  Within the framework of Lorentz-violating extended electrodynamics, the Dirac
equation for a bound electron in an external electromagnetic field is
considered assuming the interaction with a CPT-odd axial vector background
$b_\mu$. The quasi-relativistic Hamiltonian is obtained using a $1/c$-series
expansion. Relativistic Dirac eigenstates in a spherically-symmetric potential
are found accurate up to the second order in $b_0$. $b_0$-induced CPT-odd
corrections to the electromagnetic dipole moment operators of a bound electron
are calculated that contribute to the anapole moment of the atomic orbital and
may cause a specific asymmetry of the angular distribution of the radiation of
a hydrogen atom.
