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

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, $\text{H}+\text{H}+X\to X\text{H}+\text{H}$, 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 $J^{\Pi }=0^{+}$ to $5^{-}$. We have also found that there is just one three-body bound state for such systems for $J^{\Pi }=0^{+}$ and no bound states for higher angular momenta.

Figure 1

The ${}^3{\Sigma }_u$ potentials for $\text{H}+\text{H}$ and $X+\text{H}$. Among all these combinations, only $X+\text{H}$ systems have a single, weakly bound molecular state.

Figure 2

The adiabatic three-body potentials for (a) $\text{H}+\text{H}+\text{Li}$, and (b) $\text{H}+\text{H}+\text{Cs}$. The insets show the avoided crossings within the energy range we have considered for the rates and cross sections.

Figure 3

The nonadiabatic couplings for $\text{H}+\text{H}+\text{Cs}$ with $J^{\Pi }=0^{+}$. Note that $Q_{1,2}$ has been multiplied by 5000 to have a magnitude similar to $P_{1,2}$. The index $\nu$ for the adiabatic potentials starts from 0.

Figure 4

The total three-body recombination rate $K_3$ and the partial rates $K_3^{J\Pi }$ for $\text{H}+\text{H}+X\to \text{H}+X\text{H}$, where $X$ is (a) Li, (b) Na, (c) K, (d) Rb, and (e) Cs. The thermally averaged total recombination rates are shown in (f).

Figure 5

The thermally averaged total collision-induced dissociation rate $\langle D_3\rangle$ for $\text{H}+X\text{H}\to X+\text{H}+\text{H}$. For all species, the rates are shown up to 100 mK beyond the three-body break-up threshold, which is indicated by the vertical dashed line.

Figure 6

The total atom-molecule elastic cross section ${\sigma }_2$ and the partial cross sections ${\sigma }_2^{J\Pi }$ for $\text{H}+\text{KH}\to \text{H}+\text{KH}$.

Figure 7

The thermally averaged total atom-molecule elastic cross section $\langle {\sigma }_2\rangle$ for $\text{H}+X\text{H}\to \text{H}+X\text{H}$.

Figure 8

The $J^{\Pi }=0^{+}$ hyperradial channel function $F_0(R)$ for the triatomic bound states.