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

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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.