  Atom-dimer exchange and dissociation reaction rates are predicted for
different combinations of two $^4$He atoms and one of the alkaline species
among $^{6}$Li, $^{7}$Li and $^{23}$Na, by using three-body scattering
formalism with short-range two-body interactions. Our study was concerned with
low-energy reaction rates in which the $s-$, $p-$ and $d-$ wave contributions
are the relevant ones. The $^4$He is chosen as one of the atoms in the binary
mixture, in view of previous available investigations and laboratory
accessibilities. Focusing on possible experimental cold-atom realizations with
two-atomic mixtures, in which information on atom-dimer reaction rates can be
extracted, we predict the occurrence of a dip in the elastic reaction rate for
colliding energies smaller than 20 mK, when the dimer is the $^4$He$^{23}$Na
molecule. We are also anticipating a zero in the elastic $p-$wave contribution
for the $^4$He + $^4$He$^7$Li and $^4$He + $^4$He$^{23}$Na reaction processes.
With weakly-bound molecules reacting with atoms at very low colliding energies,
we interpret our results on the light of Efimov physics which supports model
independence and robustness of our predictions. Specific sensitivities on the
effective range were evidenced, highlighted by the particular inversion role of
the $p-$ and $d-$waves in the atom exchange and dissociation processes.
