Physical Review A

Three-body recombination in cold helium–helium–alkali-metal-atom collisions

Hiroya Suno, Brett D. Esry

Published Dec 2, 2009• 51 citations

Abstract

Three-body recombination in helium-helium--alkali-metal collisions at cold temperatures is studied using the adiabatic hyperspherical representation. The rates for the three-body recombination processes $^{4}\text{H}\text{e}+^{4}\text{H}\text{e}+X\ensuremath{\rightarrow}^{4}\text{H}\text{e}+^{4}\text{H}\text{e}X$ and $^{4}\text{H}\text{e}+^{4}\text{H}\text{e}+X\ensuremath{\rightarrow}{^{4}\text{H}\text{e}}_{2}+X$, with $X=^{7}\text{L}\text{i}$, $^{23}\text{N}\text{a}$, $^{39}\text{K}$, $^{85}\text{R}\text{b}$, and $^{133}\text{C}\text{s}$, are calculated at nonzero collision energies by including not only zero total angular momentum, $J=0$, states but also $J>0$ states. The three-body recombination rates show a relatively weak dependence on the alkali-metal species, differing from each other only by about one order of magnitude, except for the $^{4}\text{H}\text{e-}^{4}\text{H}\text{e-}^{23}\text{N}\text{a}$ system.

DOI: 10.1103/physreva.80.062702

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Physical Review A

Three-body recombination in cold helium–helium–alkali-metal-atom collisions

Hiroya Suno, Brett D. Esry

Published Dec 2, 2009• 51 citations

Publisher

Abstract

^{4}\text{H}\text{e}+^{4}\text{H}\text{e}+X\ensuremath{\rightarrow}^{4}\text{H}\text{e}+^{4}\text{H}\text{e}X

and

^{4}\text{H}\text{e}+^{4}\text{H}\text{e}+X\ensuremath{\rightarrow}{^{4}\text{H}\text{e}}_{2}+X

, with

X=^{7}\text{L}\text{i}

^{23}\text{N}\text{a}

^{39}\text{K}

^{85}\text{R}\text{b}

, and

^{133}\text{C}\text{s}

, are calculated at nonzero collision energies by including not only zero total angular momentum,

J=0

, states but also

J>0

states. The three-body recombination rates show a relatively weak dependence on the alkali-metal species, differing from each other only by about one order of magnitude, except for the

^{4}\text{H}\text{e-}^{4}\text{H}\text{e-}^{23}\text{N}\text{a}

system.

DOI: 10.1103/physreva.80.062702

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^{4}\text{H}\text{e}+^{4}\text{H}\text{e}+X\ensuremath{\rightarrow}^{4}\text{H}\text{e}+^{4}\text{H}\text{e}X

and

^{4}\text{H}\text{e}+^{4}\text{H}\text{e}+X\ensuremath{\rightarrow}{^{4}\text{H}\text{e}}_{2}+X

, with

X=^{7}\text{L}\text{i}

^{23}\text{N}\text{a}

^{39}\text{K}

^{85}\text{R}\text{b}

, and

^{133}\text{C}\text{s}

, are calculated at nonzero collision energies by including not only zero total angular momentum,

J=0

, states but also

J>0

states. The three-body recombination rates show a relatively weak dependence on the alkali-metal species, differing from each other only by about one order of magnitude, except for the

^{4}\text{H}\text{e-}^{4}\text{H}\text{e-}^{23}\text{N}\text{a}

system.

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 $^{4}\mathrm{He}X+^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}^{4}\mathrm{He}X+^{4}\mathrm{He}$ 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

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.

We have developed a method for calculating the rates for three-body recombination of cold atoms. This method allows us to treat not only zero total angular momentum,

J=0,

states but also

J>0

states, so that recombinations at nonzero collision energies can be considered. Our method is applied to ground-state helium atoms

{}^{4}\mathrm{He},

using a realistic interaction potential. In addition, we obtain the rates for collision induced dissociation.

R

-matrix propagation method, in order to calculate the product-state-selective total and partial recombination rates in the

^{4}\mathrm{He}+^{4}\mathrm{He} +

Ag system. Recombination at collision energies less than 10 mK is found to take place dominantly to the product molecule

^{4}\mathrm{He}\mathrm{Ag}

in its least bound state, while the three atoms recombine mainly to the

^{4}\mathrm{He}_{2}

molecule in its ground state at higher collision energies.

^{4}\mathrm{He}

{}_{2}

--alkali-metal triatomic molecular systems are studied using the adiabatic hyperspherical representation. By adopting the best pairwise He-He and He-

X

interaction potentials, we search for weakly bound states of

^{4}\mathrm{He}

{}_{2}

X

systems with

X={}^{6}

Li,

^{7}\mathrm{Li}

^{23}\mathrm{Na}

^{39}\mathrm{K}

^{40}\mathrm{K}

^{41}\mathrm{K}

^{85}\mathrm{Rb}

^{87}\mathrm{Rb}

, and

^{133}\mathrm{Cs}

. We consider not only zero total angular momentum

J=0

states, but also

J>0

states. We find that the

^{4}\mathrm{He}

{}_{2}^{6}

Li and

^{4}\mathrm{He}

{}_{2}^{7}

Li systems each possess two bound states with ${J}^{\ensuremath{\Pi}}={0}^{+}$ symmetry and none with

J>0

, while the other

^{4}\mathrm{He}

{}_{2}

--alkali-metal species are found to support one

{0}^{+}

and one ${1}^{\ensuremath{-}}$ bound state. We calculate the bound-state energies of these molecular species and discuss the essential features of the wave functions associated with these bound states.