We point out that the direct detection of dark matter via its
electro-magnetic polarizability is described by two new nuclear form factors,
which are controlled by the 2-nucleon nuclear density. The signature manifests
a peculiar dependence on the atomic and mass numbers of the target nuclei, as
well as on the momentum transfer, and can differ significantly from experiment
to experiment. We also discuss UV completions of our scenario.Comment: 18 pages in JHEP style, 3 figures, and an appendix; published versio