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Physical Review A

Halo state in realistic molecular systems

Yong Li, Qingdong Gou, Ting-Yun Shi

Published Sep 1, 2006• 26 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.74.032502

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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 4He\ensuremath-4He\ensuremath-39K^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}4He\ensuremath-4He\ensuremath-39K, 4He\ensuremath-3He\ensuremath-39K^{4}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}4He\ensuremath-3He\ensuremath-39K, and 3He\ensuremath-3He\ensuremath-39K^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}3He\ensuremath-3He\ensuremath-39K trimers, respectively. The bound state for the 3He\ensuremath-3He\ensuremath-39K^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}3He\ensuremath-3He\ensuremath-39K molecule is the halo state found in realistic molecular systems for there are no bound states in both the 3He\ensuremath-3He^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}3He\ensuremath-3He and 3He\ensuremath-39K^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}3He\ensuremath-39K dimers.
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 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 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 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 3He^{3}\mathrm{He}3He-3He^{3}\mathrm{He}3He-85Rb^{85}\mathrm{Rb}85Rb, 3He^{3}\mathrm{He}3He-4He^{4}\mathrm{He}4He-85Rb^{85}\mathrm{Rb}85Rb, and 4He^{4}\mathrm{He}4He-4He^{4}\mathrm{He}4He-85Rb^{85}\mathrm{Rb}85Rb trimers, respectively. The bound state for the 3He^{3}\mathrm{He}3He-3He^{3}\mathrm{He}3He-85Rb^{85}\mathrm{Rb}85Rb molecule is a Borromean state found in a realistic molecular systems because there are no bound states in both the 3He^{3}\mathrm{He}3He-3He^{3}\mathrm{He}3He and 3He^{3}\mathrm{He}3He-85Rb^{85}\mathrm{Rb}85Rb dimers.
The three-body Schrdinger equation is approximately solved in the hyperspherical coordinates and the binding energies of the three-body weakly bound systems are calculated with the purpose to find if He-He-Ba trimers could exist. Using the special feature of the B-spline function like the flexible and highly localized properties, hypersphercial potentials are obtained by modifying the knots distribution of the B-spline basis of different weakly bound three-atom systems. Employing the best empirical interaction potentials between each pair of particles, we obtain that in the ground state binding energies of the weakly bound typical three-atom systems, the bindings of the molecules, 4He-4He-138Ba, 4He-3He-138Ba and 3He-3He-138Ba are possible. The binding energies of these systems are shown in the order of 1 Kelvin, each system could support only one bound state. These weakly bound molecules can exist only in a very cold environment. To get insight into the geometry of the molecules, the features of the channel functions associated with the hyperspherical potential curves of each system are investigated.