Cold elastic and reactive atom-molecule collisions in helium–helium–alkali-metal triatomic systems

Atom-molecule collisions in helium–helium–alkali-metal triatomic systems at cold energies are studied using the adiabatic hyperspherical representation. We consider the elastic collision processes ${}^4\mathrm{He}X+{}^4\mathrm{He}\to {}^4\mathrm{He}X+{}^4\mathrm{He}$ and ${}^4\mathrm{He}_2+X\to {}^4\mathrm{He}_2+X$, as well as the reactive collision processes ${}^4\mathrm{He}X+{}^4\mathrm{He}\rightleftharpoons {}^4\mathrm{He}_2+X$, where $X$ is one of the bosonic alkali-metal atoms: ${}^7\mathrm{Li}$, ${}^{23}\mathrm{Na}$, ${}^{39}\mathrm{K}$, ${}^{85}\mathrm{Rb}$, or ${}^{133}\mathrm{Cs}$. The elastic and reactive collision cross sections are calculated at nonzero collision energies by including not only zero atom-molecule relative angular momentum, $L=0$, processes but also $L>0$ processes. The total cross section for ${}^4\mathrm{He}X+{}^4\mathrm{He}\to {}^4\mathrm{He}X+{}^4\mathrm{He}$ is found to increase with the scattering length between ${}^4\mathrm{He}$ and $X$, while the other collision processes are not found to have any systematic dependence on the alkali-metal species $X$.

Figure 1

The 12 lowest adiabatic hyperspherical potential curves $U_{\nu }\left(R\right)$ ($\nu =0$–11) for the ${}^4$He-${}^4$He-${}^{39}$K system in the $J^{\Pi }=1^{-}$ symmetry. The lowest, $\nu =0$, and second-lowest, $\nu =1$, potential curves represent the atom-molecule channels corresponding asymptotically to ${}^4$He${}^{39}\mathrm{K}+{}^4$He and ${}^4$He${}_2+{}^{39}$K, respectively. The higher channels, $\nu =2$–11, represent the three-body continuum channels. Inset: Threshold-energy region at large hyperradii.

Figure 2

Total and partial cross sections for elastic and reactive atom-molecule collisions involving the ${}^4$He-${}^4$He-${}^7$Li system. We show cross sections for (a) ${}^4$He${}^7$$\mathrm{Li}+{}^4$$\mathrm{He}\to {}^4$He${}^7$$\mathrm{Li}+{}^4$He, (b) ${}^4$He${}^7$$\mathrm{Li}+{}^4$$\mathrm{He}\to {}^4$He${}_2+{}^7$Li, (c) ${}^4$He${}_2+{}^7$$\mathrm{Li}\to {}^4$He${}^7$$\mathrm{Li}+{}^4$He, and (d) ${}^4$He${}_2+{}^7$$\mathrm{Li}\to {}^4$He${}_2+{}^7$Li.

Figure 3

Total and partial cross sections for elastic and reactive atom-molecule collisions involving the ${}^4$He-${}^4$He-${}^{39}$K system. We show cross sections for (a) ${}^4$He${}^{39}$$\mathrm{K}+{}^4$$\mathrm{He}\to {}^4$He${}^{39}$$\mathrm{K}+{}^4$He, (b) ${}^4$He${}^{39}$$\mathrm{K}+{}^4$$\mathrm{He}\to {}^4$He${}_2+{}^{39}$K, (c) ${}^4$He${}_2+{}^{39}$$\mathrm{K}\to {}^4$He${}^{39}$$\mathrm{K}+{}^4$He, and (d) ${}^4$He${}_2+{}^{39}$$\mathrm{K}\to {}^4$He${}_2+{}^{39}$K.

Figure 4

Total and partial cross sections for elastic and reactive atom-molecule collisions involving the ${}^4$He-${}^4$He-${}^{133}$Cs system. We show cross sections for (a) ${}^4$He${}^{133}$$\mathrm{Cs}+{}^4$$\mathrm{He}\to {}^4$He${}^{133}$$\mathrm{Cs}+{}^4$He, (b) ${}^4$He${}^{133}$$\mathrm{Cs}+{}^4$$\mathrm{He}\to {}^4$He${}_2+{}^{133}$Cs, (c) ${}^4$He${}_2+{}^{133}$$\mathrm{Cs}\to {}^4$He${}^{133}$$\mathrm{Cs}+{}^4$He, and (d) ${}^4$He${}_2+{}^{133}$$\mathrm{Cs}\to {}^4$He${}_2+{}^{133}$Cs.

Figure 5

Total cross sections for elastic and reactive atom-molecule collisions involving ${}^4$He-${}^4$He-$X$ systems with $X={}^7$Li, ${}^{23}$Na, ${}^{39}$K, ${}^{85}$Rb, and ${}^{133}$Cs. We show cross sections for (a) ${}^4$He$X+{}^4$$\mathrm{He}\to {}^4$He$X+{}^4$He, (b) ${}^4$He$X+{}^4$$\mathrm{He}\to {}^4$He${}_2+X$, (c) ${}^4$He${}_2+X\to {}^4$He$X+{}^4$He, and (d) ${}^4$He${}_2+X\to {}^4$He${}_2+X$.