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arXiv · 2509.14534

Relativistic Atomic Effects of Dark Matter Electron Scattering

Shao-Feng Ge·Jie Sheng·Chuan-Yang Xing
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Abstract

The dark matter scattering with atomic bound electrons is a crucial avenue for exploring the sub-GeV mass range. The commonly used factorization, where atomic effects are encoded in an overall form factor multiplying the free-electron scattering matrix element, is not necessarily true. Especially, the free-electron kinematics and phase space cannot consistently apply for off-shell bound electrons. Starting from the first principles of quantum field theory, we establish a theoretically consistent formalism to account for the atomic effects. By taking the scalar-type interaction as an example, we investigate the difference between the non-relativistic and relativistic calculations to show that the relativistic effects can lead to a $30\% \sim 50\%$ reduction in the scattering phase space and differential cross section. In other words, not just a theoretically consistent formalism for the atomic effects but also relativistic calculation with Dirac equation are necessary.

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Shao-Feng Ge, Jie Sheng, Chuan-Yang Xing. 2025-09-18. Relativistic Atomic Effects of Dark Matter Electron Scattering. https://doi.org/10.1140/epjc%2Fs10052-026-15838-2

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