Can the nuclear many-body problem be solved by using perturbation theory?

Abstract

A static two-body potential of Serber exchange character with a repulsive core fails to produce saturation in first-order perturbation theory, if the core is treated as a pseudo-potential. (We are designating the order of the term in a joint expansion in powers of the strength of the attractive potential and in the range of the repulsive core). Second-order terms are estimated from the condition that saturation should be achieved at the observed density without invoking many-body forces. We conclude that any static potential that produces saturation at about the empirical density must have substantial second-order terms, of magnitude 10 MeV/particle or more. We discuss the use of a velocity-dependent two-body potential to replace the infinite repulsive core, and find that second-order terms may be much smaller if we use a velocity-dependent potential.