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

According to the Hugenholtz-Van Hove theorem, nuclear symmetry energy E-sym(rho) and its slope L(rho) at an arbitrary density rho are determined by the nucleon isovector (symmetry) potential U-sym(rho, k) and its momentum dependence partial derivative U-sym/partial derivative k. The latter determines uniquely the neutron-proton effective k-mass splitting m*(n-p) (rho, delta) (m*(n) - m*(p))/m in neutron-rich nucleonic matter of isospin asymmetry delta. Using currently available constraints on the E-sym(rho(0)) and L(rho(0)) 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 m*n-p(rho(0), delta) = 0.27. delta, it is currently not possible to scientifically state surely that the m*(n-p)(rho(0), delta) is positive within the present knowledge of the uncertainties. Quantifying, better understanding and then further reducing the uncertainties using modern statistical and computational techniques in extracting the E-sym(rho(0)) and L(rho(0)) from analyzing the experimental data are much needed. (C) 2013 Elsevier B.V. All rights reserved.