  Charge-transfer cold Yb$^+$ + Rb collision dynamics is investigated
theoretically using high-level {\it ab initio} potential energy curves, dipole
moment functions and nonadiabatic coupling matrix elements. Within the
scalar-relativistic approximation, the radiative transitions from the entrance
$A^1\Sigma^+$ to the ground $X^1\Sigma^+$ state are found to be the only
efficient charge-transfer pathway. The spin-orbit coupling does not open other
efficient pathways, but alters the potential energy curves and the transition
dipole moment for the $A-X$ pair of states. The radiative, as well as the
nonradiative, charge-transfer cross sections calculated within the $10^{-3}-10$
cm$^{-1}$ collision energy range exhibit all features of the Langevin ion-atom
collision regime, including a rich structure associated with centrifugal
barrier tunneling (orbiting) resonances. Theoretical rate coefficients for two
Yb isotopes agree well with those measured by immersing Yb$^+$ ion in an
ultracold Rb ensemble in a hybrid trap. Possible origins of discrepancy in the
product distributions and relations to previously studied similar processes are
discussed.
