Searching for many-body effects and Efimov states in very weakly bound triatomics: HeNeH− and HeNeH

The rotationless, vibrational states of two weakly bound triatomic species are calculated using a variational expansion over multicentred Gaussian functions (the DGF method described in the main text) and corrections are introduced by using the three-body potentials vis a vis the sum-of-potentials approximation. The effects are seen to be very small and isotopic substitution is further introduced to evaluate changes on the vibrational structures of both systems, aiming at possibly detecting Efimov behaviour in such special trimers: no Efimov states are found with the available potentials and when the two-body potential strengths are varied. An additional study on the effects of isotopic substitutions for H atoms is also presented. 1 This paper is dedicated to Professor R.D. Levine, a great scientist and a dear friend, on the occasion of his 70th birthday.