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The interaction of elementary particles of several different spins due to the exchange of a graviton is investigated. The exact one-graviton exchange potentials are obtained, and then simplified by making various approximations. The gravitational interaction is found to be independent of the spins of the particles, provided that the distance between them is large compared with their Compton wavelengths. It is pointed out that the spin-dependent interaction terms, whose range is of the order of the Compton wavelength, may be of interest in the theory of gravitational collapse. It is also shown that the gravitational particle-anti-particle interaction differs from the corresponding particle-particle interaction only by contact interaction terms.
Barker et al. (Fri,) studied this question.