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The scattering of sub-GeV dark matter in direct detection experiments happens
at characteristic wavelengths comparable or larger than the interparticle
spacing. Collective effects in the target material must therefore be accounted
for when calculating the scattering rate. For dark matter-nucleon couplings,
this implies matching onto the appropriate phonon effective theory and
calculating single and multi-phonon scattering amplitudes. For dark
matter-electron couplings, we make use of the energy loss formalism to predict
the scattering rate. Combining both techniques allows us to derive a formula
for the Migdal effect in crystals, which differs from prior calculations
performed in atomic systems.
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