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Imaging the Structure of the Trimer Systems 4He3 and 3He4he2

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Imaging the Structure of the Trimer Systems 4He3 and 3He4he2 ARTICLE Received 10 Jul 2014 | Accepted 5 Nov 2014 | Published 9 Dec 2014 DOI: 10.1038/ncomms6765 Imaging the structure of the trimer systems 4 3 4 He3 and He He2 J. Voigtsberger1, S. Zeller1, J. Becht1, N. Neumann1, F. Sturm1, H.-K. Kim1, M. Waitz1, F. Trinter1, M. Kunitski1, A. Kalinin1,J.Wu2, W. Scho¨llkopf3, D. Bressanini4, A. Czasch1, J.B. Williams1, K. Ullmann-Pfleger1, L. Ph H. Schmidt1, M.S. Scho¨ffler1, R.E. Grisenti1, T. Jahnke1 &R.Do¨rner1 Helium shows fascinating quantum phenomena unseen in any other element. In its liquid phase, it is the only known superfluid. The smallest aggregates of helium, the dimer (He2) and the trimer (He3) are, in their predicted structure, unique natural quantum objects. While 4 one might intuitively expect the structure of He3 to be an equilateral triangle, a manifold of predictions on its shape have yielded an ongoing dispute for more than 20 years. 4 These predictions range from He3 being mainly linear to being mainly an equilateral triangle. 4 3 4 Here we show experimental images of the wave functions of He3 and He He2 obtained 4 by Coulomb explosion imaging of mass-selected clusters. We propose that He3 is a 3 4 structureless random cloud and that He He2 exists as a quantum halo state. 1 Institut fu¨r Kernphysik, Goethe Universita¨t, Max-von-Laue-Strasse 1, 60438 Frankfurt, Germany. 2 State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China. 3 Department of Molecular Physics, Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin, Germany. 4 Dipartimento di Scienza e Alta Tecnologia, University of Insubria, 22100 Como, Italy. Correspondence and requests for materials should be addressed to R.D. (email: [email protected]). NATURE COMMUNICATIONS | 5:5765 | DOI: 10.1038/ncomms6765 | www.nature.com/naturecommunications 1 & 2014 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6765 olecules are often intuitively pictured by ball-and-stick approach gives direct experimental access to the He–He distances models as having a well-defined structure. The and thus to the size of the trimer as well as to the bond angles. Mdelocalization of the relative position of the atoms dictated by quantum mechanics is usually sufficiently small to justify such structure models. This intuition of being constructed Results from well-localized subunits can also be applied to more loosely Size of the trimers. The distribution of internuclear distances R 4 4 bound aggregates as van der Waals molecules and small rare gas between two He atoms belonging to He3 is shown in Fig. 1. The 1 clusters. Ne3, for example, is a quite stiff equilateral triangle . distribution extends from 3.3 to 12 Å (full width at half max- Helium is the only element that stands out in this respect (see, for imum). Figure 1 reveals a manifold of information: first, contrary 2 4 example, a recent review by ). Its clusters still give rise to to covalently bound molecules He3 clusters are (as van der Waals controversial theoretical debates (see ref. 3 for a review of the systems) basically empty, that is, the distance between the atoms literature on this controversy). All other elements in the periodic is more than one order of magnitude larger than their diameter table have some electrons that are more loosely bound than the (which is only around 1 Å). Second, and even more important— two electrons of the helium atom. This makes the helium atom and in this respect small He clusters differ from all other ground- the most unpolarizable element. The van der Waals force between state van der Waals systems—the size of the He trimer is not well two helium atoms is therefore extremely weak and gives rise to defined. The width of the distribution is bigger than its mean 4 3 4 only a shallow potential minimum of À 0.947 meV depth at an value (which is 10.4 Å for He3 and 20.5 Å for He He2) and it internuclear distance of 2.96 Å (ref. 4). This potential supports extends far beyond the minimum of the van der Waals interac- 4 one bound state of the dimer He2 with a binding energy in the tion potential at 2.96 Å (see Fig. 1b). Typically, the width of such a order of 10 À 7 eV with the exact value still being disputed4–6. distribution stems from a superposition of vibrational ground and Substituting one 4He by the isotope 3He breaks this weak bond. excited states. For the case of the helium trimer this is different. In 4 In addition to its effect on the dimer, the combination