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The Journal of Chemical Physics

Mixed and fermionic helium trimers

K E Duffy, T. K. Lim

Published May 15, 1979• 17 citations
Publisher

Abstract

The existence of mixed and fermionic helium trimers is investigated via the Faddeev–UPE method. Each three-atom system is assumed to interact through phenomenological pairwise local potentials. The ground-state binding energy of (4He)2–3He is evaluated to be about 0.000 002–0.0008 °K while (3He)2–4He is found to be unbound as is (3He)3.

DOI
10.1063/1.437267

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International Journal of Quantum Chemistry•Sep 5, 2006•21 citations
The existence of mixed and fermionic helium trimers is investigated via the Faddeev–UPE method. Each three-atom system is assumed to interact through phenomenological pairwise local potentials. The ground-state binding energy of (4He)2–3He is evaluated to be about 0.000 002–0.0008 °K while (3He)2–4He is found to be unbound as is (3He)3.
The ground-state energies of systems of three and four identical heavy rare-gas atoms, treated as spinless bosons and assumed to interact via pairwise Morse potentials, are calculated using five different methods. Self-bound trimers and tetramers are found in every case with upper and lower bound formulas yielding energies which are extremely close. For these near-classical and massive systems, the Faddeev–UPE method is decidedly poor. On the other hand, the simple generalization of Bruch–Sawada’s upper bound is particularly effective. The plight of Faddeev–UPE here implies that great caution must be exercised in using the unitary pole expansion in chemical physics. ATMS is excellent and appears the method of choice for bound-state problems.
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