$TeO_2$ crystals are used as bolometers in experiments searching for Double Beta Decay without emission of neutrinos. One of the most important issues in this extremely delicate kind of experiments is the characterization of the background. The knowl
edge of the response to $alpha$ particles in the energy range where the signal is expected is therefore a must. In this paper we report the results on the response function of a $TeO_2$ bolometer to $alpha$s emitted by $^{147}$Sm dissolved in the crystal at the growth phase. A Quenching Factor of ($1.0076pm 0.0005$) is found, independent of the temperature in the investigated range. The energy resolution on $alpha$ peaks shows a standard calorimeter energy dependence: $sigma; [rm{keV}] = (0.56 pm 0.02) oplus (0.010 pm 0.002)sqrt{E[rm{keV}]} $. Signal pulses show no difference between $alpha$ and $betagamma$ particles
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.
