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An approach for the three-body force effect in the optical limit approximation is suggested. The differential cross sections of p−, p− and π − − d elastic scattering at 1.75 and 12.8 GeV/c for incident proton, 2 GeV/c for anti-proton and 9 GeV/c for pion are studied. The D-state and phase variation effects are considered. The experimental data is well described including the 2π -exchange three-body force. The three-body force effect, in this approach, plays a principal role over the complete range of momentum transfer square where the data is available.

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An approach for the three-body force effect is used to study p-[Formula: see text] elastic scattering at energies 350–1728[Formula: see text]MeV. The multiple scattering theory of Glauber and the optical limit approximation are used in calculations of elastic scattering differential cross-section at 350, 600, 800, 1000 and 1728[Formula: see text]MeV. The inclusion of 2[Formula: see text]-exchange three-nucleon force improves the agreement with the experimental data for both approximations. The results of optical limit approximation without three-nucleon force effect are clearly smaller than the results of multiple scattering theory for [Formula: see text] due to the absence of multiple scattering terms in the first. However, with inclusion of three-nucleon force, the results of both approximations are approximately similar.

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