  We reconsider parity violation experiments in atomic hydrogen and deuterium
in the light of existing tests of the Electroweak interactions, and assess
whether new experiments, using improved experimental techniques, could make
useful contributions to testing the Standard Model (SM). We find that, if
parity experiments in hydrogen can be done, they remain highly desirable
because there is negligible atomic-physics uncertainty and low energy tests of
weak neutral current interactions are needed to probe for new physics beyond
the SM. Of particular interest would be a measurement of the nuclear spin
independent coupling C_{1D} for the deuteron at a combined error (theory +
experiment) of 0.3%. This would provide a factor of three improvement to the
precision on sin^2 theta_W at very low momentum transfer provided by heavy atom
Atomic Parity Violation (APV) experiments. Also, experiments in H and D could
provide precise measurements of three other electron-nucleon,
weak-neutral-current coupling constants: C_{1p}, C_{2p},and C_{2D}, which have
not been accurately determined to date. Analysis of a generic APV experiment in
deuterium indicates that a 0.3% measurement of C_{1D} requires development of a
slow (77K) metastable beam of ~ 5x10^14 D(2S) s^-1 per hyperfine component. The
advent of UV radiation from free electron laser (FEL) technology could allow
production of such a beam.
