  We study theoretically interaction potentials and low energy collisions
between different alkali atoms and alkali ions. Specifically, we consider
systems like X + Y$^{+}$, where X(Y$^{+})$ is either Li(Cs$^+$) or Cs(Li$^+$),
Na(Cs$^+$) or Cs(Na$^+$) and Li(Rb$^+$) or Rb(Li$^+$). We calculate the
molecular potentials of the ground and first two excited states of these three
systems using pseudopotential method and compare our results with those
obtained by others. We derive ground-state scattering wave functions and
analyze cold collisional properties of these systems for a wide range of
energies. We find that, in order to get convergent results for the total
scattering cross sections for energies of the order 1 K, one needs to take into
account at least 60 partial waves. Low energy scattering properties calculated
in this paper may serve as a precursor for experimental exploration of quantum
collisions between an alkali atom and an alkali ion of different nucleus.
