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Journal of Physics B Atomic Molecular and Optical Physics

Ground-state characteristics of helium–alkali tetramers

Petar Stipanović, Leandra Vranješ Markić

Published Jun 8, 2018• 4 citations
Publisher

Abstract

Abstract Helium–alkali tetramers 4 He 3 A , 3 He 4 He 2 A and 3 He 2 4 HeA , where A is one of the alkali atoms 6,7 Li, 23 Na, 39,40,41 K, 85,87 Rb or 133 Cs, were studied using diffusion Monte Carlo method. Besides ground-state energies, exact distribution functions were evaluated. Spatial arrangements of atoms in clusters qualify He–A tetramers as transitional systems, which reveal halo-like spatial extension. On the one hand, swapping 4 He by 3 He atom in a He–Li tetramer, one can trace how quasi-halo structure transforms into halo structure. On the other hand, swapping 3 He by 4 He in He–A tetramer reveals behavior previously noticed in helium droplets doped with an alkali atom. Helium atoms start grouping on one side of an alkali atom, which is clearer in He–A clusters with more 4 He atoms that have stronger self-binding. The effect is the more pronounced the bigger alkali atom is, since it is then harder for the remaining He atoms to surround an alkali.

DOI
10.1088/1361-6455/aacb45

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Abstract Helium–alkali tetramers 4 He 3 A , 3 He 4 He 2 A and 3 He 2 4 HeA , where A is one of the alkali atoms 6,7 Li, 23 Na, 39,40,41 K, 85,87 Rb or 133 Cs, were studied using diffusion Monte Carlo method. Besides ground-state energies, exact distribution functions were evaluated. Spatial arrangements of atoms in clusters qualify He–A tetramers as transitional systems, which reveal halo-like spatial extension. On the one hand, swapping 4 He by 3 He atom in a He–Li tetramer, one can trace how quasi-halo structure transforms into halo structure. On the other hand, swapping 3 He by 4 He in He–A tetramer reveals behavior previously noticed in helium droplets doped with an alkali atom. Helium atoms start grouping on one side of an alkali atom, which is clearer in He–A clusters with more 4 He atoms that have stronger self-binding. The effect is the more pronounced the bigger alkali atom is, since it is then harder for the remaining He atoms to surround an alkali.
Weakly bound triatomic molecules consisting of two helium atoms and one alkali metal atom are studied by means of the diffusion Monte Carlo method. We determined the stability of 4He2A, 4He3HeA, and 3He2A, where A is one of the alkali atoms Li, Na, K, Rb, or Cs. Some of the trimers with 3He are predicted to be self-bound for the first time, but this is observed to be dependent on the He–A interaction potential model. In addition to the ground-state energy of the trimers, we determined their density, radial, and angular distributions. Many of them are spatially very extended, which qualifies them as quantum halo states.
The universality of quantum halo states enables a comparison of systems from different fields of physics, as demonstrated in two- and three-body clusters. In the present work, we studied weakly bound helium tetramers in order to test whether some of these four-body realistic systems qualify as halos. Their ground-state binding energies and structural properties were thoroughly estimated using the diffusion Monte Carlo method with pure estimators. Helium tetramer properties proved to be less sensitive on the potential model than previously evaluated trimer properties. We predict the existence of realistic four-body halo 4 He 2 3 He 2, whereas 4 He 4 and 4 He 3 3 He are close to the border and thus can be used as prototypes of quasi-halo systems. Our results could be tested by the experimental determination of the tetramers’ structural properties using a setup similar to the one developed for the study of helium trimers.
The interactions between alkali atoms and 4 He, as well as those between H - and 4 He, are known to be even weaker than those between two helium atoms. In this work we show that when the three-particle potential energy surface is obtained as a sum of two-body functions, the ensuing ground state configurations are indeed very weakly bound and acquire spatial shapes difficult to describe in simple configurational terms. We have employed the quantum diffusion Monte Carlo method to analyse the He 2 Li, He 2 Na and He 2 H - systems, for which possible molecular `shapes' are extracted from the final DMC distributions by defining within them conventional chemical structures with varying degree of `stiffness' attached to the nuclear positions.
Small helium (4He) clusters containing the lighter isotope He3 are studied by means of quantum Monte Carlo methods. Accurate ground state energies and structural properties are obtained using accurate trial wave functions and the Tang–Tonnies–Yiu (TTY) helium–helium pair potential. The dimer He4–3He is not bound; as well as the trimer He4He23. The smallest cluster containing He3 is He24He3 with a nonrigid structure having a marked linear contribution. Interestingly, this weakly bound system, with an energy one order of magnitude less than the He34 trimer, is able to bind another He3 atom, forming the tetramer He24He23, which shows the odd feature of having five out of six unbound pairs. In general, the substitution of a single He4 atom in a pure cluster with a He3 atom leads to an energetic destabilization, as the pair He4–3He is not bound. The isotopic impurity is found to perturb only weakly the distributions of the remaining He4 atoms, which retain the high floppiness already found in the pure clusters. As the number of atoms increases the isotopic impurity has the marked tendency to stay on the surface of the cluster. This behavior is consistent with the formation of the so-called “Andreev states” of a single He3 in liquid He4 helium and droplets, where the impurity tends to form single-particle states on the surface of the pure He4.
Spectroscopy of doped helium nanodroplets has become, in recent years, a popular tool for the study of bothfinite size samples of the helium quantum fluid and molecules isolated in this sub Kelvin environment. Whilemany dopants migrate to the center of the droplet, alkali (Ak) atoms in their ground electronic state, becauseof their so weak interaction with He, remain at the surface, the latter being in this way slightly distortedexhibiting a dimple. However, when in their first excited states, Ak atoms are forming exciplexes. These areanisotropic with the central atom surrounded by a ring of He atoms located in the nodal plane of the valenceelectron pz orbital. Structural properties, obtained by DMC and PIMC, are presented here for some Ak -Hen exciplexes.Ak2 dimers in helium environment have also gained interest in this last decade, in connexion with the generationof ultracold molecules. When attached to helium droplets, Ak atoms can float on the surface andform molecules in cold collisions. DMC and PIMC methods are used to compute energetics and structuralinformations for Rb2 in helium. In particular, the orientation of the dimer relative to the droplet surface isexamined.
The ground-state properties of 3He{}^{3}\mathrm{He}3He and 4He{}^{4}\mathrm{He}4He 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 3He{}^{3}\mathrm{He}3He with spin 3/2) and tetramers are bound. In infinite 2D space the binding energy of 4He{}^{4}\mathrm{He}4He trimer is $\ensuremath{-}183(1) \mathrm{mK}$ and of tetramer $\ensuremath{-}435(1) \mathrm{mK}.$ In the same environment for 3He,{}^{3}\mathrm{He},3He, 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 3He{}^{3}\mathrm{He}3He 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.