# Compton Scattering Energy Spectrum for Si and Ge Systems

## TL;DR

This paper analyzes the Compton scattering energy spectrum for silicon and germanium, using theoretical models to improve understanding relevant for dark matter detection experiments.

## Contribution

It provides a detailed quantitative analysis of Compton scattering spectra for Si and Ge using FEA and RIA, including ab initio relativistic calculations for atomic states.

## Key findings

- Spectra calculated for low-energy transfer regions.
- Comparison of FEA and RIA results.
- Implications for dark matter detection sensitivity.

## Abstract

In the present work, we study the atomic Compton Scattering which could have great impacts on dark matter direct detection experiments. We give a quantitative analysis of the Compton scattering energy spectrum for Si and Ge atomic systems. The theoretical results on Compton scattering are calculated within the frameworks of free electron approximation (FEA) and relativistic impulse approximation (RIA). The low-energy transfer and near photoionization threshold regions are especially considered in this work. In RIA calculation, to obtain the atomic ground states, we adopt an \emph{ab initio} calculation in the fully relativistic Dirac-Fock theory.