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The Journal of Physical Chemistry A

The Structure of the Asymmetric Helium Trimer3He4He2

Dario Bressanini

Published May 14, 2014• 8 citations
Publisher

Abstract

Despite their apparent simplicity, the properties of the two helium trimers, (4)He3 and (3)He(4)He2, are still not completely understood. In particular, the existence of a bound state of the asymmetric trimer (3)He(4)He2 was established many years ago, using different theoretical approaches, and later it was experimentally detected. However its structural properties have not been thoroughly investigated so far, probably because an accurate theoretical description of this very weakly bound system is computationally quite demanding. In this work we give for the first time an accurate and complete theoretical description of the geometrical structure of this fragile system using quantum Monte Carlo techniques employing the TTY potential and compare its properties with those of (4)He2 and (4)He3. We compute average values of distances and angles, along with the angle-angle distribution function: a two-dimensional probability distribution well suited to discuss the shape of a trimer. Our analysis shows that the lighter isotope is very diffuse and can be found at large distances from the other two atoms, but also close to the center of mass of the system in nearly linear configurations. For this system the concept of "equilibrium structure" is meaningless and all kinds of three-atom configurations must be taken into account in its description.

DOI
10.1021/jp503090f

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Despite their apparent simplicity, the properties of the two helium trimers, (4)He3 and (3)He(4)He2, are still not completely understood. In particular, the existence of a bound state of the asymmetric trimer (3)He(4)He2 was established many years ago, using different theoretical approaches, and later it was experimentally detected. However its structural properties have not been thoroughly investigated so far, probably because an accurate theoretical description of this very weakly bound system is computationally quite demanding. In this work we give for the first time an accurate and complete theoretical description of the geometrical structure of this fragile system using quantum Monte Carlo techniques employing the TTY potential and compare its properties with those of (4)He2 and (4)He3. We compute average values of distances and angles, along with the angle-angle distribution function: a two-dimensional probability distribution well suited to discuss the shape of a trimer. Our analysis shows that the lighter isotope is very diffuse and can be found at large distances from the other two atoms, but also close to the center of mass of the system in nearly linear configurations. For this system the concept of "equilibrium structure" is meaningless and all kinds of three-atom configurations must be taken into account in its description.
Despite its apparent simplicity and extensive theoretical investigations, the issue of what is the shape of the helium trimer is still debated in the literature. After reviewing previous conflicting interpretations of computational studies, we introduce the angle-angle distribution function as a tool to discuss in a simple way the shape of any trimer. We compute this function along with many different geometrical distributions using variational and diffusion Monte Carlo methods. We compare them with the corresponding ones for the neon and argon trimers. Our analysis shows that while Ne(3) and Ar(3) fluctuate around an equilibrium structure that is an equilateral triangle, (4)He(3) shows an extremely broad angle-angle distribution function, and all kinds of three-atom configurations must be taken into account in its description. Classifying (4)He(3) as either equilateral or linear or any other particular shape, as was done in the past, is not sensible, because in this case the intuitive notion of equilibrium structure is ill defined. Our results could help the interpretation of future experiments aimed at measuring the geometrical properties of the helium trimer.
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.
Abstract The structural properties of helium triatomic systems are studied using hyperspherical coordinates. A slow variable discretization approach is adopted to solve the three-body Schrödinger equation, in which the Schrödinger equation in hyperangular coordinates is solved using basis splines at a series of fixed FEM-DVR (finite-element methods–discrete variable representation) hyperradii. We focus on studying the geometrical structure of the 4 He 3 and 3 He 4 He 2 triatomic systems. Using the bound state wave functions obtained, we calculate and analyze the one-dimensional pair distribution and angle distribution functions as well as the two-dimensional angle–angle distributions. All these bound states are found to exhibit such a floppy nature that classifying them into particular geometrical shapes does not appear to be sensible. A comparison will be made with some bound states of the neon trimer, which are expected to be more tightly bound.
When studying the structure formation and fragmentation of complex atomic and nuclear systems it is preferable to start with simple systems where all details can be explored. Some of the knowledge gained from studies of atomic dimers can be generalised to more complex systems. Adding a third atom to an atomic dimer gives a first chance to study how the binding between two atoms is affected by a third. Few-body physics is an intermediate area which helps us to understand some but not all phenomena in many-body physics.Very weakly bound, spatially very extended quantum systems with a wave function reaching far beyond the classical forbidden region and with low angular momentum are characterized as halo systems. These unusual quantum systems, first discovered in nuclear physics may also exist in systems of neutral atoms.Since the first clear theoretical prediction in 1977, of a halo system possessing an Efimov state, manifested in the excited state of the bosonic van der Waals helium trimer 42He3, small helium and different spin-polarised halo hydrogen clusters and their corresponding isotopologues have been intensively studied the last three decades.In the work presented here, the existence of the spin-polarized tritium trimer ground state, 31H3, is demonstrated, verifying earlier predictions, and the system's properties elucidated. Detailed analysis has found no found evidence for other bound states and shape resonances in this system. The properties of the halo helium trimers, 42He3 and 42He2-32He have been investigated. Earlier predictions concerning the ground state energies and structural properties of these systems are validated using our three-dimensional finite element method. In the last part of this work we present results on the bound states and structural properties of the van der Waals bosonic atomic trimers Ne3 and Ar3. We believe to be the first to find evidence of a possible shape resonance just above the three-body dissociation limit of the neon trimer.
When studying the structure formation and fragmentation of complex atomic and nuclear systems it is preferable to start with simple systems where all details can be explored. Some of the knowledge gained from studies of atomic dimers can be generalised to more complex systems. Adding a third atom to an atomic dimer gives a first chance to study how the binding between two atoms is affected by a third. Few-body physics is an intermediate area which helps us to understand some but not all phenomena in many-body physics. Very weakly bound, spatially very extended quantum systems with a wave function reaching far beyond the classical forbidden region and with low angular momentum are characterized as halo systems. These unusual quantum systems, first discovered in nuclear physics may also exist in systems of neutral atoms. Since the first clear theoretical prediction in 1977, of a halo system possessing an Efimov state, manifested in the excited state of the bosonic van der Waals helium trimer 42He3, small helium and different spin-polarised halo hydrogen clusters and their corresponding isotopologues have been intensively studied the last three decades. In the work presented here, the existence of the spin-polarized tritium trimer ground state, 31H3, is demonstrated, verifying earlier predictions, and the system's properties elucidated. Detailed analysis has found no found evidence for other bound states and shape resonances in this system. The properties of the halo helium trimers, 42He3 and 42He2-32He have been investigated. Earlier predictions concerning the ground state energies and structural properties of these systems are validated using our three-dimensional finite element method. In the last part of this work we present results on the bound states and structural properties of the van der Waals bosonic atomic trimers Ne3 and Ar3. We believe to be the first to find evidence of a possible shape resonance just above the three-body dissociation limit of the neon trimer.
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.