Physical Review A

Cold three-body recombination in helium-helium-silver-atom collisions using the hybrid slow-variable-discretization–adiabatic hyperspherical R -matrix approach

Hiroya Suno

Published Apr 11, 2024• 3 citations

Abstract

We study three-body recombination in the helium-helium-silver system at cold collision energies. The three-body Schr\"odinger equation is solved combining the slow variable discretization and adiabatic approaches with the $R$-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.

DOI: 10.1103/physreva.109.042814

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Physical Review A

Cold three-body recombination in helium-helium-silver-atom collisions using the hybrid slow-variable-discretization–adiabatic hyperspherical R -matrix approach

Hiroya Suno

Published Apr 11, 2024• 3 citations

Publisher

Abstract

We study three-body recombination in the helium-helium-silver system at cold collision energies. The three-body Schr"odinger equation is solved combining the slow variable discretization and adiabatic approaches with the

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.

DOI: 10.1103/physreva.109.042814

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

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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.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.

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Yujun Wang, José Paulo D'Incao, Brett D. Esry

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 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.

arXiv:1012.0680Physical Review AMar 8, 201133 citations

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.

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.

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.

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.