Classical Description of He₂⁺ Recombination

The ternary association reaction He⁺ + 2He → He₂⁺ + He has been studied extensively for its application in obtaining ion temperatures in cryogenic rf traps. The temperature-dependent rate coefficient for this reaction is the basis for calibrating the translational energy distribution of trapped He⁺ ions, which has been experimentally determined in the temperature range 10K – 350 K. Theoretical descriptions aimed at capturing the recombination rate coefficient have relied on quantum dynamical studies based on a two-step Lindemann mechanism, which predict a significant decline of the rate coefficient at low temperatures, demonstrating a significant deviation from experimental results. In this talk, we present a study of the helium ion recombination from a purely classical approach by utilizing classical trajectories in hyperspherical coordinates. The resulting temperature-dependent recombination rate coefficient shows excellent agreement with experimental data while preserving the classical power-law threshold for termolecular ion recombination at low temperatures, exhibiting the classical nature of this reaction.