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Journal of Physics B Atomic Molecular and Optical Physics

Ground states of weakly bound three-atom systems: energies and shapes of 4He2X clusters from Monte Carlo calculations

Cono Di Paola, Franco Antonio Gianturco, Francesco Paesani, Gerardo Delgado-Barrio, Salvador Miret-Artés, Pablo Villarreal, I. Baccarelli, Tomás González‐Lezana

Published Jun 6, 2002• 25 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/35/12/302

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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.
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.
We report accurate ground state energies and structural properties for small clusters of 4He computed with the diffusion quantum Monte Carlo (DMC) method combined with high quality trial wave functions and using the recent analytical pair potential of Tang, Toennies, and Yiu [Phys. Rev. Lett. 74, 1546 (1995)]. Calculations based on the older HFD-B(He) potential are reported for comparison. The clusters are found to be extremely floppy and to be characterized by very diffuse wave functions. The DMC results for 4He2 and 4He3 are in excellent agreement with other calculations using conventional methods. 4He3 is found to have a noticeable contribution from nearly linear geometries. The internal structure of the clusters is described by a three particle correlation function which reveals a significantly non-spherical internal cluster structure. The energies for all cluster sizes are found to be slightly higher than those obtained with the HFD-B(He) pair potential. Exploratory calculations on the helium trimer indicate that the effects of three body interactions do not exceed the uncertainty margin provided by different state of the art pair potentials.
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 possible existence of bound states in small helium clusters containing atomic and molecular hydrogen has been investigated by means of three completely independent sets of calculations. The first set employs the Jacobi–Davidson filtering procedure recently implemented in the Distributed Gaussian Functions (DGF) approach, the second one is based on the solution of the Faddeev equation by means of the hyperspherical adiabatic expansion method and the third follows the Quantum Monte Carlo approach. The partners within each complex are taken to interact via two-body potentials chosen among the most accurate existing in the literature. All the present quantum treatments show that no bound states are found for H(4He)2 and for D(4He)2 while only one very diffuse bound state is present in T(4He)2, where H, D and T are the three isotopes of hydrogen. The substitution of the atomic dopant with its molecular counterpart, H2, also gives rise to only one bound state whose spatial attributes are reported and analysed, underlining again the ultraweak nature of the interaction forces and the need to implement highly specific tools for the investigation of the ensuing bound states.
The 4He3 weakly interacting system is analysed by constructing the full interaction as a sum of two-body (2B) potentials chosen among the most recent proposals from the literature. The spatial density distributions of the three bound atoms are obtained using a diffusion Monte Carlo (DMC) algorithm and a stochastic analysis under specific geometric constraints is carried out with the resulting densities in order to recover a more conventional structural picture for such floppy system. The total binding energies were obtained with the chosen potentials analysed in the present work, using the DMC algorithm, and are compared with previous published results. The ensuing spatial distributions are analysed in some detail to select the dominant structures from a conventional triangular description of this very floppy molecule.
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.