We investigate the performances of two ZnMoO4 scintillating crystals operated as bolometers, in view of a next generation experiment to search the neutrinoless double beta decay of Mo-100. We present the results of the alpha vs beta/gamma discrimination, obtained through the scintillation light as well as through the study of the shape of the thermal signal alone. The discrimination capability obtained at the 2615 keV line of Tl-208 is 8 sigma, using the heat-light scatter plot, while it exceeds 20 sigma using the shape of the thermal pulse alone. The achieved FWHM energy resolution ranges from 2.4 keV (at 238 keV) to 5.7 keV (at 2615 keV). The internal radioactive contaminations of the ZnMoO4 crystals were evaluated through a 407 hours background measurement. The obtained limit is < 32 microBq/kg for Th-228 and Ra-226. These values were used for a Monte Carlo simulation aimed at evaluating the achievable background level of a possible, future array of enriched ZnMoO4 crystals.
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