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

O mogućnosti postojanja dvoatomske molekule helija

Kilić, S., Sunarić, S.

Published Jan 1, 1979• 0 citations
OpenAlex

Abstract

The ground state energics of the helium dimers interacting via Lennard-Jones (12,6) pair potential in two dimensions are evaluated by means of variational calculus. The Ljolje type of pair function is employed. The self-bound states of dimers 4He -4He and 3He –4He are found, while the binding of the dimers 3He -3He is not obtained.

Related papers

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

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

Variational Study of Fermionic Helium Dimer and Trimer in Two Dimensions

Leandra Vranješ Markić, Srećko Kilić

In variational calculation, we have obtained the binding energy of helium 3 dimer in two dimensions.The existence of one bound state, with the binding energy -0.014 mK, has been definitively found.Also, the existence of a binding state of helium 3 trimer having spin -1/2 with the energy below -0.0057 mK is indicated.This reopens the question of the existence of the gas phase of many helium 3 atoms on the surface of superfluid helium 4. Key words: helium dimer, helium trimer, binding energy of helium 3 dimer. # Dedicated to Academician Krunoslav Ljolje on the occasion of his 70th birthday.

Croatica Chemica Acta•Dec 4, 2000•1 citation

Green’s function Monte Carlo calculation for the ground state of helium trimers

F. Cabral, Malvin H. Kalos

The ground state energy of weakly bound boson trimers interacting via Lennard-Jones (12,6) pair potentials is calculated using a Monte Carlo Green’s Function Method. Threshold coupling constants for self binding are obtained by extrapolation to zero binding.

The Journal of Chemical Physics•Feb 1, 1981•0 citations

A variational calculation of the binding energy of the fermionic 3He tetramer

S. Nakaichi-Maeda, T. K. Lim, Y. Akaishi

A variational calculation is performed for the (3He)4 system interacting pairwise through the Lennard-Jones He–He potential. Use of an integrodifferential Euler equation is made to determine an optimum wave function, leading to results showing that the existence of this molecule is unlikely. It is confirmed that states of the system with nonzero orbital angular momentum yield lower energies. Also, it appears that the number of 3He atoms needed to form self-bound molecules must be larger than 5.

The Journal of Chemical Physics•Dec 1, 1982•7 citations

Near-threshold behavior of the ground-state binding energies of the few-atom systems of He4 and other bosons in two and three dimensions

T. K. Lim, S. Nakaichi, Y. Akaishi +1 more

The results of accurate variational calculations for the ground-state binding energies of several $N$-boson systems in two and three dimensions are reported; the systems specifically considered are small ($N=2, 3, 4, \mathrm{and} 5$) clusters of $^{4}\mathrm{He}$ atoms interacting through pairwise Lennard-Jones potentials. Evidence is found strongly suggesting each set of systems have a common functional relationship linking the binding energies and the De Boer quantum constant near threshold for self-binding. These calculations also confirm the existence of a unique threshold value of the interaction strength for all $N$-boson systems in $2D$. In addition, the linear relation between the binding energies of helium clusters present in $3D$ holds ture in $2D$ as well.

Physical Review A•Jul 1, 1980•17 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.
In variational calculation, we have obtained the binding energy of helium 3 dimer in two dimensions.The existence of one bound state, with the binding energy -0.014 mK, has been definitively found.Also, the existence of a binding state of helium 3 trimer having spin -1/2 with the energy below -0.0057 mK is indicated.This reopens the question of the existence of the gas phase of many helium 3 atoms on the surface of superfluid helium 4. Key words: helium dimer, helium trimer, binding energy of helium 3 dimer. # Dedicated to Academician Krunoslav Ljolje on the occasion of his 70th birthday.
A variational calculation is performed for the (3He)4 system interacting pairwise through the Lennard-Jones He–He potential. Use of an integrodifferential Euler equation is made to determine an optimum wave function, leading to results showing that the existence of this molecule is unlikely. It is confirmed that states of the system with nonzero orbital angular momentum yield lower energies. Also, it appears that the number of 3He atoms needed to form self-bound molecules must be larger than 5.
The results of accurate variational calculations for the ground-state binding energies of several NNN-boson systems in two and three dimensions are reported; the systems specifically considered are small (N=2,3,4,and5N=2, 3, 4, \mathrm{and} 5N=2,3,4,and5) clusters of 4He^{4}\mathrm{He}4He atoms interacting through pairwise Lennard-Jones potentials. Evidence is found strongly suggesting each set of systems have a common functional relationship linking the binding energies and the De Boer quantum constant near threshold for self-binding. These calculations also confirm the existence of a unique threshold value of the interaction strength for all NNN-boson systems in 2D2D2D. In addition, the linear relation between the binding energies of helium clusters present in 3D3D3D holds ture in 2D2D2D as well.