Revisiting 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 $^{12}$C, $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb using a dispersive optical model (DOM) constrained by all relevant data including the energy of the ground state. For $^{12}$C, the energy density is also calculated using the variational 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 4$\pi r^2$ phase space factor. Thus, the volume contribution to the energy in the interior is not well constrained. The DOM energy densities are in reasonable 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 letter indicate that the binding energy of saturated nuclear matter does not require the canonical value of 16 MeV per particle but only about 13-14 MeV when the interior of $^{208}$Pb is considered.