The contributions of three different types of driving terms are included in the estimation of the pd -> pd eta reaction at low energies. Near threshold, it is predicted that a two-step model involving an intermediate pion should be the most important but, as the energy approaches the threshold for eta production in the free nucleon--nucleon reaction, a pick-up mechanism with a spectator proton should become dominant. The total cross sections are underestimated by about a factor of two compared to experimental data but the discrepancies in the angular distributions are more serious, with no sign in the data for the peaks corresponding to the pick--up diagram.
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