  We present a theoretical investigation of reactive and non-reactive
collisions of Li and Rb atoms with C$_{2}^{-}$ molecular anions at low
temperatures in the context of sympathetic cooling in hybrid trap experiments.
Based on recently reported accurate potential energy surfaces for the singlet
and triplet states of the Li-C$_{2}^{-}$ and Rb-C$_{2}^{-}$ systems, we show
that the associative electronic detachment reaction is slow if the colliding
partners are in their ground state, but fast if they are excited. The results
are expected to be representative of the alkali-metal series. We also
investigate rotationally inelastic collisions in order to explore the cooling
of the translational and rotational degrees of freedom of C$_2^-$ in hybrid
ion-atom traps. The effect of micromotion is taken into account by considering
Tsallis distributions of collision energies. We show that the translational
cooling occurs much more rapidly than rotational cooling and that the presence
of excited atoms leads to losses of anions on a timescale comparable to that of
rotational cooling.
