  We examine how nuclear masses are related to the density dependence of the
symmetry energy. Using a macroscopic nuclear model we calculate nuclear masses
in a way dependent on the equation of state of asymmetric nuclear matter. We
find by comparison with empirical two-proton separation energies that a smaller
symmetry energy at subnuclear densities, corresponding to a larger density
symmetry coefficient L, is favored. This tendency, which is clearly seen for
nuclei that are neutron-rich, nondeformed, and light, can be understood from
the property of the surface symmetry energy in a compressible liquid-drop
picture.
