Calculations and estimates of the ground state energy of helium trimers

Abstract

Variational calculations of the ground state energy of ⁴He trimers are reported and are compared with the Hall‐Post‐Stenschke lower bound on the ground state energy. The variational result for the ground state energy for a range of model pair potentials is in the range $\text{−0.05}$ to $\text{−0.2\hspace{0.17em}}\mathrm{K}$ ; the effect of the triplet nonadditive term is estimated to be less than 1% of the contribution of the pair potentials. A study of the variation of the ground state energy of 3 bosons with pair potential coupling constant is also reported for a Lennard‐Jones and a Morse potential model. There is no bound spin 3/2 ³He trimer; a lower bound is given for the ground state energy of the spin 1/2 trimer and analogy with the boson results is used to argue that the spin 1/2 trimer is probably not bound. This paper contains computational applications of formal results derived elsewhere.