The DAMA experiment using ultra low background NaI(Tl) crystal scintillators has measured an annual modulation effect in the keV region which satisfies all the peculiarities of an effect induced by Dark Matter particles. In this paper we analyze this annual modulation effect in terms of mirror Dark Matter, an exact duplicate of ordinary matter from parallel hidden sector, which chemical composition is dominated by mirror helium while it can also contain significant fractions of heavier elements as Carbon and Oxygen. Dark mirror atoms are considered to interact with the target nuclei in the detector via Rutherford-like scattering induced by kinetic mixing between mirror and ordinary photons, both being massless. In the present analysis we consider various possible scenarios for the mirror matter chemical composition. For all the scenarios, the relevant ranges for the kinetic mixing parameter have been obtained taking also into account various existing uncertainties in nuclear and particle physics quantities.
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