Abstract 

A formalism has been developed for calculating the signal of violation of
time-reversal invariance, provided that
space-reflection ({\color{blue} parity}) invariance
is conserved during the scattering of tensor-polarized deuterons on vector-polarized
 ones. The formalism is 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 of $T_p=0.1$--$1.2$ 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 time-reversal non-invariant
{\color{blue} parity} conserving
 $NN$ 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.
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