Can sub-GeV dark matter coherently scatter on the electrons in the Atom?
A novel detection of sub-GeV dark matter is proposed in the paper. The electron cloud is boosted by the dark matter and emits an electron when it is dragged back by the heavy nucleus, namely the coherent scattering of the electron cloud of the atom. The survey in the X-ray diffraction shows that the atomic form factors are much more complicate than the naive consideration. The results of the relativistic Hartree-Fock(RHF) method give non-trivial shapes of the atoms. The detailed calculation of the recoil of the electron cloud, the kinetics, the fiducial cross section and the corresponding calculation of detection rate are given analytically. The numerical results show that the limits of the RHF form factors are much stringent than the recoil of a single electron, almost 4 orders stronger, and also gives tight limitations comparing to the Migdal effect below about several hundred MeV. The physical picture and the corresponding results are promising and need further explorations.