The nucleon effective mass and its isovector splitting

Abstract

Using an energy density functional (EDF) based on the thermodynamic Gibbs-Duhem relation, found equivalent to the standard Skyrme EDF for infinite nuclear matter, it is demonstrated that the parameters of this EDF are not uniquely determined from the fit of the empirical and theoretical data related to nuclear matter. This prevents an unambiguous determination of the nucleon effective mass ($\frac{m_0^*}{m}$) and its isovector splitting ($Δm_0^*$). Complementary information from dipole polarizability of atomic nuclei helps in removing this ambiguity and plausible values of $\frac{m_0^*}{m}$ and $Δm_0^*$ can be arrived at. Presently considered fit data on infinite nuclear matter and dipole polarizability of finite nuclei yield $\frac{m_0^*}{m} =0.68 \pm 0.04 $ and $Δm_0^* =(-0.20 \pm 0.09)δ$. This EDF is consistent with the constraint on the maximum mass of the neutron star.