What can we learn about the neutron-proton effective mass splitting from constraints on the density dependence of nuclear symmetry energy around normal density?    [PDF]

Bao-An Li, Xiao Han
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 24 recent analyses of various terrestrial nuclear laboratory experiments and astrophysical observations, we infer the corresponding neutron-proton effective k-mass splitting $m^*_{n-p}(\rho_0,\delta)$. While the mid-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$=0.24\cdot\delta$, reduced experimental error bars and more complete information about the uncertainties in extracting the \es0 and \l0 from data using various models are much needed in order to access more accurately how reliably the inferred $m^*_{n-p}(\rho_0,\delta)$ can be used in investigating many interesting issues in both nuclear physics and astrophysics.
View original: http://arxiv.org/abs/1304.3368