First-Order Symmetry Energy Induced by Neutron–Proton Mass Difference

The 1st-order symmetry energy coefficient of nuclear matter induced merely by the neutron–proton (n–p) mass difference is derived analytically, which turns out to be completely model-independent. Based on this result, the 1st-order symmetry energy E_\rm sym,1^(\rm npDM)(A) of heavy nuclei such as ^208Pb induced by the n–p mass difference is investigated with the help of a local density approximation combined with the Skyrme energy density functionals. Although E_\rm sym,1^(\rm npDM)(A) is small compared with the second-order symmetry energy, it cannot be dropped simply for an accurate estimation of nuclear masses as it is still larger than the rms deviation given by some accurate mass formulas. It is therefore suggested that one perhaps needs to distinguish the neutron mass from the proton one in the construction of nuclear density functionals.