  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.
