Neutron-proton mass splitting and pygmy dipole resonance inPb208

Abstract

The pygmy dipole resonance (PDR) of $^{208}\mathrm{Pb}$ is studied with random phase approximation method. The effect of the neutron-proton mass splitting is discussed in the framework of relativistic mean field theory via including the scalar-isovector meson $\ensuremath{\delta}$ explicitly. The model is calibrated with nuclear bulk properties as well as finite nuclei data, and is further checked by terrestrial experimental and astrophysical constraints. The inclusion of $\ensuremath{\delta}$ meson reduces the neutron skin thickness of $^{208}\mathrm{Pb}$ as well as $^{48}\mathrm{Ca}$, which are turned out to be closely related. The energy of pygmy dipole resonance is in a large extent dominated by the excitations of neutrons near the Fermi surface. We found that the peak positions of the giant dipole resonance (GDR) and the PDR are sensitive to the nucleon-meson coupling in the scalar-isovector channel. A linear correlation between the neutron-proton effective mass splitting at saturation density and the relative offset of GDR and PDR is identified in $^{208}\mathrm{Pb}$.