  In the leading paradigm of modern cosmology, about 80% of our Universe's
matter content is in the form of hypothetical, as yet undetected particles.
These do not emit or absorb radiation at any observable wavelengths, and
therefore constitute the so-called Dark Matter (DM) component of the Universe.
Detecting the particles forming the Milky Way DM component is one of the main
challenges for astroparticle physics and basic science in general. One
promising way to achieve this goal is to search for rare DM-electron
interactions in low-background deep underground detectors. Key to the
interpretation of this search is the response of detectors' materials to
elementary DM-electron interactions defined in terms of electron wave
functions' overlap integrals. In this work, we compute the response of atomic
argon and xenon targets used in operating DM search experiments to general, so
far unexplored DM-electron interactions. We find that the rate at which atoms
can be ionized via DM-electron scattering can in general be expressed in terms
of four independent atomic responses, three of which we identify here for the
first time. We find our new atomic responses to be numerically important in a
variety of cases, which we identify and investigate thoroughly using effective
theory methods. We then use our atomic responses to set 90% confidence level
(C.L.) exclusion limits on the strength of a wide range of DM-electron
interactions from the null result of DM search experiments using argon and
xenon targets.
