Trimer ground-state energies in the Faddeev-UPE approximation

Elena A. Kolganova, Y. K. Ho, Alexander Konstantinovich Motovilov

F. Cabral

Vladimir Roudnev, Sergei Leonidovich Yakovlev

T. K. Lim, K E Duffy, S. Nakaichi +2 more

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.

Peter W. Langhoff, A. J. Hernández

K E Duffy, T. K. Lim

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.