  We combine the non-relativistic effective theory of dark matter (DM) -
electron interactions with linear response theory to obtain a formalism that
fully accounts for screening and collective excitations in DM-induced
electronic transition rate calculations for general DM-electron interactions.
In the same way that the response of a dielectric material to an external
electric field in electrodynamics is described by the dielectric function, so
in our formalism the response of a detector material to a DM perturbation is
described by a set of generalised susceptibilities which can be directly
related to densities and currents arising from the non-relativistic expansion
of the Dirac Hamiltonian. We apply our formalism to assess the sensitivity of
non-spin-polarised detectors, and find that in-medium effects significantly
affect the experimental sensitivity if DM couples to the detector's electron
density, while being decoupled from other densities and currents. Our formalism
can be straightforwardly extended to the case of spin-polarised materials.
