$TeO_2$ 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 knowledge 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
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