We measured the branching ratios of the He+ + H- and He+ + D- mutual neutralization at a collision energy below 25 meV. Those are correctly reproduced using the Landau-Zener model applied to potential energy curves computed by an anion-centered asymptotic model. The analyticity of both models allows getting a deeper insight into the reaction. It allows defining a low collision energy regime for the mutual neutralization at which the collision energy no longer affects the branching ratios. Using those models, we explain how heavier isotopes favor the production of higher excited states.