Mobility and Clustering of Barium Ions and Dications in High Pressure Xenon Gas

The clustering and drift properties of barium ions in xenon gas are explored theoretically, using density functional theory and computational ion mobility theory, with the goal of better understanding barium ion transport for neutrinoless double beta decay. We derive the equilibrium conformations, energies and entropies of molecular ions in the Ba$^{+}$-Xe and Ba$^{++}$-Xe systems, which yield a predictive model of cluster formation in high pressure gas. We calculate ion-neutral interaction potential curves for these species and use them to predict effective molecular ion mobilities. Our calculation consistently reproduces experimental data on effective mobility and molecular ion formation for the Ba$^+$ system, and predicts strong cluster formation in the Ba$^{++}$ system, dominated by stable [BaXe$_6$]$^{++}$,[BaXe$_7$]$^{++}$, [BaXe$_8$]$^{++}$ and [BaXe$_9$]$^{++}$ complexes in the range of interest. Some implications for barium tagging in gas-phase neutrinoless double beta decay experiments are discussed, and the first predictions of pressure-dependent mobility of the doubly charged Ba$^{++}$ species are presented.