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arXiv:0809.5111 · Physical Review A

Adiabatic hyperspherical study of triatomic helium systems

Hiroya Suno, Brett D. Esry

Published Dec 1, 2008• 83 citations
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Abstract

The $^{4}\mathrm{He}_{3}$ system is studied using the adiabatic hyperspherical representation. We adopt the current state-of-the-art helium interaction potential including retardation and the nonadditive three-body term to calculate all low-energy properties of the triatomic $^{4}\mathrm{He}$ system. The bound state energies of the $^{4}\mathrm{He}$ trimer are computed as well as the $^{4}\mathrm{He}+^{4}\mathrm{He}_{2}$ elastic scattering cross sections, the three-body recombination, and collision induced dissociation rates at finite temperatures. We also treat the system that consists of two $^{4}\mathrm{He}$ and one $^{3}\mathrm{He}$ atoms, and compute the spectrum of the isotopic trimer $^{4}\mathrm{He}_{2}^{3}\mathrm{He}$, the $^{3}\mathrm{He}+^{4}\mathrm{He}_{2}$ elastic scattering cross sections, the rates for three-body recombination, and the collision induced dissociation rate at finite temperatures. The effects of retardation and the nonadditive three-body term are investigated. Retardation is found to be significant in some cases, while the three-body term plays only a minor role for these systems.

DOI
10.1103/physreva.78.062701

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The 4He3^{4}\mathrm{He}_{3}4He3​ system is studied using the adiabatic hyperspherical representation. We adopt the current state-of-the-art helium interaction potential including retardation and the nonadditive three-body term to calculate all low-energy properties of the triatomic 4He^{4}\mathrm{He}4He system. The bound state energies of the 4He^{4}\mathrm{He}4He trimer are computed as well as the 4He+4He2^{4}\mathrm{He}+^{4}\mathrm{He}_{2}4He+4He2​ elastic scattering cross sections, the three-body recombination, and collision induced dissociation rates at finite temperatures. We also treat the system that consists of two 4He^{4}\mathrm{He}4He and one 3He^{3}\mathrm{He}3He atoms, and compute the spectrum of the isotopic trimer 4He23He^{4}\mathrm{He}_{2}^{3}\mathrm{He}4He23​He, the 3He+4He2^{3}\mathrm{He}+^{4}\mathrm{He}_{2}3He+4He2​ elastic scattering cross sections, the rates for three-body recombination, and the collision induced dissociation rate at finite temperatures. The effects of retardation and the nonadditive three-body term are investigated. Retardation is found to be significant in some cases, while the three-body term plays only a minor role for these 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 $^{4}\mathrm{He}X+^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}^{4}\mathrm{He}X+^{4}\mathrm{He}$ and $^{4}\mathrm{He}_{2}+X\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}^{4}\mathrm{He}_{2}+X$, as well as the reactive collision processes $^{4}\mathrm{He}X+^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightleftharpoons}^{4}\mathrm{He}_{2}+X$, where XXX is one of the bosonic alkali-metal atoms: 7Li^{7}\mathrm{Li}7Li, 23Na^{23}\mathrm{Na}23Na, 39K^{39}\mathrm{K}39K, 85Rb^{85}\mathrm{Rb}85Rb, or 133Cs^{133}\mathrm{Cs}133Cs. The elastic and reactive collision cross sections are calculated at nonzero collision energies by including not only zero atom-molecule relative angular momentum, L=0L=0L=0, processes but also L>0L>0L>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 4He^{4}\mathrm{He}4He and XXX, while the other collision processes are not found to have any systematic dependence on the alkali-metal species XXX.
The adiabatic hyperspherical method is used to investigate the spectrum of the helium trimer and to explore effects on the spectrum of varying the helium masses as well as the interaction strength. When a realistic helium dimer potential is adopted, only two isotopic combinations are observed to have three-body bound states: 4He3^{4}\mathrm{He}_{3}4He3​ and 4He23^{4}\mathrm{He}_{2}^{3}4He23​He. By artificially adjusting the dimer potential, we also determine the range of interaction strengths for which halo states can result. The existence of Efimov states for both physical and unphysical systems is also examined. \textcopyright{} 1996 American Institute of Physics.
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=7LiX=^{7}\text{L}\text{i}X=7Li, 23Na^{23}\text{N}\text{a}23Na, 39K^{39}\text{K}39K, 85Rb^{85}\text{R}\text{b}85Rb, and 133Cs^{133}\text{C}\text{s}133Cs, are calculated at nonzero collision energies by including not only zero total angular momentum, J=0J=0J=0, states but also J>0J>0J>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 4He-4He-23Na^{4}\text{H}\text{e-}^{4}\text{H}\text{e-}^{23}\text{N}\text{a}4He-4He-23Na system.
We have studied hydrogen-hydrogen-alkali three-body systems in the adiabatic hyperspherical representation. For the spin-stretched case, there exists a single XXXH molecular state when XXX is one of the bosonic alkali atoms: 7Li^{7}\mathrm{Li}7Li, 23Na^{23}\mathrm{Na}23Na, 39K^{39}\mathrm{K}39K, 87Rb^{87}\mathrm{Rb}87Rb, or 133Cs^{133}\mathrm{Cs}133Cs. As a result, the only recombination process is the one that leads to formation of XXXH 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 H+XH\text{H}+X\text{H}H+XH 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,J=0,J=0, states but also J>0J>0J>0 states, so that recombinations at nonzero collision energies can be considered. Our method is applied to ground-state helium atoms 4He,{}^{4}\mathrm{He},4He, using a realistic interaction potential. In addition, we obtain the rates for collision induced dissociation.