Measurement of the branching ratios Γ ( D s + → D s + π 0 ) / Γ ( D s + → D s + γ ) and Γ ( D 0 → D 0 π 0 ) / Γ ( D 0 → D 0 γ )

Data samples corresponding to the isospin-violating decay $D_s^{*+}\to D_s^+ \pi^0$ and the decays $D_s^{*+}\to D_s^+\gamma$, $D^{*0}\to D^0\pi^0$ and $D^{*0}\to D^0\gamma$ are reconstructed using 90.4 ${\rm fb}^{-1}$ of data recorded by the BaBar detector at the PEP-II asymmetric-energy $e^+e^-$ collider. The following branching ratios are extracted: $\Gamma(D_s^{*+}\to D_s^+ \pi^0)/\Gamma(D_s^{*+}\to D_s^+\gamma) = 0.062\pm0.005 ({\rm stat.})\pm0.006 ({\rm syst.})$ and $\Gamma(D^{*0}\to D^0\pi^0)/\Gamma(D^{*0}\to D^0\gamma) = 1.74\pm0.02 ({\rm stat.})\pm0.13 ({\rm syst.})$. Both measurements represent significant improvements over present world averages.