Determining the nuclear form factor for detection of dark matter in the relativistic mean field theory

TL;DR

This paper derives a nuclear form factor for dark matter detection using relativistic mean field theory, showing deviations from traditional models and analyzing energy dependence for Xe and Ge nuclei.

Contribution

It introduces a new nuclear form factor based on relativistic mean field theory, providing more accurate modeling for dark matter detection experiments.

Findings

Form factor slightly above 2PF model by 4-8%

Deviates from Helm form factor by 15-25%

Shows energy dependence for Xe and Ge nuclei

Abstract

In this work, we derive the nuclear form factor for the spin-independent collision between the WIMPs and nucleus in terms of the relativistic mean field (RMF) theory. Comparison with the traditional form factors which are commonly used in literature is given and it is found that our results are slightly above that of the 2PF model by 4% to 8%, but deviate from the Helm form factor by 15% to 25% for the whole recoil energy spectrum of 0$\sim $ 100 keV. Moreover, taking Xe and Ge as examples, we show the dependence of the form factor on the recoil energy.