Milli-interacting Dark Matter

We present a dark matter model reproducing well the results from DAMA/LIBRA and CoGeNT and having no contradiction with the negative results from XENON100 and CDMS-II/Ge. Two new species of fermions F and G form hydrogen-like atoms with standard atomic size through a dark U(1) gauge interaction carried out by a dark massless photon. A Yukawa coupling between the nuclei F and neutral scalar particles S induces an attractive shorter-range interaction. This dark sector interacts with our standard particles because of the presence of two mixings, a kinetic photon-dark photon mixing, and a mass {\sigma}-S mixing. The dark atoms from the halo diffuse elastically in terrestrial matter until they thermalize and then reach underground detectors with thermal energies, where they form bound states with nuclei by radiative capture. This causes the emission of photons that produce the signals observed by direct-search experiments.