Notes on T-invariance and polarization effects in the elastic scattering of a particle with spin 1/2 on the unpolarized target

In the frames of T-invariance the analysis of the general dependence of the elastic scattering effective cross section of a particle with spin 1/2 on the unpolarized target with arbitrary spin upon the initial and final polarizations of the particle has been performed. On the base of the T-symmetry of the differential scattering cross section only, without traditional consideration of the spin structure of scattering amplitudes, a simple proof of the Wolfenstein theorem is obtained (this theorem states that the degree of transverse polarization, arising in the elastic scattering of an unpolarized particle on the unpolarized target, is equal to the coefficient of left-right asymmetry in the elastic scattering of the same but transversally polarized particle on the same target). Meantime, it is ascertained that in the case of P-parity violation (conserving T-invariance) there exists no analogous universal relation between the degree of longitudinal polarization and the coefficient of P-odd spin asymmetry in the scattering of longitudinally polarized particles. It is shown, further, that under T-invariance the amplitude and cross section of 'backward' scattering of neutrons on zero-spin nuclei do not depend on spin, and the observation of such a dependence would testify unambiguously to the T-invariance violation. However, according to the fulfilled estimates, the T-noninvariant spin asymmetry in the 'backward' scattering is very small (about 10-8 - 10-7)