  We discuss the propagation of hydrogen atoms in static electric and magnetic
fields in a longitudinal atomic beam spin echo (lABSE) apparatus. There the
atoms acquire geometric (Berry) phases that exhibit a new manifestation of
parity-(P-)violation in atomic physics. We provide analytical as well as
numerical calculations of the behaviour of the metastable 2S states of
hydrogen. The conditions for electromagnetic field configurations that allow
for adiabatic evolution of the relevant atomic states are investigated. Our
results provide the theoretical basis for the discussion of possible
measurements of P-violating geometric phases in lABSE experiments.
