Axionlike Particles (ALPs) can be produced in the Sun and is a viable candidate to the Cosmological Dark Matter. It can decay to two photons or interact with matter via Inverse Primakoff (IP) scattering. We identify inelastic channels to the IP-processes due to atomic excitation and ionization in additional to the elastic scattering. Their cross-sections are derived with full electromagnetic fields of atomic charge and current densities, and computed by well-benchmarked atomic many-body methods. New constraints on Axion-photon-photon coupling can be probed by current and future dark matter detectors.