Many-Body Forces and Nuclear Saturation

Abstract

Nuclear saturation is studied with many-body interactions derived from pseudoscalar meson theory with pseudoscalar coupling. All parameters appearing in this calculation are fixed on the basis of the work of L\'evy, who has shown that leading terms in a perturbation deduction of the two-body interaction are well fitted to reproduce the experimental data. The leading term in the $n$-body potential depends only on the interparticle distances and is repulsive (attractive) for $n$ odd (even). The energy of the nucleus is calculated with potentials up through five-body interactions and with neglect of Coulomb and surface effects. Saturation properties derived from these considerations are in accord with experience. Antisymmetrization of the nuclear wave function reduces the many-body interaction energies considerably by inhibiting the close approach of many particles. Thus the Pauli exchange terms are found to reduce the five-body interaction energy by 76 percent and to give a rapid convergence for the expansion in $n$-body forces.