Ion-atom-atom recombination into shallow molecular ions

This work presents a full quantum mechanical study on ion-atom-atom three-body recombination into shallow molecular ions. In particular, we consider a heavy positive ion ($A^+$) and two light neutral atoms ($B$) and our theoretical framework addresses the finite range of atom-ion and atom-atom interactions. For fixed and positive atom-ion scattering length ($a_{A^+B}$), the scaling behavior of the three-body recombination coefficient versus the atom-atom scattering length ($a_{BB}$) is obtained. We identify two distinct regimes where the three-body recombination coefficient possesses different scaling behavior with respect to $a_{BB}$. More specifically, these two regimes are indicated by the magnitude of the atom-ion scattering length relative to the corresponding atom-ion interaction length scale ($R_{A^+B}$).

In the case of $a_{A^+B}>R_{A^+B}$ the three-body recombination coefficient is linear with respect to $a_{BB}$ whereas in the case $a_{A^+B} The latter implies that the production of highly excited molecular ions is more sensitive to $a_{BB}$ if the range of the atom-ion interaction is the most dominant length scale in the three-body system.

Also, our analysis demonstrates that the observed scaling laws of the three-body recombination coefficient regardless the mass ratios between the ion and the atom.