Measurement of the Branching Ratios Gamma(D_s*+ -> D_s+ pi0)/Gamma(D_s*+ -> D_s+ gamma) and Gamma(D0+ -> D0 pi0)/Gamma(D0* -> D0 gamma)

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.