  In a recent experiment by Schaetz group \cite{weckesser2021}, the quantum
$s$-wave regime has been attained for alkali and alkaline-earth atom-ion
combination (Li-Ba$^+$). We investigate possible outcomes from interaction of
this ion-atom pair at quantum regimes from a theoretical point of view. For
this purpose, Born-Oppenheimer potential energy surfaces are constructed for
the lowest three dissociation channels of (Ba-Li)$^+$ molecular system using a
multireference configuration interaction (MRCI) electronic structure
calculation. We present elastic, spin-exchange (SE), and diffusion cross
sections at different energy regimes. The collisional properties of this system
are calculated in terms of the scattering phase shifts and scattering cross
sections, and the semiclassical behavior at a relatively large energy limit is
also examined. For SE collisions, phase locking is obtained towards lower
partial waves.
