Diverse searches for direct dark matter in effective electromagnetic and leptophilic interactions resulting from new physics, as well as weakly interactive massive particles with unconventional electronic recoils, are intensively pursued. Low-energy backgrounds from radioactive $\gamma$ rays via Compton scattering and photon coherent scattering are unavoidable in terrestrial detectors. The interpretation of dark matter experimental data is dependent on a better knowledge of the background in the low-energy region. We provide a 2.3% measurement of atomic Compton scattering in the low-momentum transfer range of $180\mathrm{eV}/c$ to $25\mathrm{keV}/c$, using a 10 g germanium detector bombarded by a ${}^{137}\mathrm{Cs}$ source with a 7.2 m-Ci radioactivity, and the scattered photon collected by a cylindrical NaI[Tl] detector. The ability to detect Compton scattering’s doubly differential cross section gives a special test for clearly identifying the kinematic restraints in atomic many-body systems, notably, the Livermore model. Additionally, a low-energy-background comparison is made between coherent photon scattering and Compton scattering, replacing the scattering function of geant4 software, which uses a completely relativistic impulse approximation together with multiconfiguration Dirac-Fock wave functions. For the purpose of investigating sub-GeV mass and electronic recoil dark matter theories, signatures including low-energy backgrounds via high-energy $\gamma$ rays in germanium targets are discussed.

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• Dark matter direct detection
• Compton scattering