Time-Reversal Violation in Threshold $\vec{n}$ $\vec{p}$ Scattering

We investigate parity and time-reversal violation in neutron-proton scattering in the optical regime. We calculate the neutron spin rotation and analyzing power in scattering on polarized protons. This allows us to quantify the sensitivity that such experiments should aim for in order to be competitive to present-day measurements of the neutron electric dipole moment in constraining the $P$- and $T$-odd two-nucleon interaction. While state-of-the-art techniques fall short by some three orders of magnitude for the neutron-proton case, specific neutron-nucleus experiments look promising, provided certain experimental and theoretical challenges are met.