Sensitivity of dark matter detectors to scalar-nucleon coupling

We consider a model of scalar field dark matter interacting with the visible matter through the scalar-nucleon Yukawa-type coupling. We show that such dark matter particles may be absorbed by atoms with ejection of atomic electrons if the mass of the scalar field exceeds atomic ionization potential. We derive the cross section of this process and show that it is strongly dominated by the dipole matrix element. We express this cross section through the one of the photoionization process in the leading electric dipole approximation. This relation allows one to look for signatures of the scalar dark matter with scalar-nucleon interaction in experiments based on the liquid noble gas and solid state detectors. Repurposing the null results of XENONnT experiment, we find limits on the scalar-nucleon interaction constant, $|g_{\phi n}|<1.2\times 10^{-10}$ at $m_\phi = 3$ keV. For applications to other liquid noble gas and solid state detectors, we numerically calculate the ionization cross section due to the scalar-nucleon interaction in Na, Si, Ar, Ge, I, Xe, and Tl atoms. Files with numerical data are provided. We also calculate the cross section for relativistic scalar particles which may be emitted from the Sun.