Axio-electric effect

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 an analytical formula which fits numerical calculations for the absorption cross sections and can be applied to 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.