Comparative classical and quantal study of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>HeNa</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/199

The $\mathrm{He}+\mathrm{He}+{\mathrm{Na}}^{+}\ensuremath{\rightarrow}\mathrm{He}+\mathrm{He}{\mathrm{Na}}^{+}$ and $\mathrm{He}+\mathrm{He}+{\mathrm{K}}^{+}\ensuremath{\rightarrow}\mathrm{He}+\mathrm{He}{\mathrm{K}}^{+}$ termolecular association reactions are studied at low temperature using both the Monte Carlo classical trajectories and quantum close-coupling approaches. In order to achieve this objective, two potential energy surfaces are constructed, and the bound and quasibound states of the resulting diatomic cations are calculated. The quantum approach is developed within the two-step mechanism. The first step involves the formation of a metastable diatomic system in thermal equilibrium with a system of two freely moving atoms. The second step is the relaxation step, where the collision of the metastable diatomic system with a third atom may produce a stable diatomic system. The relaxation rates are calculated by an accurate quantum collision approach, and the three-body association rates is obtained within the framework of the local thermodynamic equilibrium hypothesis. The comparison between the classical and quantum approaches allows us to gain complementary insight into the temperature dependence of the three-body association rate.