Abstract
Recently, the importance of the electronic many-body effect in the dark matter (DM) detection has been recognized and a coherent formulation of the DM-electron scattering in terms of the dielectric response of the target material has been well established in literatures. In this paper, we put relevant formulas into practical density functional theory (DFT) estimation of the excitation event rates for the diamond and silicon semiconductor targets. Moreover, we compare the event rates calculated from the energy loss functions with and without the local field effects. For a consistency check of this numerical method, we also compare the differential spectrum and detection reach of the silicon with those computed with the $\mathtt{GPAW}$ code. It turns out that this DFT approach is quite consistent and robust. As an interesting extension, we also investigate the in-medium effect on the detection of the solar-reflected DM flux in silicon-based detectors, where the screening effect is found to be also remarkable in the optically thick regime, and to turn insignificant in the optically thin regime, depending on the energies of the reflected DM particles.
Highlights
In recent years, both theorists and experimentalists began to shift their focus in other directions beyond the weakly interacting massive particles (WIMPs)
The importance of the electronic many-body effect in the dark matter (DM) detection has been recognized, and a coherent formulation of the DM-electron scattering in terms of the dielectric response of the target material has been well established in literatures
We perform a detailed derivation of the electronic excitation event rate induced by the DM-electron interaction, taking into account the screening effect, which is described by the energy loss function (ELF), or the inverse dielectric function
Summary
Both theorists and experimentalists began to shift their focus in other directions beyond the weakly interacting massive particles (WIMPs). As is seen from the following discussions, only the diagonal components of the inverse dielectric function are relevant for the description of the screening effect, if the crystal structure is approximated as isotropic In this case, the effective inverse dielectric function Im1⁄2−1=εðQ; ωÞ is approximated as the diagonal components Im1⁄2ε−G1;Gðq; ωÞ averaged over G and q. [29], there exists an alternative definition of ELF, where one first averages the diagonal elements εG;Gðq; ωÞ over G and q to obtained an effective dielectric function εðQ; ωÞ, and the inverse dielectric function is approximated as Im1⁄2−1=εðQ; ωÞ. In this case, the LFEs are not included.
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