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The standard interpretation of direct-detection limits on dark matterinvolves particular assumptions of the underlying WIMP-nucleus interaction,such as, in the simplest case, the choice of a Helm form factor thatphenomenologically describes an isoscalar spin-independent interaction. Ingeneral, the interaction of dark matter with the target nuclei may well proceedvia different mechanisms, which would lead to a different shape of thecorresponding nuclear structure factors as a function of the momentum transfer$q$. We study to what extent different WIMP-nucleus responses can bedifferentiated based on the $q$-dependence of their structure factors (or "formfactors"). We assume an overall strength of the interaction consistent withpresent spin-independent limits and consider an exposure corresponding toXENON1T-like, XENONnT-like, and DARWIN-like direct detection experiments. Wefind that, as long as the interaction strength does not lie too much belowcurrent limits, the DARWIN settings allow a conclusive discrimination of manydifferent response functions based on their $q$-dependence, with immediateconsequences for elucidating the nature of dark matter.

Discriminating WIMP-nucleus response functions in present and future XENON-like direct detection experiments