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 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.
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.
The ground state of weakly bound dimers and trimers with a radius extending well into the classically forbidden region is explored, with the goal to test the predicted universality of quantum halo states. The focus of the study is molecules consisting of T↓, D↓, ^{3}He, ^{4}He, and alkali atoms, where the interaction between particles is much better known than in the case of nuclei, which are traditional examples of quantum halos. The study of realistic systems is supplemented by model calculations in order to analyze how low-energy properties depend on the interaction potential. The use of variational and diffusion Monte Carlo methods enabled a very precise calculation of both the size and binding energy of the trimers. In the quantum halo regime, and for large values of scaled binding energies, all clusters follow almost the same universal line. As the scaled binding energy decreases, Borromean states separate from tango trimers.
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.
Abstract Over the years many He–He interaction potentials have been developed, some very sophisticated, including various corrections beyond the Born–Oppenheimer approximation. Most of them were used to predict properties of helium dimers and trimers, examples of exotic quantum states, whose experimental study proved to be very challenging. Recently, detailed structural properties of helium trimers were measured for the first time, allowing a comparison with theoretical predictions and possibly enabling the evaluation of different interaction potentials. The comparisons already made included adjusting the maxima of both theoretical and experimental correlation functions to one, so the overall agreement between theory and experiment appeared satisfactory. However, no attempt was made to evaluate the quality of the interaction potentials used in the calculations. In this work, we calculate the experimentally measured correlation functions using both new and old potentials, compare them with experimental data and rank the potentials. We use diffusion Monte Carlo simulations at T = 0, which give within statistical noise exact results of the ground state properties. All models predict both trimers 4 He 3 and 4 He He to be in a quantum halo state.
We report results for the ground-state energy and structural properties of small (4)He-T↓ clusters consisting of up to four T↓ and eight (4)He atoms. These results have been obtained using very well-known (4)He-(4)He and T↓- T↓ interaction potentials and several models for the (4)He- T↓ interatomic potential. All the calculations have been performed with variational and diffusion Monte Carlo methods. It takes at least three atoms to form a mixed bound state. In particular, for small clusters the binding energies are significantly affected by the precise form of the (4)He- T↓ interatomic potential but the stability limits remain unchanged. The only exception is the (4)He(2)T↓ trimer whose stability in the case of the weakest (4)He- T↓ interaction potential is uncertain while it seems stable for other potentials. The mixed trimer (4)He(T↓)(2), a candidate for the Borromean state, is not bound. All other studied clusters are stable. Some of the weakest bound clusters can be classified as quantum halo as a consequence of having high probability of being in a classically forbidden region.
The ground-state properties of 3He and 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 with spin 3/2) and tetramers are bound. In infinite 2D space the binding energy of 4He trimer is $\ensuremath{-}183(1) \mathrm{mK}$ and of tetramer $\ensuremath{-}435(1) \mathrm{mK}.$ In the same environment for 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 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.