of weak He3 there is apart from the ground state only one other predicted van der Waals attraction and small mass of 4He is also the origin of superfluidity found in bulk and in large clusters of 4He (ref. 7). QMC theory 4He –3He (this work) Helium clusters composed of three atoms are even more 1.2 2 Experiment 4He –3He intriguing quantum systems. Owing to the very large scattering 2 QMC theory 4He (this work) E 2 4 3 length ( 10 Å) of the helium atom, the isotopically pure He3 1.0 4 Experiment He3 trimer offers a unique atomic system to study the universality of a Random cloud (this work) three-body problem8. In addition, it represents the most 0.8 4 promising candidate for the Efimov effect in a naturally existing He 4 system9. By replacing one of the three 4He atoms by the lighter He isotope 3He, the predicted trimer binding energy reduces by 0.6 4He 4 about one order of magnitude with respect to the E0.011 meV He 4 10 4He He3 binding energy as a result of the increase in zero-point counts Relative 0.4 11,12 3 4 3He motion . This feature thus makes the He He2 trimer the most weakly bound three-body molecule, which also exhibits many 0.2 4 similarities to the first excited Efimov state in He3. It is a so- called Tango state13,14 where only one out of the three dimer-like 4 4 0.0 subsystems is bound ( He– He). 10 20 30 40 50 4 Our knowledge of He3 today stems almost exclusively from theory. The reason is that traditional experimental approaches to 0.0 chemical structure determination such as vibrational and –0.5 rotational spectroscopy cannot be applied to these extremely fragile molecules as the centrifugal force already makes the first (meV) Potential –1.0 excited rotational state unbound. The only experimental 4 0.14 4 technique giving access to some geometrical feature of He3 is Experiment He3 15 þ 4 Krishna and Whaley18 matter wave diffraction , which gives a mean size of 11 À 5 Å 0.12 (ref. 16) without providing any further information on the Barletta and Kievsky19 3 4 Gonzalez-Lezana et al.22 structure. Furthermore, the existence of the isotopic He He2 0.10 33 trimer has recently been confirmed by means of such matter wave Paola et al. Blume et al.34 diffraction experiments17. Although there is theoretical consensus 0.08 4 3 4 concerning the floppy nature of both the He3 and He He2 0.06 4 molecules, the geometrical shape is a matter of extensive current counts Relative He 4 4 debates. In the particular case of the He3 trimer some 0.04 He 18–20 calculations suggest an equilateral triangular structure , 4He while others indicate a significant contribution of linear 0.02 21,22 configurations . It has also been recently suggested that this 0.00 controversy is often mislead by drawing false conclusions from 0 10 20 30 40 50 correctly calculated distributions3. Internuclear distance ( ) Towards resolving this dispute, we present experimental results 4 3 4 on the structure of mass-selected He3 and He He2 trimers. Our Figure 1 | Internuclear two-body distances. (a) Experimental distribution 4 4 4 4 3 3 4 experimental technique is based on femtosecond laser pulse of the He– He distance of He3 and the He– He distances of He He2 ionization of the helium atoms constituting the trimer and compared with QMC theory (this work) and a random cloud model (this subsequent imaging of the momentum vectors of the Coulomb work). Error bars result from the statistical errors. (b) He–He potential exploding fragment ions using cold target recoil ion momentum energy curve provided from the authors of ref. 4. (c) 4He–4He comparison spectoscropy (COLTRIMS)23,24 (see Methods). Our experimental with theoretical predictions. 2 NATURE COMMUNICATIONS | 5:5765 | DOI: 10.1038/ncomms6765 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6765 ARTICLE vibrational state. That excited state, however, has not been 16 observed so far and is predicted to be an Efimov state with a size 1.0 4 9,25 Experiment He3 about 10 times larger than the ground state . If it were present QMC theory (this work) in our gas jet with the expansion parameters employed during the Krishna and Whaley18 0.8 experiment, it would show up clearly in our data (see Methods). Paola et al.33 Therefore, the width of the distribution of internuclear distances Gonzalez-Lezana et al.35 results from the delocalized quantum nature of a single state. This 0.6 Random cloud (this work) quantum feature is uniquely strong for He3 and becomes directly visible if one 4He atom of the trimer is substituted by its isotope 3 0.4 He (see Fig. 1a). Changing the mass does not effect the molecular 4He potential.
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