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

## TL;DR

This study uses a dynamical approach with improved interactions to constrain nuclear symmetry energy and neutron-proton effective mass splitting via giant resonance data in lead-208, providing specific parameter ranges.

## Contribution

It introduces an advanced isospin- and momentum-dependent interaction and applies a transport model to simultaneously constrain symmetry energy slope and effective mass splitting.

## Key findings

- Constrained L to approximately 54-64 MeV depending on the effective mass.
- Determined neutron-proton effective mass splitting to be slightly negative or positive within uncertainties.
- Provided improved bounds on nuclear matter properties relevant for nuclear physics and astrophysics.

## 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 $m_{n-p}^*=(m_n^*-m_p^*)/m$ on the centroid energy of the isovector giant dipole resonance and the electric dipole polarizability in $^{208}$Pb. With the isoscalar nucleon effective mass $m_s^*=0.7m$ constrained by the empirical optical potential, we obtain a constraint of $L=64.29\pm11.84 (\rm MeV)$ 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 $^{208}$Pb, we obtain a constraint of $L=53.85\pm10.29 (\rm MeV)$ and $m_{n-p}^*= (0.216 \pm 0.114)\delta$.