Physical Review A

Structure of the weakly bound triatomic He2Li and He2Na molecules

Hiroya Suno

Published Jul 11, 2017• 14 citations

Abstract

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 ${\mathrm{He}}_{2}\mathrm{Li}$ and ${\mathrm{He}}_{2}\mathrm{Na}$ 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 $^{4}\mathrm{He}_{2}^{6}\mathrm{Li}$ and $^{4}\mathrm{He}_{2}^{7}\mathrm{Li}$ are found to constitute giant triatomic molecules with their size amounting to several hundred bohrs.

DOI: 10.1103/physreva.96.012508

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Physical Review A

Structure of the weakly bound triatomic He2Li and He2Na molecules

Hiroya Suno

Published Jul 11, 2017• 14 citations

Publisher

Abstract

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

{\mathrm{He}}_{2}\mathrm{Li}

and

{\mathrm{He}}_{2}\mathrm{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

^{4}\mathrm{He}_{2}^{6}\mathrm{Li}

and

^{4}\mathrm{He}_{2}^{7}\mathrm{Li}

are found to constitute giant triatomic molecules with their size amounting to several hundred bohrs.

DOI: 10.1103/physreva.96.012508

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The Journal of Chemical PhysicsJan 4, 20178 citations

{\mathrm{He}}_{2}\mathrm{Li}

and

{\mathrm{He}}_{2}\mathrm{Na}

{J}^{\mathrm{\ensuremath{\Pi}}}={0}^{+}

excited states of

^{4}\mathrm{He}_{2}^{6}\mathrm{Li}

and

^{4}\mathrm{He}_{2}^{7}\mathrm{Li}

are found to constitute giant triatomic molecules with their size amounting to several hundred bohrs.

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

and

^{3}\mathrm{He}_{2}\mathrm{Ag}

) or scalene (

^{3}\mathrm{He}^{4}\mathrm{He}\mathrm{Ag}

) triangle configurations where the He-Ag distances are nearly fixed and the Ag bond angle is variable.

^{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.

{}^{3}

He-

{}^{3}

He-

{}^{40}

Ca,

{}^{3}

He-

{}^{4}

He-

{}^{40}

Ca, and

{}^{4}

He-

{}^{4}

He-

{}^{40}

Ca 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.