An accurate calculation of the three-body potential for the ground state of the helium trimer

Abstract

An extended group function model has been applied to determine the three-body potential for the ground state of the helium trimer. The basis set for the calculations is an uncontracted (17s,6p,4d,3f) set of Gaussian type functions contracted to [8s,6p,4d,3f]. Three different types of configurations were considered: (i) equilateral triangles of side R, R∈{3.5,4.0,...,8.5,9.0} a.u., (ii) linear configurations with R12=R23, R12∈{3.5,4.0,...,8.5,9.0} a.u., and (iii) a set of pseudo-random configurations. For the equilateral triangular configurations and the linear configurations, and with equal distances larger than 5.5 a.u., the magnitude of the ratio between the three-body potential and the sum of the corresponding two-body potentials, is less than 0.003. The value of the three-body potential for the triangular and the linear configuration with equal distance R=5.669 289 a.u.=3 Å, is respectively 0.040 μH and −0.045 μH. In the long range region the calculated three-body potential is very close to the Axilrod–Teller triple-dipole energy.

Weakly bound states of the He-He-Ca triatomic system

“…The total interaction potential V (R,φ,θ) used in this work is expressed as a sum of the pair interactions of the three atoms, since any possible three-body interaction is expected to be small and it has been shown to affect less than 1% of the ground-state energy in the cases of the He-He-He and He-He-Be systems [25][26][27].…”

Weakly bound states of the He-He-Mg trimer

“…(6) is solved by using B-spline expansion. The three-body interaction is expected to be small for the He-He-Mg molecule, and in the case of the He-He-He system, it has been shown to affect less than 1% of the ground-state energy [24,25]. Therefore, we do not consider any possible three-body interaction in our calculations, and the interactions of the system are the two-body interactions between each atom.…”

Universality and the three-body parameter of4He trimers

“…Its scattering length is 100.01 Å which is 18.6 times the van der Waals length l vdW = (mC 6 / ) 1/4 . The threebody interaction has been shown to bring only small corrections [34][35][36], and we neglect it in this study. Thus, in our calculation, the 3-body phase which fixes the energy of Efimov trimers builds up only from the LM2M2 two-body interaction.…”