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Feshbach resonances and molecule formation in ultracold mixtures of Rb and Yb($^3$P) atoms

We have investigated magnetically tunable Feshbach resonances in ultracold collisions of Rb with Yb in its metastable $^3$P$_2$ and $^3$P$_0$ states, using coupled-channel scattering and bound-state calculations. For the $^3$P$_2$ state, we find sharp resonances when both atoms are in their lowest Zeeman sublevels. However, these resonances are decayed by inelastic processes that produce Yb atoms in $^3$P$_1$ and $^3$P$_0$ states. The molecules that might be produced by magnetoassociation at the $^3$P$_2$ thresholds can decay by similar pathways and would have lifetimes no more than a few microseconds. For the $^3$P$_0$ state, by contrast, there are resonances that are promising for magnetoassociation. There are resonances due to both rotating and non-rotating molecular states that are significantly stronger than the analogous resonances for Yb($^1$S). The ones due to rotating states are denser in magnetic field; in contrast to Yb($^1$S), they exist even for bosonic isotopes of Yb($^3$P$_0$).