  Using the relativistic Hartree-Fock approximation, we calculate the rates of
atomic ionization by absorption of axions of the energies up to 100 keV and for
an arbitrary value of the axion mass. We present numerical results for atoms
used in the low radioactive background searches of dark matter (e.g. Ar, Ge and
Xe), as well as the analytical formula which fits numerical calculations for
the absorption cross sections and can be applied for other atoms, molecules and
condensed matter systems. Using the cross-sections for the axio-electric
effect, we derive the counting rates induced by solar axions and set limits on
the axion coupling constants.
