The formation of dimers and trimers in free jet He4 cryogenic expansions

Bruch, L. W.; Schöllkopf, Wieland; Toennies, J. P.

doi:10.1063/1.1486442

Cited by 80 publications

(134 citation statements)

References 74 publications

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“…The clusters are produced in a free-jet gas expansion 30,31 of pure 4 He (respectively, a mixture of 99% 3 He, 1% 4 He) source gas. A nozzle of 5 mm diameter was cooled down to 12 K at a driving pressure of 3 bar.…”

Section: Methodsmentioning

confidence: 99%

Imaging the structure of the trimer systems 4He3 and 3He4He2

et al. 2014

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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 (He 2 ) and the trimer (He 3 ) are, in their predicted structure, unique natural quantum objects. While one might intuitively expect the structure of 4 He 3 to be an equilateral triangle, a manifold of predictions on its shape have yielded an ongoing dispute for more than 20 years. These predictions range from 4 He 3 being mainly linear to being mainly an equilateral triangle. Here we show experimental images of the wave functions of 4 He 3 and 3 He 4 He 2 obtained by Coulomb explosion imaging of mass-selected clusters. We propose that 4 He 3 is a structureless random cloud and that 3 He 4 He 2 exists as a quantum halo state.

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Section: Methodsmentioning

confidence: 99%

Imaging the structure of the trimer systems 4He3 and 3He4He2

et al. 2014

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“…However, the experimental information on clusters of 4 He bound states with more than two atoms is rather limited. While the 4 He trimer and larger clusters have been observed, no quantitative information about their binding energies is available [15,16]. On the other hand, various "realistic" potentials have been developed (see, e.g.…”

Section: The Three-boson System At Nnlomentioning

confidence: 99%

“…Since the atom-atom scattering length is a 2 = 104 +8 −18 Å while the typical van der Waal's forces between the Helium atoms have a range R ≈ 7Å, in this case the expansion parameter R/a 2 < ∼ 10%. The 4 He trimer, tetramer, and several larger 4 He clusters have been observed [15,16], but unfortunately there are no measurements of trimer binding energies, and so we use precise few-body calculations [17,18,19,20,21], based on quite complicated inter-atomic potentials [22,23], to provide the two input ratios for our EFT. We then compare the EFT's predictions with the corresponding results obtained in Refs.…”

Section: Introductionmentioning

confidence: 99%

The Three-Boson System at Next-to-Next-to-Leading Order

2006

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We discuss effective field theory treatments of the problem of three particles interacting via short-range forces (range R ≪ a 2 , with a 2 the two-body scattering length). We show that forming a once-subtracted scattering equation yields a scattering amplitude whose low-momentum part is renormalization-group invariant up to corrections of O(R 3 /a 3 2 ). Since corrections of O(R/a 2 ) and O(R 2 /a 2 2 ) can be straightforwardly included in the integral equation's kernel, a unique solution for 1+2 scattering phase shifts and three-body bound-state energies can be obtained up to this accuracy. We use our equation to calculate the correlation between the binding energies of Helium-4 trimers and the atom-dimer scattering length. Our results are in excellent agreement with the recent three-dimensional Faddeev calculations of Roudnev and collaborators that used phenomenological inter-atomic potentials.

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“…[7] for collision energies E ranging from 46 K to 348 K. Since the Xe atom is so much heavier than a He atom, each of the atoms in the He dimer carries approximately 1 2 the collision energy E. The analog of our factorization formula in Eq. (10) …”

Section: Eric Braaten and Dongqing Zhangmentioning

confidence: 99%

Factorization in breakup and recombination processes for atoms with a large scattering length

Braaten

Zhang

2006

Phys. Rev. A

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Break-up and recombination processes for loosely-bound molecules composed of atoms with a large scattering length a necessarily involve interactions that are nonperturbative in the exact 2-body interaction. If these processes involve atoms with relative momenta much larger thanh/|a|, the leading contributions to their rates can be separated into short-distance factors that are insensitive to a and long-distance factors that are insensitive to the range of the interaction. These factorization contributions can be obtained from the leading term in a perturbation expansion in the exact atomatom scattering amplitude. The short-distance factors are atom-atom cross sections at a lower collision energy. In the special case of inclusive break-up cross sections for atom-molecule scattering, the long-distance factors simply count the number of atoms in the molecule. 12.38.Bx, 13.20.Gd, 14.40.Gx Nonrelativistic particles with short-range interactions that have been tuned, either by the experimenter or fortuitously by nature, so that their S-wave scattering length a is much larger than the range, have universal low-energy properties that depend on a but are otherwise insensitive to their interactions at short distances. (See Ref.[1] and references therein.) If the particles form loosely-bound 2-body or higher N -body clusters whose sizes are comparable to |a|, the clusters also have universal properties. A classic example in atomic physics is 4 He atoms whose scattering length a ≈ 100Å is much larger than their effective range r s ≈ 7Å. The 4 He dimer and the excited state of the 4 He trimer both have sizes comparable to a. A classic example in nuclear physics is nucleons. The deuteron is a bound state of the neutron and proton associated with a large scattering length in the spin-triplet channel.The large scattering length implies that interactions between atoms whose relative momenta are comparable toh/|a| are nonperturbative in the 2-body scattering amplitude. A simple consequence of these strong interactions with a > 0 is the existence of a loosely-bound dimer whose binding energy is given byIn some cases (for example, identical bosons), the strong interactions produce the Efimov effect: as a → ±∞, there are increasingly many loosely-bound trimers with an accumulation point at the 3-atom threshold [2]. In the limit a = ±∞, the trimers have an asymptotically exponential spectrum:where s 0 is a numerical constant whose value for identical bosons is 1.00624, n * is an arbitrary integer, and κ * is a 3-body parameter [1]. The strong interactions can also lead to intricate dependence on the scattering length a. An example in the case of identical bosons is the event rate constant in the low-energy limit for 3-body recombination into the loosely-bound dimer:(3) The log-periodic dependence on a in Eq. (3) was discovered in Refs. [3]. The completely analytic expression was derived more recently by Petrov [4]. The coefficient of ha 4 /m on the right side of Eq. (3) can range from 0 to 402.7 depending on the value of the 3-bo...

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The formation of dimers and trimers in free jet He4 cryogenic expansions

Cited by 80 publications

References 74 publications

Imaging the structure of the trimer systems 4He3 and 3He4He2

Imaging the structure of the trimer systems 4He3 and 3He4He2

The Three-Boson System at Next-to-Next-to-Leading Order

Factorization in breakup and recombination processes for atoms with a large scattering length

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