A Semi-classical Landau-Zener model is employed to theoretically study mutual neutralization in the collisions of $\mathrm{^4He^+}$ and $\mathrm{H^-}$/$\mathrm{D^-}$. The model includes ten covalent states and an ion-pair state of $\mathrm{^2\Sigma^+}$ symmetry for the $\mathrm{HeH}$ molecular system. Here the assumption is that only two states are interacting at a given internuclear position. In the diabatic representation, the nuclear dynamics relevant for mutual neutralization is modelled for collision energies below 100 $\mathrm{eV}$. The mutual neutralization reaction cross section and final states distribution are computed and compared with previous theoretical and experimental results.

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