Pion Theory of Three-Body Forces

Three-body forces among three nucleons are calculated on the basis of the static pion theory. It is assumed that only one pion each is exchanged between nucleon (1) and (2), and between (2) and (3), although any number of pions may be emitted and absorbed by the same nucleon. The validity of this calculation is therefore limited to the case when every nucleon is well separated from the other. This three-body potential has a contribution of about 0.22 Mev to the triton binding. In a heavy nucleus the binding energy due to this potential is attractive and about ten percent of that due to two-body interaction. This effect can be roughly stated as follows. Within a nuclear matter the potential between two nucleons takes a different shape due to many body forces. The depth is increased by 9 percent and the range is decreased by 13 percent.