  We discuss and calculate parity conserving (PC) and parity violating (PV)
geometric phases for the metastable 2S states of hydrogen and deuterium. The
atoms are supposed to be subjected to slowly varying electric and magnetic
fields which act as external parameters for the atoms. Geometric flux density
fields are introduced which allow for an easy overview how to choose the paths
in parameter space in order to obtain only PC or only PV geometric phases. The
PV phases are calculated in the Standard Model of particle physics. Even if
numerically they come out small they have interest of principle as a new
manifestation of parity violation in atomic physics.

Atomic Physics;High Energy Physics - Phenomenology