Direct detection experiments are looking for nuclear recoils from scattering of sub-GeV dark matter (DM) in crystals, and have thresholds as low as $\sim 10\mathrm{eV}$ or DM masses of $\sim 100\mathrm{MeV}$. Future experiments are aiming for even lower thresholds. At such low energies, the free nuclear recoil prescription breaks down, and the relevant final states are phonons in the crystal. Scattering rates into single as well as multiple phonons have already been computed for a harmonic crystal. However, crystals typically exhibit some anharmonicity, which can significantly impact scattering rates in certain kinematic regimes. In this work, we estimate the impact of anharmonic effects on scattering rates for DM in the mass range $\sim 1–10\mathrm{MeV}$, where the details of multiphonon production are most important. Using a simple model of a nucleus in a bound potential, we find that anharmonicity can modify the scattering rates by up to two orders of magnitude for DM masses of $\mathcal{O}(\mathrm{MeV})$. However, such effects are primarily present at high energies where the rates are suppressed, and thus only relevant for very large DM cross sections. We show that anharmonic effects are negligible for masses larger than $\sim 10\mathrm{MeV}$.

中文翻译：

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亚GeV暗物质核反冲的非简谐效应

直接检测实验正在寻找晶体中亚 GeV 暗物质 (DM) 散射产生的核反冲，阈值低至$～10\mathrm{电子伏特}$或 DM 质量$～100\mathrm{兆伏}$。未来的实验目标是更低的阈值。在如此低的能量下，自由核反冲规定失效，相关的最终状态是晶体中的声子。谐波晶体的单个和多个声子的散射率已经被计算出来。然而，晶体通常表现出一定的非谐性，这会显着影响某些运动状态下的散射率。在这项工作中，我们估计了质量范围内非谐效应对 DM 散射率的影响$～1–10\mathrm{兆伏}$，其中多声子产生的细节是最重要的。使用束缚势中的原子核的简单模型，我们发现对于 DM 质量，非谐性可以将散射率修改最多两个数量级$\mathcal{氧}（\mathrm{兆伏}）$。然而，这种效应主要出现在速率受到抑制的高能量下，因此仅与非常大的DM横截面相关。我们表明，对于大于 的质量，非谐波效应可以忽略不计$～10\mathrm{兆伏}$。