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Physical Review A

Search for Borromean states in the He-He-Rb triatomic system

Yong Li, Wenjuan Zhang, Qingdong Gou, Hongwei Song, Ting-Yun Shi

Published Aug 30, 2010• 19 citations
Publisher

Abstract

We search for the existence of weakly bound He-He-Rb molecules. The He-He-Rb 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 $^{3}\mathrm{He}$-$^{3}\mathrm{He}$-$^{85}\mathrm{Rb}$, $^{3}\mathrm{He}$-$^{4}\mathrm{He}$-$^{85}\mathrm{Rb}$, and $^{4}\mathrm{He}$-$^{4}\mathrm{He}$-$^{85}\mathrm{Rb}$ trimers, respectively. The bound state for the $^{3}\mathrm{He}$-$^{3}\mathrm{He}$-$^{85}\mathrm{Rb}$ molecule is a Borromean state found in a realistic molecular systems because there are no bound states in both the $^{3}\mathrm{He}$-$^{3}\mathrm{He}$ and $^{3}\mathrm{He}$-$^{85}\mathrm{Rb}$ dimers.

DOI
10.1103/physreva.82.022515

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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 the weakly bound He-He-K 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, the Schr\"odinger equation for the triatomic systems is solved using hyperspherical coordinates in the adiabatic approximation. A bound state is found for each of the $^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$, $^{4}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$, and $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$ trimers, respectively. The bound state for the $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$ molecule is the halo state found in realistic molecular systems for there are no bound states in both the $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}$ and $^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$ dimers.
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.
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.