Cold three-body collisions in hydrogen–hydrogen–alkali-metal atomic systems

Abstract

We have studied hydrogen-hydrogen-alkali three-body systems in the adiabatic hyperspherical representation. For the spin-stretched case, there exists a single $X$H molecular state when $X$ is one of the bosonic alkali atoms: $^{7}\mathrm{Li}$, $^{23}\mathrm{Na}$, $^{39}\mathrm{K}$, $^{87}\mathrm{Rb}$, or $^{133}\mathrm{Cs}$. As a result, the only recombination process is the one that leads to formation of $X$H molecules, $\text{H}+\text{H}+X\ensuremath{\rightarrow}X\text{H}+\text{H}$, and such molecules will be stable against vibrational relaxation. We have calculated the collision rates for recombination and collision-induced dissociation as well as the elastic cross sections for $\text{H}+X\text{H}$ collisions up to a temperature of 0.5 K, including the partial wave contributions from ${J}^{\ensuremath{\Pi}}={0}^{+}$ to ${5}^{\ensuremath{-}}$. We have also found that there is just one three-body bound state for such systems for ${J}^{\ensuremath{\Pi}}={0}^{+}$ and no bound states for higher angular momenta.