  Ultracold hybrid ion-atom traps offer the possibility of microscopic
manipulation of quantum coherences in the gas using the ion as a probe.
However, inelastic processes, particularly charge transfer can be a significant
process of ion loss and has been measured experimentally for the Yb$^{+}$ ion
immersed in a Rb vapour. We use first-principles quantum chemistry codes to
obtain the potential energy curves and dipole moments for the lowest-lying
energy states of this complex. Calculations for the radiative decay processes
cross sections and rate coefficients are presented for the total decay
processes. Comparing the semi-classical Langevin approximation with the quantum
approach, we find it provides a very good estimate of the background at higher
energies. The results demonstrate that radiative decay mechanisms are important
over the energy and temperature region considered. In fact, the Langevin
process of ion-atom collisions dominates cold ion-atom collisions. For spin
dependent processes \cite{kohl13} the anisotropic magnetic dipole-dipole
interaction and the second-order spin-orbit coupling can play important roles,
inducing couplingbetween the spin and the orbital motion. They measured the
spin-relaxing collision rate to be approximately 5 orders of magnitude higher
than the charge-exchange collision rate \cite{kohl13}. Regarding the measured
radiative charge transfer collision rate, we find that our calculation is in
very good agreement with experiment and with previous calculations.
Nonetheless, we find no broad resonances features that might underly a strong
isotope effect. In conclusion, we find, in agreement with previous theory that
the isotope anomaly observed in experiment remains an open question.
