The two-pion exchange three-body nuclear force is discussed, and an effective two-body interaction derived which is capable of reproducing approximately its effect in nuclear matter. Treating the three-body interaction as a perturbation, the first order contribution to the binding energy of nuclear matter is derived using the actual three-body interaction, the effective interaction, and a recently suggested method in which the three-body effects are tarn approximately tint account by modifying the pion mass in the one-pion exchange potential. Although the latter method leads to a simple prescription for calculating the three-body effects hen no nucleon-nucleon cut-off is applied, the calculation is show to be considerably more difficult for the realistic case when a cut-off is applied, the calculation is shown to be considerably more difficult for the realistic case when a cut-off is introduced, and the modified pion mass is momentum dependent.
On the other hand, the effective interaction is found to reproduce quite well the actual three-body effects in first order. This fact is used as a basis for calculating the second order contribution using the effective interaction, and so an estimated of the three-body effects n nuclear matter is obtained. For a reasonable value of nucleon-nucleon cut-off, the three-body forces are shown to contribute approximately 6MeV additional binding to nuclei matter.