Nuclear Saturation and Two-Body Forces. II. Tensor Forces

The method developed in a previous paper for the treatment of the problem of nuclear saturation has been extended to the case of tensor forces. The general result obtained expresses the many-body potential energy as a function of the triplet and singlet eigen phase shifts for scattering. One consequence is that the tensor force, which averages to zero if Born approximation is used to evaluate the scattering, now gives a very sizable contribution to the potential energy. Phase shifts have been determined for a specific potential model derived from pseudoscalar meson theory, and are shown to give scattering up to 90 Mev which is in good agreement with total cross section and in approximate agreement with angular distributions. Use of these results to evaluate the total energy (neglecting Coulomb effects) in heavy nuclei shows that for a typical case ($A=300\mathrm{}$) saturation occurs at a radius $1.15\times {10}^{-13\mathrm{}}{A}^{\frac{1}{3}}$ with a binding energy of 10 Mev per particle. If surface effects are neglected, however, the density at saturation increases by a factor of 1.74 with an increase in mean binding energy to 39 Mev. The potential energy per particle has also been determined as a function of its momentum. In the finite nucleus ($A=300\mathrm{}$) the potential depth varies from -82 Mev for a particle of zero momentum to -32 Mev for a particle at the top of the Fermi momentum distribution. Arguments are presented which suggest that this effect is to a large extent independent of the model used.