Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Physical Society of Japan

Threshold Condition for Forming an Atomic4He Trimer

H. W. Graben, Kai-Ning Chang

Published Mar 15, 1980• 0 citations
Publisher

Abstract

The Rayleigh-Ritz variational principle is used to formulate a rigorous bound on the threshold conditions under which three helium four atoms will form a bound state when their pair interaction is represented by the Lennard-Jones (n, 6) model and their nonadditive interaction is taken to be the Muto-Axilrod-Teller triple-dipole potential. The accepted parameter values of the model with n equal to 12 predict a bound-state trimer. The oversight, that of failing to use the (12, 6) parameter values of Kihara, Midzuno and Shizume in the extensive work on liquid helium, is pointed out.

DOI
10.1143/jpsj.48.1043

Related papers

Calculations and estimates of the ground state energy of helium trimers

Ludwig W. Bruch, Ian J. McGee

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 Journal of Chemical Physics•Jul 1, 1973•87 citations

Trimer binding in two dimensions

F. Cabral, Ludwig W. Bruch

The ground state energies of loosely bound boson and fermion trimers interacting via Lennard-Jones (12,6) pair potentials in two dimensions are evaluated with variational calculations. Threshold coupling constants for self-binding are determined by extrapolation to zero binding energy. The results are used to give estimates of the binding energy of the 4He trimer and in a discussion of the ordering of dimer and trimer thresholds in two dimensions.

The Journal of Chemical Physics•May 15, 1979•24 citations

The interaction potential of a symmetric helium trimer

Aniket Bhattacharya, James B. Anderson

The interaction potential of three helium atoms in symmetric linear configurations is calculated under the Born–Oppenheimer approximation using an ‘‘exact’’ Green’s function quantum Monte Carlo method. The results are compared with those of ‘‘exact’’ quantum Monte Carlo calculations for the helium dimer and the Axilrod–Teller triple-dipole energy expression. For nearest neighbor separations of 5.6 bohrs, the equilibrium distance for a helium dimer, the corresponding trimer energy is −21.5±1.9 K, compared to −22.3±0.2 K, calculated for pairwise additive behavior. For all internuclear separations in the neighborhood of the van der Waals well (∼5.6 bohrs), the nonadditive contribution is found to be very small.

The Journal of Chemical Physics•Jun 15, 1994•19 citations

Efimov States for H4e Trimers?

Tomás González‐Lezana, Jesús Rubayo‐Soneira, Salvador Miret-Artés +3 more

Helium trimer bound states are calculated with a variational method described in terms of pair atom coordinates and distributed Gaussian functions by assuming zero total angular momentum. With the two-body interaction potential used, a weakly bound state for the dimer and only two bound states for the trimer are found. Although strictly speaking the first excited trimer state is not an Efimov state, we show that this state presents several characteristics of the Efimov behavior which are extensively discussed in the present work. Special emphasis is placed on the main geometrical configurations contributing to the two bound trimer states, and suggestions are made on the possible ways of experimentally detecting the Efimov-type state.

Physical Review Letters•Feb 22, 1999•72 citations

On a Threshold Condition for Forming a Helium-Four Trimer

Kai-Ning Chang

•Jan 1, 1978•0 citations

Universality in the three-body problem for 4He atoms

Eric Braaten, H.‐W. Hammer

The two-body scattering length a for ${}^{4}\mathrm{He}$ atoms is much larger than their effective range ${r}_{s}.$ As a consequence, low-energy few-body observables have universal characteristics that are independent of the interaction potential. Universality implies that, up to corrections suppressed by ${r}_{s}/a,$ all low-energy three-body observables are determined by a and a three-body parameter ${\ensuremath{\Lambda}}_{*}.$ We give simple expressions in terms of a and ${\ensuremath{\Lambda}}_{*}$ for the trimer binding-energy equation, the atom-dimer scattering phase shifts, and the rate for three-body recombination at threshold. We determine ${\ensuremath{\Lambda}}_{*}$ for several ${}^{4}\mathrm{He}$ potentials from the calculated binding energy of the excited state of the trimer and use it to obtain the universality predictions for the other low-energy observables. We also use the calculated values for one potential to estimate the effective range corrections for the other potentials.

arXiv:cond-mat/0203421•Physical Review A•Apr 11, 2003•70 citations
The Rayleigh-Ritz variational principle is used to formulate a rigorous bound on the threshold conditions under which three helium four atoms will form a bound state when their pair interaction is represented by the Lennard-Jones (n, 6) model and their nonadditive interaction is taken to be the Muto-Axilrod-Teller triple-dipole potential. The accepted parameter values of the model with n equal to 12 predict a bound-state trimer. The oversight, that of failing to use the (12, 6) parameter values of Kihara, Midzuno and Shizume in the extensive work on liquid helium, is pointed out.
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 interaction potential of three helium atoms in symmetric linear configurations is calculated under the Born–Oppenheimer approximation using an ‘‘exact’’ Green’s function quantum Monte Carlo method. The results are compared with those of ‘‘exact’’ quantum Monte Carlo calculations for the helium dimer and the Axilrod–Teller triple-dipole energy expression. For nearest neighbor separations of 5.6 bohrs, the equilibrium distance for a helium dimer, the corresponding trimer energy is −21.5±1.9 K, compared to −22.3±0.2 K, calculated for pairwise additive behavior. For all internuclear separations in the neighborhood of the van der Waals well (∼5.6 bohrs), the nonadditive contribution is found to be very small.
Helium trimer bound states are calculated with a variational method described in terms of pair atom coordinates and distributed Gaussian functions by assuming zero total angular momentum. With the two-body interaction potential used, a weakly bound state for the dimer and only two bound states for the trimer are found. Although strictly speaking the first excited trimer state is not an Efimov state, we show that this state presents several characteristics of the Efimov behavior which are extensively discussed in the present work. Special emphasis is placed on the main geometrical configurations contributing to the two bound trimer states, and suggestions are made on the possible ways of experimentally detecting the Efimov-type state.
The two-body scattering length a for 4He{}^{4}\mathrm{He}4He atoms is much larger than their effective range rs.{r}_{s}.rs​. As a consequence, low-energy few-body observables have universal characteristics that are independent of the interaction potential. Universality implies that, up to corrections suppressed by rs/a,{r}_{s}/a,rs​/a, all low-energy three-body observables are determined by a and a three-body parameter ${\ensuremath{\Lambda}}_{*}.$ We give simple expressions in terms of a and ${\ensuremath{\Lambda}}_{*}$ for the trimer binding-energy equation, the atom-dimer scattering phase shifts, and the rate for three-body recombination at threshold. We determine ${\ensuremath{\Lambda}}_{*}$ for several 4He{}^{4}\mathrm{He}4He potentials from the calculated binding energy of the excited state of the trimer and use it to obtain the universality predictions for the other low-energy observables. We also use the calculated values for one potential to estimate the effective range corrections for the other potentials.