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

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 $m_{n-p}^{*}=(m_n^{*}-m_p^{*})/m$ on the centroid energy of the isovector giant dipole resonance and the electric dipole polarizability in ${}^{208}\mathrm{Pb}$. With the isoscalar nucleon effective mass $m_s^{*}=0.7m$ constrained by the empirical optical potential, we obtain a constraint of $L=64.29\pm 11.84\left(\mathrm{MeV}\right)$ and $m_{n-p}^{*}=(-0.019\pm 0.090)\delta$, with $\delta$ being the isospin asymmetry of nuclear medium. With the isoscalar nucleon effective mass $m_s^{*}=0.84m$ extracted from the excitation energy of the isoscalar giant quadruple resonance in ${}^{208}\mathrm{Pb}$, we obtain a constraint of $L=53.85\pm 10.29\left(\mathrm{MeV}\right)$ and $m_{n-p}^{*}=(0.216\pm 0.114)\delta$.

Figure 1

Single-particle potentials in symmetric nuclear nuclear matter at the saturation density as a function of the nucleon energy subtracted by the nucleon rest mass from the ImMDI interaction with different isoscalar nucleon effective mass $m_s^{*}$. The real part of the optical potential extracted from proton-nucleus scatterings by Hama et al. [62, 63] is shown by scatters for comparison.

Figure 2

The time evolution of the isoscalar giant quadruple moment in ${}^{208}\mathrm{Pb}$ (a) and the correlation between the corresponding excitation energy $E_x$ and the isoscalar nucleon effective mass $m_s^{*}$ (b).

Figure 3

The time evolution of the isovector giant dipole moment (a) and the corresponding strength function (b) in ${}^{208}\mathrm{Pb}$ with $m_s^{*}=0.7m$.

Figure 4

The linear relations between the symmetry energy slope parameter $L$ as well as the isovector nucleon effective mass $m_v^{*}$ and the centroid energy $E_{-1}$ as well as the electric dipole polarizability ${\alpha }_D$ from the IVGDR in ${}^{208}\mathrm{Pb}$, respectively, with the isoscalar nucleon effective mass $m_s^{*}=0.7m$.

Figure 5

Same as Fig. 3 but with the isoscalar nucleon effective mass $m_s^{*}=0.84m$.

Figure 6

Same as Fig. 4 but with the isoscalar nucleon effective mass $m_s^{*}=0.84m$.