Constraining the neutron-proton effective mass splitting using empirical constraints on the density dependence of nuclear symmetry energy around normal density

Understand

According to the Hugenholtz-Van Hove theorem, nuclear symmetry energy \esym and its slope \lr at an arbitrary density $\rho$ are determined by the nucleon isovector (symmetry) potential \usym and its momentum dependence $\frac{\partial U_{sym}}{\partial k}$.

• The latter determines uniquely the neutron-proton effective k-mass splitting $m^*_{n-p}(\rho,\delta)\equiv (m_{\rm n}^*-m_{\rm p}^*)/m$ in neutron-rich nucleonic matter of isospin asymmetry $\delta$.
• Using currently available constraints on the \es0 and \l0 at normal density $\rho_0$ of nuclear matter from 28 recent analyses of various terrestrial nuclear laboratory experiments and astrophysical observations, we try to infer the corresponding neutron-proton effective k-mass splitting $m^*_{n-p}(\rho_0,\delta)$.
• While the mean values of the $m^*_{n-p}(\rho_0,\delta)$ obtained from most of the studies are remarkably consistent with each other and scatter very closely around an empirical value of \emass$=0.27\cdot\delta$, it is currently not possible to scientifically state surely that the \emass is positive within the present knowledge of the uncertainties.