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 throws away 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 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.
