  We theoretically investigate the collisional dynamics of laser-cooled
$^{87}$Rb ground-state atoms and $^{40}$Ca$^+$ ground-state ions in the context
of the hybrid trap experiment of Ref. [Phys. Rev. Lett. 107, 243202 (2011)],
leading to ion losses. Cold $^{87}$Rb$^{40}$Ca$^+$ ground-state molecular ions
are created by radiative association, and we demonstrate that they are
protected against photodissociation by black-body radiation and by the
$^{40}$Ca$^+$ cooling laser at 397~nm. This study yields an interpretation of
the direct observation of $^{87}$Rb$^{40}$Ca$^+$ ions in the experiment, in
contrast to other hybrid trap experiments using other species. Based on novel
molecular data for the spin-orbit interaction, we also confirm that the
non-radiative charge-exchange is the dominant loss process for Ca$^+$ and
obtain rates in agreement with experimental observations and a previous
calculation.

Chemical Physics