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In most direct detection experiments, the free nuclear recoil description ofdark matter scattering breaks down for masses $\lesssim$ 100 MeV, or when therecoil energy is comparable to a few times the typical phonon energy. For darkmatter lighter than 1 MeV, scattering via excitation of a single phonondominates and has been computed previously, but for the intermediate mass rangeor higher detector thresholds, multiphonon processes dominate. We perform thefirst calculation of the scattering rate via multiphonon production for theentire keV-GeV dark matter mass range, assuming a harmonic crystal target. Weprovide an analytic description that connects the single phonon, multiphonon,and the nuclear recoil regimes. Our results are implemented in the publicpackage $\texttt{DarkELF}$.

Dark matter direct detection from the single phonon to the nuclear recoil regime