Bulletin of the Russian Academy of Sciences Physics

Weakly Bound Triatomic LiHe2 Molecules

Elena A. Kolganova, Vladimir Roudnev

Published Apr 1, 2020• 1 citation

Abstract

Abstract The properties of triatomic LiHe2 clusters are studied. The binding energies and lengths of atom scattering on a weakly bound dimer are calculated using Faddeev differential equations.

DOI: 10.3103/s1062873820040140

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Bulletin of the Russian Academy of Sciences Physics

Weakly Bound Triatomic LiHe2 Molecules

Elena A. Kolganova, Vladimir Roudnev

Published Apr 1, 2020• 1 citation

Publisher

Abstract

Abstract The properties of triatomic LiHe2 clusters are studied. The binding energies and lengths of atom scattering on a weakly bound dimer are calculated using Faddeev differential equations.

DOI: 10.3103/s1062873820040140

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Theoretical Study of Weakly-Bound Triatomic Systems with Faddeev Equations in the Total Orbital Momentum Representation

Виталий Александрович Градусов, Vladimir Roudnev, E. A. Yarevsky +1 more

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The mean-square radii of the molecules ${}^{4}{\mathrm{He}}_{3},$ ${}^{4}{\mathrm{He}}_{2}{\ensuremath{-}}^{6}\mathrm{Li},$ ${}^{4}{\mathrm{He}}_{2}{\ensuremath{-}}^{7}\mathrm{Li},$ and ${}^{4}{\mathrm{He}}_{2}{\ensuremath{-}}^{23}\mathrm{Na}$ are calculated using a three-body model with contact interactions. They are obtained from a universal scaling function calculated within a renormalized scheme for three particles interacting through pairwise Dirac-$\ensuremath{\delta}$ interaction. The root-mean-square distance between two atoms of mass ${m}_{A}$ in a triatomic molecule are estimated to be of the order of $\mathcal{C}\sqrt{{\ensuremath{\Elzxh}}^{2}/[{m}_{A}{(E}_{3}\ensuremath{-}{E}_{2})]},$ where ${E}_{2}$ is the dimer and ${E}_{3}$ is the trimer binding energies, and $\mathcal{C}$ is a constant (varying from $\ensuremath{\sim}0.6$ to $\ensuremath{\sim}1),$ which depends on the ratio between ${E}_{2}$ and ${E}_{3}.$ Considering previous estimates for the trimer energies, we also predict the sizes of rubidium and sodium trimers in atomic traps.The mean-square radii of the molecules ${}^{4}{\mathrm{He}}_{3},$ ${}^{4}{\mathrm{He}}_{2}{\ensuremath{-}}^{6}\mathrm{Li},$ ${}^{4}{\mathrm{He}}_{2}{\ensuremath{-}}^{7}\mathrm{Li},$ and ${}^{4}{\mathrm{He}}_{2}{\ensuremath{-}}^{23}\mathrm{Na}$ are calculated using a three-body model with contact interactions. They are obtained from a universal scaling function calculated within a renormalized scheme for three particles interacting through pairwise Dirac-$\ensuremath{\delta}$ interaction. The root-mean-square distance between two atoms of mass ${m}_{A}$ in a triatomic molecule are estimated to be of the order of $\mathcal{C}\sqrt{{\ensuremath{\Elzxh}}^{2}/[{m}_{A}{(E}_{3}\ensuremath{-}{E}_{2})]},$ where ${E}_{2}$ is the dimer and ${E}_{3}$ is the trimer binding energies, and $\mathcal{C}$ is a constant (varying from $\ensuremath{\sim}0.6$ to $\ensuremath{\sim}1),$ which depends on the ratio between ${E}_{2}$ and ${E}_{3}.$ Considering previous estimates for the trimer energies, we also predict the sizes of rubidium and sodium trimers in atomic traps.

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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.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.

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The mean-square radii of the molecules

{}^{4}{\mathrm{He}}_{3},

${}^{4}{\mathrm{He}}_{2}{\ensuremath{-}}^{6}\mathrm{Li},$ ${}^{4}{\mathrm{He}}_{2}{\ensuremath{-}}^{7}\mathrm{Li},$ and ${}^{4}{\mathrm{He}}_{2}{\ensuremath{-}}^{23}\mathrm{Na}$ are calculated using a three-body model with contact interactions. They are obtained from a universal scaling function calculated within a renormalized scheme for three particles interacting through pairwise Dirac-$\ensuremath{\delta}$ interaction. The root-mean-square distance between two atoms of mass

{m}_{A}

in a triatomic molecule are estimated to be of the order of $\mathcal{C}\sqrt{{\ensuremath{\Elzxh}}^{2}/[{m}_{A}{(E}_{3}\ensuremath{-}{E}_{2})]},$ where

{E}_{2}

is the dimer and

{E}_{3}

is the trimer binding energies, and

\mathcal{C}

is a constant (varying from $\ensuremath{\sim}0.6$ to $\ensuremath{\sim}1),$ which depends on the ratio between

{E}_{2}

and

{E}_{3}.

Considering previous estimates for the trimer energies, we also predict the sizes of rubidium and sodium trimers in atomic traps.

{\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.