Croatica Chemica Acta

Variational Study of Fermionic Helium Dimer and Trimer in Two Dimensions

Leandra Vranješ Markić, Srećko Kilić

Published Dec 4, 2000• 1 citation

Abstract

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.

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Croatica Chemica Acta

Variational Study of Fermionic Helium Dimer and Trimer in Two Dimensions

Leandra Vranješ Markić, Srećko Kilić

Published Dec 4, 2000• 1 citation

OpenAlex

Abstract

Related papers

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The Journal of Chemical PhysicsMar 1, 199425 citations

The ground-state properties of

{}^{3}\mathrm{He}

and

{}^{4}\mathrm{He}

trimers and tetramers in infinite and restricted two-dimensional and quasi-two-dimensional (2D) space are studied. Using Monte Carlo calculation in two stages successively, simple variational Monte Carlo and diffusion Monte Carlo, we find that all trimers (except one of

{}^{3}\mathrm{He}

with spin 3/2) and tetramers are bound. In infinite 2D space the binding energy of

{}^{4}\mathrm{He}

trimer is $\ensuremath{-}183(1) \mathrm{mK}$ and of tetramer $\ensuremath{-}435(1) \mathrm{mK}.$ In the same environment for

{}^{3}\mathrm{He},

using Jastrow-Feenberg-Bruch wave functions trimer (spin 1/2) is bound with $\ensuremath{-}0.013(1) \mathrm{mK}$ and tetramer with $\ensuremath{-}0.021(1) \mathrm{mK}.$ Employing in the same procedure ``dimerlike'' wave functions for

{}^{3}\mathrm{He}

molecules in infinite 2D space it is discovered that trimer prefers the structure of one dimer and one separate particle while a composition of two separate dimers is preferable for tetramer. In this case binding energies are $\ensuremath{-}0.020(1) \mathrm{mK}$ for trimer and $\ensuremath{-}0.040(1) \mathrm{mK}$ for tetramer. The binding energies of mixed molecules in infinite 2D space are $\ensuremath{-}74.3(4)$ mK ${(}^{3}\mathrm{He}{\ensuremath{-}}^{4}{\mathrm{He}}_{2});$ $\ensuremath{-}14(1)$ mK ${(}^{3}{\mathrm{He}}_{2}{\ensuremath{-}}^{4}\mathrm{He});$ $\ensuremath{-}254(4)$ mK ${(}^{3}\mathrm{He}{\ensuremath{-}}^{4}{\mathrm{He}}_{3});$ $\ensuremath{-}118(2)$ mK ${(}^{3}{\mathrm{He}}_{2}{\ensuremath{-}}^{4}{\mathrm{He}}_{2});$ $\ensuremath{-}11(1)$ mK ${(}^{3}{\mathrm{He}}_{3}{\ensuremath{-}}^{4}\mathrm{He}).$ In holding potentials with well-adjusted parameters there is a drastic increase of binding for trimer and tetramer in both sorts of helium atoms.