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Physical Review A

Adiabatic hyperspherical study of weakly bound helium–helium–alkali-metal triatomic systems

Hiroya Suno, Brett D. Esry

Published Dec 29, 2010• 24 citations
Publisher

Abstract

$^{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.

DOI
10.1103/physreva.82.062521

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^{4}\mathrm{He}$${}_{2}--alkali-metal triatomic molecular systems are studied using the adiabatic hyperspherical representation. By adopting the best pairwise He-He and He-XXX interaction potentials, we search for weakly bound states of ^{4}\mathrm{He}$${}_{2}$$X systems with X=6X={}^{6}X=6Li, 7Li^{7}\mathrm{Li}7Li, 23Na^{23}\mathrm{Na}23Na, 39K^{39}\mathrm{K}39K, 40K^{40}\mathrm{K}40K, 41K^{41}\mathrm{K}41K, 85Rb^{85}\mathrm{Rb}85Rb, 87Rb^{87}\mathrm{Rb}87Rb, and 133Cs^{133}\mathrm{Cs}133Cs. We consider not only zero total angular momentum J=0J=0J=0 states, but also J>0J>0J>0 states. We find that the ^{4}\mathrm{He}$${}_{2}^{6}Li and ^{4}\mathrm{He}$${}_{2}^{7}Li systems each possess two bound states with J\ensuremathΠ=0+{J}^{\ensuremath{\Pi}}={0}^{+}J\ensuremathΠ=0+ symmetry and none with J>0J>0J>0, while the other ^{4}\mathrm{He}$${}_{2}--alkali-metal species are found to support one 0+{0}^{+}0+ and one 1\ensuremath−{1}^{\ensuremath{-}}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.
We study the structure of triatomic molecules containing two helium atoms and one alkali-metal atom X (X = Li, Na). The three-body Schr\"odinger equation is solved in hyperspherical coordinates using the He-He and He-X pair van der Waals potentials available in the literature. We calculate the structural properties of the He2Li{\mathrm{He}}_{2}\mathrm{Li}He2​Li and He2Na{\mathrm{He}}_{2}\mathrm{Na}He2​Na bound states, and analyze one-dimensional pair and angle distribution functions as well as two-dimensional pair-pair and angle-angle distribution functions. These bound states are characterized by so peculiar weakly bound structures that classifying them into particular sizes and geometrical shapes appears to be elusive. Particularly, the ${J}^{\mathrm{\ensuremath{\Pi}}}={0}^{+}$ excited states of 4He26Li^{4}\mathrm{He}_{2}^{6}\mathrm{Li}4He26​Li and 4He27Li^{4}\mathrm{He}_{2}^{7}\mathrm{Li}4He27​Li are found to constitute giant triatomic molecules with their size amounting to several hundred bohrs.
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.
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 study the existence of stable bound states of triatomic molecules containing two helium atoms and one alkali atom X (X = Li, Na) and examine the dependence of their binding energies on the mass of the constituent atoms. The three-body systems are solved within the adiabatic approximation in hyperspherical coordinates using the He - He and He - X pair van der Waals interactions that are available in the literature. The binding energies of these systems are shown to be of less than 1 K for some isotope combinations. For the lighter isotopes it is shown that no bound states exist. We found no evidence of the existence of halo states or Efimov states for these systems.
We investigate for the existence of the weakly bound He-He-Ca molecules. By employing the best empirical interaction between each pair of particles, the Schr\"odinger equation for the triatomic system is solved using hyperspherical coordinates in the adiabatic approximation. The bound states are found for each of the 3{}^{3}3He-3{}^{3}3He-40{}^{40}40Ca, 3{}^{3}3He-4{}^{4}4He-40{}^{40}40Ca, and 4{}^{4}4He-4{}^{4}4He-40{}^{40}40Ca trimers, respectively. The binding energies of such molecules are estimated. We discuss the features of the channel functions associated with the hyperspherical potential curves of each system to obtain insight into the geometry of the molecules.
We searched for the existence of weakly bound He-He-H, He-He-H - and He-H-H molecules where the binding energies are expected to be of the order of degrees Kelvin. By employing the best empirical interaction between each pair of particles, we solved the Schrödinger equation for the triatomic systems using hyperspherical coordinates in the adiabatic approximation. We found no bound states for 4 He- 4 He- 1 H, three bound states for 4 He- 4 He- 1 H - and one bound state for 4 He- 1 H- 1 H. Bound states for other isotope combinations are also examined.