CUORE is a 1 ton scale cryogenic experiment aiming at the measurement of the Majorana mass of the electron neutrino. The detector is an array of 988 TeO2 bolometers used for a calorimetric detection of the two electrons emitted in the BB0n of 130Te. The sensitivity of the experiment to the lowest Majorana mass is determined by the rate of background events that can mimic a BB0n. In this paper we investigate the contribution of external sources i.e. environmental gammas, neutrons and cosmic ray muons to the CUORE background and show that the shielding setup designed for CUORE guarantees a reduction of this external background down to a level <1.0E-02 c/keV/kg/y at the Q-value, as required by the physical goal of the experiment.
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