  We discuss the geometric phases and flux densities for the metastable states
of hydrogen with principal quantum number n=2 being subjected to adiabatically
varying external electric and magnetic fields. Convenient representations of
the flux densities as complex integrals are derived. Both, parity conserving
(PC) and parity violating (PV) flux densities and phases are identified.
General expressions for the flux densities following from rotational invariance
are derived. Specific cases of external fields are discussed. In a pure
magnetic field the phases are given by the geometry of the path in magnetic
field space. But for electric fields in presence of a constant magnetic field
and for electric plus magnetic fields the geometric phases carry information on
the atomic parameters, in particular, on the PV atomic interaction. We show
that for our metastable states also the decay rates can be influenced by the
geometric phases and we give a concrete example for this effect. Finally we
emphasise that the general relations derived here for geometric phases and flux
densities are also valid for other atomic systems having stable or metastable
states, for instance, for He with n=2. Thus, a measurement of geometric phases
may give important experimental information on the mass matrix and the electric
and magnetic dipole matrices for such systems. This could be used as a check of
corresponding theoretical calculations of wave functions and matrix elements.
