AI 中文总结
研究暗物质与原子核相互作用从相干散射到非相干散射的过渡问题，采用一维N格点晶格模型精确计算暗物质散射，揭示相干与非相干散射区别及动量守恒约束变化，获三维晶体中相关计算的定量验证。
AI 中文摘要
暗物质与原子核的相互作用如何从产生单声子的相干散射 regime 过渡到单个核反冲 regime？回答这个问题依赖于理解多声子激发。多声子对解释低阈值直接探测实验很重要，但计算上难以处理。本文采用一维N格点晶格模型，其中暗物质散射可精确计算。我们表明相干和非相干散射的唯一区别在于相干散射中晶体动量守恒。随着产生更多声子，动量守恒约束变得不那么重要，从而过渡到非相干散射。通过一维结构因子的数值计算，我们还获得了在现实三维晶体中使用非相干近似计算亚GeV暗物质散射的定量验证。
英文摘要
How do dark matter-nucleus interactions transition from the regimes of coherent scattering, where single phonons are produced, to that of individual nuclear recoils? Answering this question relies on understanding multiphonon excitations. Multiphonons are important for interpreting low-threshold direct detection experiments, yet are computationally prohibitive to compute. In this paper, we employ a 1D $N$-site crystal lattice model where dark matter scattering can be computed exactly. We show that the only difference between coherent and incoherent scattering is that conservation of crystal momentum is enforced in coherent scattering. The momentum conservation constraint becomes less important as more phonons are produced, yielding the transition to incoherent scattering. Using numerical calculations of the 1D structure factor, we also obtain quantitative validation of using an incoherent approximation to compute sub-GeV dark matter scattering in realistic 3D crystals.
