  Background: Time-reversal-invariance violation, or equivalently CP violation,
may explain the observed cosmological baryon asymmetry as well as signal
physics beyond the Standard Model. In the decay of polarized neutrons, the
triple correlation D<J_{n}>\cdot(p_{e}\timesp_{\nu}) is a parity-even,
time-reversal- odd observable that is uniquely sensitive to the relative phase
of the axial-vector amplitude with respect to the vector amplitude. The triple
correlation is also sensitive to possible contributions from scalar and tensor
amplitudes. Final-state effects also contribute to D at the level of 1e-5 and
can be calculated with a precision of 1% or better. Purpose: We have improved
the sensitivity to T-odd, P-even interactions in nuclear beta decay. Methods:
We measured proton-electron coincidences from decays of longitudinally
polarized neutrons with a highly symmetric detector array designed to cancel
the time-reversal-even, parity-odd Standard-Model contributions to polarized
neutron decay. Over 300 million proton-electron coincidence events were used to
extract D and study systematic effects in a blind analysis. Results: We find D
= [-0.94\pm1.89(stat)\pm0.97(sys)]e-4. Conclusions: This is the most sensitive
measurement of D in nuclear beta decay. Our result can be interpreted as a
measurement of the phase of the ratio of the axial-vector and vector coupling
constants (CA/CV= |{\lambda}|exp(i{\phi}_AV)) with {\phi}_AV = 180.012{\deg}
\pm0.028{\deg} (68% confidence level) or to constrain time-reversal violating
scalar and tensor interactions that arise in certain extensions to the Standard
Model such as leptoquarks. This paper presents details of the experiment,
analysis, and systematic- error corrections.
