Bulletin of the Russian Academy of Sciences Physics

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

Виталий Александрович Градусов, Vladimir Roudnev, E. A. Yarevsky, Sergei Leonidovich Yakovlev

Published May 1, 2021• 0 citations

Abstract

Abstract Results are presented from calculating the spectra of weakly-bound triatomic molecular systems: the Helium trimer and helium–helium alkali molecules. Calculations are made on the basis of the Faddeev equations in the total orbital momentum representation. The existence of excited states with nonzero total orbital momentum of some molecules is confirmed.

DOI: 10.3103/s1062873821050099

Related papers

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

Hiroya Suno, Brett D. Esry

Physical Review ADec 29, 201024 citations

Weakly bound triatomic 4He23He and 3He24He molecules

Bingcong Gou, Fei Wang

International Journal of Quantum ChemistryOct 13, 20041 citation

Helium trimer in the framework of Faddeev approach

Elena A. Kolganova

Differential Faddeev equations in total angular momentum representation are used for the calculations of Helium trimer system. Numerical results on binding energies of the 4 He 3 and ultra-cold collisions of 4 He atom on 4 He dimer are reviewed.

Physics of Particles and NucleiNov 25, 20103 citations

Weakly Bound Triatomic LiHe2 Molecules

Elena A. Kolganova, Vladimir Roudnev

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.

Bulletin of the Russian Academy of Sciences PhysicsApr 1, 20201 citation

Search for weakly bound states of the He-He-Be triatomic system

Yong Li, Hongwei Song, Qingdong Gou +2 more

Physical Review AFeb 5, 20098 citations

Weakly bound triatomic He2Li and He2Na molecules

Jianmin Yuan, C. D. Lin

Journal of Physics B Atomic Molecular and Optical PhysicsAug 14, 199850 citations

Bulletin of the Russian Academy of Sciences Physics

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

Виталий Александрович Градусов, Vladimir Roudnev, E. A. Yarevsky, Sergei Leonidovich Yakovlev

Published May 1, 2021• 0 citations

Publisher

Abstract

DOI: 10.3103/s1062873821050099

Related papers

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

Hiroya Suno, Brett D. Esry

$^{4}\mathrm{He}$ ${}_{2}$ --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.$^{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.

Physical Review ADec 29, 201024 citations

Weakly bound triatomic 4He23He and 3He24He molecules

Bingcong Gou, Fei Wang

Abstract The bound rotational excited states of weakly bound 4He23He and 3He24He molecules have been searched for. Including pair interaction between helium atoms, we solved the Schrödinger equation for the triatomic systems with hyperspherical coordinates in the adiabatic approximation. The resulting potential curves are mostly repulsive for nonzero angular momenta. We conclude that no bound rotational excited states exist in both 4He23He and 3He24He molecules. The stability of the systems depends sensitively on the quantum symmetry and the masses of the particles. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005Abstract The bound rotational excited states of weakly bound 4He23He and 3He24He molecules have been searched for. Including pair interaction between helium atoms, we solved the Schrödinger equation for the triatomic systems with hyperspherical coordinates in the adiabatic approximation. The resulting potential curves are mostly repulsive for nonzero angular momenta. We conclude that no bound rotational excited states exist in both 4He23He and 3He24He molecules. The stability of the systems depends sensitively on the quantum symmetry and the masses of the particles. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

International Journal of Quantum ChemistryOct 13, 20041 citation

Helium trimer in the framework of Faddeev approach

Elena A. Kolganova

Physics of Particles and NucleiNov 25, 20103 citations

Weakly Bound Triatomic LiHe2 Molecules

Elena A. Kolganova, Vladimir Roudnev

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.

Bulletin of the Russian Academy of Sciences PhysicsApr 1, 20201 citation

Search for weakly bound states of the He-He-Be triatomic system

Yong Li, Hongwei Song, Qingdong Gou +2 more

We search for the existence of weakly bound He-He-Be molecules. The He-He-Be molecule is treated as a three-body system. By using hyperspherical coordinates, the Schr\"odinger equation for the triatomic system is solved in the adiabatic approximation. A bound state is found for each of the $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{9}\mathrm{Be}$, $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}^{9}\mathrm{Be}$, and $^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}^{9}\mathrm{Be}$ trimers.We search for the existence of weakly bound He-He-Be molecules. The He-He-Be molecule is treated as a three-body system. By using hyperspherical coordinates, the Schr\"odinger equation for the triatomic system is solved in the adiabatic approximation. A bound state is found for each of the $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{9}\mathrm{Be}$, $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}^{9}\mathrm{Be}$, and $^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}^{9}\mathrm{Be}$ trimers.

Physical Review AFeb 5, 20098 citations

Weakly bound triatomic He2Li and He2Na molecules

Jianmin Yuan, C. D. Lin

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 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.

Journal of Physics B Atomic Molecular and Optical PhysicsAug 14, 199850 citations

^{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.