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

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., $m_v^{\ast }({\rho }_0)=(0.77\pm 0.03)m$ 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 $m_s^{\ast }({\rho }_0)=(0.91\pm 0.05)m$ 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 $[m_n^{\ast }({\rho }_0,\delta )-m_p^{\ast }({\rho }_0,\delta )]/m=\Delta m_1^{\ast }({\rho }_0)\delta +O({\delta }^3)$ with the linear isospin splitting coefficient $\Delta m_1^{\ast }({\rho }_0)=0.33\pm 0.16$. 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 $m_v^{\ast }({\rho }_0)=(0.80\pm 0.03)m$ and reduces the linear isospin splitting coefficient to $\Delta m_1^{\ast }({\rho }_0)=0.27\pm 0.15$. Furthermore, the constraints on $m_v^{\ast }(\rho )$, $m_s^{\ast }(\rho )$ and $\Delta m_1^{\ast }(\rho )$ at other densities are obtained from the similar analyses and we find that the $\Delta m_1^{\ast }(\rho )$ increases with the density.

Comments: 7 pages, 3 figures. New results and discussions added. Accepted version to appear in PRC