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$TeO_2$ crystals are used as bolometers in experiments searching for DoubleBeta Decay without emission of neutrinos. One of the most important issues inthis extremely delicate kind of experiments is the characterization of thebackground. The knowledge of the response to $\alpha$ particles in the energyrange where the signal is expected is therefore a must. In this paper we reportthe results on the response function of a $TeO_2$ bolometer to $\alpha$'semitted by $^{147}$Sm dissolved in the crystal at the growth phase. A QuenchingFactor of ($1.0076\pm 0.0005$) is found, independent of the temperature in theinvestigated range. The energy resolution on $\alpha$ peaks shows a standardcalorimeter 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 $\beta\gamma$ particles

Response of a TeO_2 bolometer to alpha particles