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Atomic Form Factors and Inverse Primakoff Scattering of Axion

We reexamine the inverse Primakoff scattering of axions, whose scattering cross section depends on the distribution of electrons in target atoms. We evaluate it using a form factor computed with a relativistic Hartree-Fock wave function and compare it with the previous results obtained with those based on the screened Coulomb potential for the electrostatic field in the atom. We take xenon as an example for the target atom and show that the scattering cross section was overestimated by more than an order of magnitude for axions with $\lesssim O(10)$ keV energies, like solar axions. It is also found that inelastic scattering processes, in which the final state contains an excited or ionized atom, can be comparable or even be dominant when the size of momentum transfer is $\lesssim 1$ keV. For more energetic axions, on the other hand, the total scattering cross section is found to be well approximated by a simple expression and has little dependence on the atomic structure. As an application of this result, we consider supernova axions, whose energy is 10-100 MeV, and show that $O(1)$ inverse Primakoff events are expected for axions from a nearby supernova in the future neutrino experiments, which may warrant a more detailed study on the search strategy of this process.