Time-reversal invariance violation effect in $\bm{dd}$ scattering

A formalism has been developed for calculating the signal of violation of $T$ invariance, provided that $P$ invariance is preserved during the scattering of tensor-polarized deuterons on vector-polarized ones based on the Glauber theory with the full consideration of spin dependence of $NN$ elastic scattering amplitudes and spin structure of colliding deuterons. The numerical calculations have been carried out in the range of laboratory proton energies $T_p=0.1$--$1.2$ GeV using the SAID database for spin amplitudes and in the energy region of the SPD NICA experiment corresponding to the invariant mass of the interacting nucleon pairs $\sqrt{s_{NN}}= 2.5$--$25$ GeV, using two phenomenological models of $pN$ elastic scattering. It is found that only one type of the $T$ non-invariant $P$-invariant $NN$ interaction gives a non-zero contribution to the signal in question, that is important for isolating an unknown constant of this interaction from the corresponding data.