UC San Diego

In dark matter direct detection experiments, the free nuclear recoil description breaks down as the de Broglie wavelength of dark matter approaches the typical atomic spacing of the target material. In this work, we investigate the particular case of scattering off of crystal targets, whose collective excitations are well understood as phonons. As experimental energy thresholds decrease, it becomes increasingly important to understand the response of targets to energy depositions below the nuclear recoil scale. For dark matter masses lighter than 1 MeV, the scattering rate is dominated by single phonons, while at masses larger than 100 MeV, we expect the scattering to approach the free nuclear recoil result. Starting from the phonon formalism in the harmonic crystal approximation, we perform the first calculations of scattering rates in the intermediate 1-100 MeV mass regime where multiphonon process dominate and demonstrate how the multiphonon response smoothly approaches free nuclear recoil. We then drop the harmonic approximation and calculate possible corrections to the scattering rates due to crystal anharmonicity. We find these anharmonic corrections to be large at small dark matter masses ∼ MeV and large experimental thresholds ∼ 100 MeV, but approach the harmonic result as the DM mass increases.