Collisions between Ca cations and Rb atoms are computed within a quantum approach that generates the most relevant potential energy curves from accurate ab initio methods and carries out the low-energy scattering calculations by including nonadiabatic and spin-orbit coupling terms. The cross sections are obtained at relative energies typical for the likely arrangements of Rb atoms in a Magneto-Optical Trap overlapped with a Coulomb Crystal of Ca cations. The dominant nonadiabatic process is clearly identified and the efficiency of the nonadiabatic coupling terms which lead to the charge-exchange process is discussed.