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The Journal of Chemical Physics

Calculations and estimates of the ground state energy of helium trimers

Ludwig W. Bruch, Ian J. McGee

Published Jul 1, 1973• 87 citations

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 −0.05 to −0.2 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.

DOI: 10.1063/1.1679820

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Physical Review A•May 1, 1973•4 citations

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 −0.05 to −0.2 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.

The ground state of molecular trimers is studied in three dimensions for these pair potential models: the square well, the exponential, the Yukawa, the Gaussian, and the Lennard-Jones 12–6. Three spin cases are considered: three spin-zero bosons and the spin- (1/2) and spin- (3/2) states of three spin- (1/2) fermions. Variational wavefunctions are constructed which satisfy the exchange symmetry requirements for these cases. Bounds are obtained for the threshold coupling constants at which self-bound trimers occur. Consequences for possible self-bound trimers of 3He are discussed.

Through a variational calculation, the ground-state binding energy of the

^{4}\mathrm{He}

trimer is computed using the ab initio potential of Bertoncini and Wahl. These results indicate a stable trimer bound by 0.3 \ifmmode^\circ\else\textdegree\fi{}K.