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International Journal of Quantum Chemistry

Finite element investigation of the ground states of the helium trimers 4He3 and 4He2–3He

Moses Salci, E. A. Yarevsky, S. B. Levin, Nils Elander

Published Sep 5, 2006• 21 citations
Publisher

Abstract

Abstract A three‐dimensional finite element method is applied to the ground states of the symmetric and asymmetric atomic helium trimers 4He3 and 4He2–3He. Three different He–He interaction potentials of hard‐core nature were studied. Two extrapolation procedures based on the convergence properties of the finite element method are investigated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

DOI
10.1002/qua.21095

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Abstract A three‐dimensional finite element method is applied to the ground states of the symmetric and asymmetric atomic helium trimers 4He3 and 4He2–3He. Three different He–He interaction potentials of hard‐core nature were studied. Two extrapolation procedures based on the convergence properties of the finite element method are investigated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
Abstract We have shown that a simple model based on pairwise deltafunction potentials can, with an appropriate choice of parameters, represent the general behavior of ultra‐low temperature helium dimers and trimers, including all possible isotopomers. The species 4He2, 4He3, and 4He23He are stable, with binding energies of approximately 1.3, 100, and 10 mK, respectively. An Efimov state for 4He23He is also predicted, bound by 2.4 mK. The remaining dimers and trimers, 4He 3He, 3He2, 4He 3He2, and 3He3, are evidently unstable. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001
We report accurate ground state energies and structural properties for small clusters of 4He computed with the diffusion quantum Monte Carlo (DMC) method combined with high quality trial wave functions and using the recent analytical pair potential of Tang, Toennies, and Yiu [Phys. Rev. Lett. 74, 1546 (1995)]. Calculations based on the older HFD-B(He) potential are reported for comparison. The clusters are found to be extremely floppy and to be characterized by very diffuse wave functions. The DMC results for 4He2 and 4He3 are in excellent agreement with other calculations using conventional methods. 4He3 is found to have a noticeable contribution from nearly linear geometries. The internal structure of the clusters is described by a three particle correlation function which reveals a significantly non-spherical internal cluster structure. The energies for all cluster sizes are found to be slightly higher than those obtained with the HFD-B(He) pair potential. Exploratory calculations on the helium trimer indicate that the effects of three body interactions do not exceed the uncertainty margin provided by different state of the art pair potentials.
Weakly bound triatomic molecules consisting of two helium atoms and one alkali metal atom are studied by means of the diffusion Monte Carlo method. We determined the stability of 4He2A, 4He3HeA, and 3He2A, where A is one of the alkali atoms Li, Na, K, Rb, or Cs. Some of the trimers with 3He are predicted to be self-bound for the first time, but this is observed to be dependent on the He–A interaction potential model. In addition to the ground-state energy of the trimers, we determined their density, radial, and angular distributions. Many of them are spatially very extended, which qualifies them as quantum halo states.