  The standard interpretation of direct-detection limits on dark matter
involves particular assumptions of the underlying WIMP-nucleus interaction,
such as, in the simplest case, the choice of a Helm form factor that
phenomenologically describes an isoscalar spin-independent interaction. In
general, the interaction of dark matter with the target nuclei may well proceed
via different mechanisms, which would lead to a different shape of the
corresponding nuclear structure factors as a function of the momentum transfer
$q$. We study to what extent different WIMP-nucleus responses can be
differentiated based on the $q$-dependence of their structure factors (or "form
factors"). We assume an overall strength of the interaction consistent with
present spin-independent limits and consider an exposure corresponding to
XENON1T-like, XENONnT-like, and DARWIN-like direct detection experiments. We
find that, as long as the interaction strength does not lie too much below
current limits, the DARWIN settings allow a conclusive discrimination of many
different response functions based on their $q$-dependence, with immediate
consequences for elucidating the nature of dark matter.
