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We investigate the superconducting mechanism and the transition temperatureof heav y fermion superconductor UPd_2Al_3 on the basis of a single bandtwo-dimensional Hubbard model on triangular lattice, whi ch represents the mostheavy band of UPd_2Al_3. Both normal and anomalous self-energies are calculatedup to third order with respect to the Coulomb repulsion U between itinerantelectrons. The superconducting transition temperature is obtained by solvingthe Eliashberg's equation. Reasonable transition temperatures are obtained formoderately large U. It is fou nd that the momentum and frequency dependence ofspin fluctuations given by RPA-like terms gives rise to the d-wave pairingstate, while the vertex correction terms are important for obtaining reasonabletransition tempe ratures. These results seem to show that the superconductivityin UPd_2Al_3 can be explained by the perturbation theory with respect to U.Comment: 26 page

Perturbation Theory on the Superconductivity of Heavy Fermion Superconductor UPd2Al3