3\) agree well with microscopic predictions and results from other isovector indicators.