Determining Nuclear Form factor for Detection of Dark Matter in Relativistic Mean Field Theory

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 ∽ 100keV. Moreover, taking Xe and Ge as examples, we show the dependenceof the form factor on the recoil energy.