Constraining simultaneously nuclear symmetry energy and neutron-proton effective mass splitting with nucleus giant resonances from a dynamical approach

Abstract

With a newly improved isospin- and momentum-dependent interaction and an isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, we have investigated the effects of the slope parameter $L$ of the nuclear symmetry energy and the isospin splitting of the nucleon effective mass $m_{n-p}^{\ast }=(m_n^{\ast }-m_p^{\ast })/m$ on the centroid energy of the isovector giant dipole resonance and the electric dipole polarizability in ${}^{208}$Pb. With the isoscalar nucleon effective mass $m_s^{\ast }=0.7m$ constrained by the empirical optical potential, we obtain a constraint of $L=64.29\pm 11.84(\mathrm{MeV})$ and $m_{n-p}^{\ast }=(-0.019\pm 0.090)\hat{I}´$, with $\hat{I}´$ being the isospin asymmetry of nuclear medium. With the isoscalar nucleon effective mass $m_s^{\ast }=0.84m$ extracted from the excitation energy of the isoscalar giant quadruple resonance in ${}^{208}$Pb, we obtain a constraint of $L=53.85\pm 10.29(\mathrm{MeV})$ and $m_{n-p}^{\ast }=(0.216\pm 0.114)\hat{I}´$.

10 pages, 6 figures, tighter constraints with more statistics