The integrated cross section $widetildesigma$ for a special type of double polarized proton-deuteron scattering constitutes a null test forvtime-invariance violating but P-parity conserving effects. Using the Glauber theory for the $pd$ elastic scattering and different types of phenomenological T-odd P-even NN-interactions we show that the contribution of the lowest mass meson exchange, i.e. the $rho$-meson, to the null-test signal $widetildesigma$ vanishes. Variation of the cross section $widetildesigma$ due to strong hadronic and Coulomb interaction is studied and its energy dependence is calculated in the GeV region.
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