Hartree-Fock calculations have been performed for the even-even $N=Z$ nuclei from $A=4\mathrm{}$ to $A=40\mathrm{}$. The calculations use a velocity-dependent interaction which contains two-body spin-orbit and tensor terms, and which was especially derived for use in HF calculations. Effects of truncation are made minimal by using a basis of Cartesian harmonic-oscillator wave functions. Nuclear sizes and single-particle energies are in reasonable agreement with experiment; however, total binding energies are much too small. Comparison is made with other recent calculations.

A formalism, proposed previously, which represents a generalization of the separable-potential model is applied to the four-nucleon system. It consists essentially in approximating the off-shell nucleon-deuteron scattering amplitude—as obtained in the separable-potential model—again by separable expressions. We arrive thereby at effective two-particle equations which are solvable by standard methods. The determination of the required separable terms is studied in detail. A first attempt to solve approximately our final integral equations is made. The results demonstrate the applicability of the method.

The Thomas-Fermi integral theory of the nuclear surface is shown to have singular solutions for the nuclear density. This failure is traced to its inadequate representation of the behavior of wave functions in a potential. A new theory based on approximate wave functions is developed and shown to be asymptotic to the Thomas-Fermi theory in the interior of the nucleus. An improved treatment of exchange forces is shown to be essential to obtaining realistic solutions.