Bayesian inference on the isospin splitting of nucleon effective mass from giant resonances in $^{208}$Pb

TL;DR

This paper uses Bayesian analysis of giant resonance data in lead-208 to constrain nucleon effective masses and symmetry energy, revealing a positive isospin splitting and precise symmetry energy at subsaturation density.

Contribution

It introduces a Bayesian framework to extract isoscalar and isovector effective masses from nuclear resonance data, providing new constraints on nucleon effective mass splitting and symmetry energy.

Findings

Effective masses at saturation density: $m_{s,0}^*/m=0.87 ext{--}0.91$ and $m_{v,0}^*/m=0.78 ext{--}0.83$.

Positive isospin splitting of nucleon effective mass: $m_{n-p}^*/m imes ext{isospin asymmetry}$.

Symmetry energy at $ ho^{ ext{*}}=0.05~ ext{fm}^{-3}$: $16.7 ext{--}18.0$ MeV.

Abstract

From a Bayesian analysis of the electric dipole polarizability, the constrained energy of isovector giant dipole resonance, the peak energy of isocalar giant quadrupole resonance and the constrained energy of isocalar giant monopole resonance in $^{208}$Pb, we extract the isoscalar and isovector effective masses in nuclear matter at saturation density $\rho_0$ as $m_{s,0}^{\ast}/m=0.87_{-0.04}^{+0.04}$ and $m_{v,0}^{\ast}/m = 0.78_{-0.05}^{+0.06}$ at $90\%$ confidence level. The obtained constraints on $m_{s,0}^{\ast}$ and $m_{v,0}^{\ast}$ lead to a positive isospin splitting of nucleon effective mass in asymmetric nuclear matter of isospin asymmetry $\delta$ at $\rho_0$ as $m_{n-p}^* / m=(0.20^{+0.15}_{-0.14})\delta$. In addition, the symmetry energy at the subsaturation density $\rho^{\ast}=0.05~\mathrm{fm}^{-3}$ is determined to be $E_{\mathrm{sym}}(\rho^{\ast})=16.7\pm1.3$ MeV at $90\%$ confidence level.