Reexamining the relation between the binding energy of finite nuclei and the equation of state of infinite nuclear matter

The energy density is calculated in coordinate space for C12, Ca40, Ca48, and Pb208 using a dispersive optical model constrained by all relevant data including the corresponding energy of the ground state. The energy density of Be8 is also calculated using the Green's-function Monte Carlo method employing the Argonne-Urbana two- and three-body interactions. The nuclear interior minimally contributes to the total binding energy due to the 4πr2 phase-space factor. Thus, the volume contribution to the energy in the interior is not well constrained. The dispersive-optical-model energy densities are in good agreement with ab initio self-consistent Green's-function calculations of infinite nuclear matter restricted to treat only short-range and tensor correlations. These results call into question the degree to which the equation of state for nuclear matter is constrained by the empirical mass formula. In particular, the results in this paper indicate that saturated nuclear matter does not require the canonical value of 16-MeV binding per particle but only about 13-14 MeV when the interior of Pb208 is considered.