Isospin splitting of nucleon effective mass from giant resonances in $^{208}$Pb

TL;DR

This study constrains the isovector and isoscalar effective masses in nuclear matter using giant resonance data in $^{208}$Pb, revealing the density dependence of the isospin splitting of nucleon effective mass.

Contribution

It provides new constraints on the isovector effective mass and its isospin splitting in nuclear matter based on experimental giant resonance data.

Findings

Isovector effective mass at saturation density: 0.77±0.03 m

Isoscalar effective mass at saturation density: 0.91±0.05 m

Isospin splitting coefficient: 0.33±0.16

Abstract

Based on mean field calculations with Skyrme interactions, we extract a constraint on the isovector effective mass in nuclear matter at saturation density $\rho_0$, i.e., $m_{v}^{\ast}(\rho_0)=(0.77\pm0.03) m$ by combining the experimental data of the centroid energy of the isovector giant dipole resonance (IVGDR) and the electric dipole polarizability $\alpha_{\mathrm{D}}$ in $^{208}$Pb. Meanwhile, the isoscalar effective mass at $\rho_0$ is determined to be $m_{s}^{\ast}(\rho_0)=(0.91\pm0.05) m$ by analyzing the measured excitation energy of the isoscalar giant quadrupole resonance (ISGQR) in $^{208}$Pb. From the constrained $m_{s}^{\ast}(\rho_0)$ and $m_{v}^{\ast}(\rho_0)$, we obtain the isospin splitting of nucleon effective mass in asymmetric nuclear matter of isospin asymmetry $\delta$ at $\rho_0$ as $[m_n^{\ast}(\rho_0,\delta)-m_p^{\ast}(\rho_0,\delta)]/m = \Delta m^*_1(\rho_0) \delta + O(\delta^3)$ with the linear isospin splitting coefficient $\Delta m^*_1(\rho_0) = 0.33\pm0.16$. We notice that using the recently corrected data on the $\alpha_{\mathrm{D}}$ in $^{208}$Pb with the contribution of the quasideuteron effect subtracted slightly enhances the isovector effective mass to $m_{v}^{\ast}(\rho_0)=(0.80\pm0.03) m$ and reduces the linear isospin splitting coefficient to $\Delta m^*_1(\rho_0) = 0.27\pm0.15$. Furthermore, the constraints on $m_{v}^{\ast}(\rho)$, $m_{s}^{\ast}(\rho)$ and $\Delta m^*_1(\rho)$ at other densities are obtained from the similar analyses and we find that the $\Delta m^*_1(\rho)$ increases with the density.