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We investigate the prospects of controlling charge-exchange in ultracoldcollisions of heteroisotopic combinations of atoms and ions of the sameelement. The treatment, readily applicable to alkali or alkanine-earth metals,is illustrated in the process $^9$Be$^{+}$ + $^{10}$Be $\leftrightarrow$$^{9}$Be + $^{10}$Be$^{+}$, which exhibits favorable electronic, nuclear, andhyperfine structure. Feshbach resonances are obtained from quantum scatteringcalculations in a standard coupled-channel formalism with non-BO termsoriginating from the nuclear kinetic operator. Near a narrow resonancepredicted at 322 G, we find the charge-exchange rate coefficient to rise frompractically zero to values larger than $10^{-12}$ cm$^3$/s. Our results suggestcontrollable charge-exchange reactions between different isotopes of suitableatom-ion pairs with potential applications to quantum systems engineered tostudy charge diffusion in trapped cold atom-ion mixtures and emulate many-bodyphysics.

Charge transfer in ultracold gases via Feshbach resonances