The energy-density formalism is applied to finite nuclei. The total energy of the many-nucleon system is expressed as a functional $E\left(\rho \right)$ of the local density $\rho \mathrm{}\left(r\right)\mathrm{}$, and the ground-state density distribution is found by minimization with respect to $\rho \mathrm{}\left(r\right)\mathrm{}$. The functional of the potential energy is directly derived from a nuclear-matter calculation with variable neutron excess by Brueckner et al. The density-gradient correction which takes care of the density variation at the nuclear surface contains an exchange- and a correlation-energy part. In a first attempt, proton and neutron densities are assumed proportional; therefore the present calculation is limited to light nuclei. The density distributions are found to be of the so-called modified Gaussian type with a cubic polynomial. Binding energy, radius, and surface thickness are in good agreement with experiment.

• Received 19 February 1968

DOI:https://doi.org/10.1103/PhysRev.171.1188