  On the basis of a three-dimensional Hubbard model, the superconducting
mechanism of CeIn3 under high pressure is investigated by the third-order
perturbation theory with respect to the on-site Coulomb interaction U. Here we
propose the d-wave pairing state induced by antiferromagnetic spin
fluctuations. The estimated superconducting transition temperature is lower by
one order than that in the two-dimensional system for the same value of U/W
(W=bandwidth). This result is consistent with the difference between CeIn3 and
CeRhIn5.
