T violation can be related with the CP-violation through Luders-Pauli's CPT theorem, which is related with a local Lorentz invariant field theory. The CP violation was discovered experimentally in the K 0 -meson decays about 35 years ago. The T violating interaction related with the CP violation violates parity as well. However, an extension of the theory beyond the locality of the interactions might violate the CPT theorem. The result of CPLEAR experiment [Angelopolos A. et al., (1998), "First direct observation of time-reversal non-invariance in the neutral-kaon system", Phys. Lett. B 444 43], which has given direct evidence of T violation in the elementary-particle phenomena, could be considered under assumption of the CPT invariance.

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A new method for the study of time reversal violation is described. It consists of measurements of the forward-backward asymmetry in individual gamma-ray transitions resulting from unpolarized neutron capture in p-wave resonances. An experiment with a 1,3 Cd target performed at the Dubna pulsed neutron source has been analyzed and a limit on the time reversal odd, parity even interaction extracted. The possibility of experiments using the powerful pulsed neutron source at Los Alamos is considered.PACS numbers: 25.40.Ny, 1 UO.Er CP nonconservation or T (time reversal) noninvariance was observed in the decay of neutral kaons long ago [1]. Attempts to search for this phenomenon in other processes have failed. Recently some possible tests using neutron optics experiments were discussed in a paper by Weidenmuller [2] and references therein. Interest in the neutron-nucleus interaction was stimulated by the discovery [3,4] of large P-(parity-) nonconserving effects near neutron p-wave resonances. These effects appeared to be enhanced by 3 to 6 orders of magnitude compared to the single-particle estimate Gm£ -10~7 (in units of h =c = 1 and G = \0~5m p~2 ).The enhancement was explained in terms of the P-nonconserving mixing of compound nuclear states with opposite parity (mixing of the p-wave resonance with the nearest s-wave resonances [5,6]). The concept of the spreading width of the weak interaction was brought into practice based on recent experimental results [7], It was shown by Bunakov and Gudkov [8,9] that possible T-noninvariant effects may be enhanced near p-wave resonances in the same manner as P-nonconserving effects. It has been suggested that a serach be made for P-conserving, T-noninvariant effects in polarized neutron transmission through aligned nuclear targets [10][11][12]. Such an effect would occur due to an s-[kxlKkl) term in the neutron-nucleus elastic forward scattering amplitude. Here s and I are the neutron and nucleus spins and k is neutron momentum. Bunakov [9] showed that the maximum value of the experimental polarization asymmetry in the cross section p is connected to the Tnoninvariant matrix element vj and to the /7-wave resonance level spacing D p by the approximate relation P^vJ/Dp.(1)

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