Nuclear binding energies and liquid drop parameters in the extended Thomas-Fermi approximation

Using the extended Thomas-Fermi model, we calculate average nuclear binding energies with Skyrme type effective interactions. The total energy is minimized with respect to variations of the nucleon densities without the use of wave functions or adjustable parameters. We obtain binding energies only ～2–7 MeV higher than self consistenly averaged Hartree-Fock energies. By least-square fits we determine the liquid drop parameters of different effective interactions very accurately. Shell effects are added perturbatively and lead to total energies within 5–10 MeV of the exact Hartree-Fock results.