Unrestricted Hartree-Fock Treatment of Finite Nuclei

A smooth, nonlocal interaction which fits two-body scattering data reasonably well is used in a Hartree-Fock calculation of the binding energies and quadrupole moments of the even-even nuclei with $A$ between 4 and 40. The calculation is unrestricted in that the orbitals of all the particles are determined self-consistently with both radial and angular variations allowed. For the deformed nuclei, a naive rotational correction is made to allow comparison with experiment. The second-order term is computed in a perturbation expansion for which the Hartree-Fock result is the first-order term. The perturbation series apparently converges, and the results to second order agree quite well with experiment. The single-particle energies of the various nuclei are calculated in first and second order with polarization taken into account. Finally, the symmetry energy is studied in the $A=48\mathrm{}$ system.