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Observation of the Efimov state of the helium trimer

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Science  01 May 2015:
Vol. 348, Issue 6234, pp. 551-555
DOI: 10.1126/science.aaa5601
  • Fig. 1

    Theoretical basis for the Efimov state of the He trimer. (A) Dependence of the binding energies [sign(E) × |E|1/4] of the ground (GS) and first excited (1st ES) states of the He trimer on the scattering length [sign(a) × |a|-1/2] calculated by artificially scaling the He-He potential. The blue line on the positive scattering length side shows the binding energy of the He dimer. The vertical dashed line corresponds to the naturally occurring 4He system with a two-body scattering length of 90.4 Å (11). (B and C) Theoretical structures of the excited and ground states of the hypothetical He trimer corresponding to the scaled He-He potential with an infinite scattering length. The structures are plotted in the principal axis frame (abc) as shown in the inset. The center of mass of the trimer was shifted to the origin, and the structures were rotated so that the principal axis with the smallest moment of inertia (shown by the red vector a in the inset) lay along the y axis. Additionally, if required, the structure was mirrored with respect to the x or y axis in order to get one He atom in the first quadrant and the other two in the third and fourth quadrants, so that the second quadrant is always empty. The linear color scale encodes the number of entries.

  • Fig. 2

    Experimental observation of the He3 excited state. (A) The KER distributions of Coulomb exploded 4He trimers. The experimental distributions correspond to the mixture of the ground and excited states (black, expansion conditions: 8 K, 330 mbar) and to the ground state only (blue, expansion conditions: 8 K, 1.7 bar). The difference spectrum is shown in red with error bars (corresponding to a confidence interval of 95%). The ground-state–only distribution (blue) is normalized so that it agrees with the mixture distribution (black) for KER around 3 to 5 eV. The theoretical KER distribution for the excited state of the 4He trimer, obtained from our full quantum-mechanical calculation, is shown in violet. Note the logarithmic scale on both axes. arb., arbitrary units. (B) Dependence of the 4He cluster rates on the back pressure at a temperature of 8 K for a nozzle with a 5-μm orifice. The very low rate of the He3 excited state (red) is scaled by a factor of 103. The background caused by ground-state structures has been subtracted from the excited-state rate. The error bars correspond to a confidence interval of 68%. The rates for the He3 ground state and He2 are shown in blue and black, respectively.

  • Fig. 3

    Pair distance distributions Ppair(R) of the He3 excited state. The red circles represent the difference between the mixture of the excited- and ground-state distribution (measured at a nozzle pressure of 330 mbar and a temperature of 8 K) and the ground-state–only distribution (1.7 bar, 8 K, blue line). The error bars correspond to a confidence interval of 68%. The ground-state distribution was normalized to the quantity of ground-state structures under conditions where the excited state was measured (300 mbar, 8 K). The black histogram corresponds to the distribution that was obtained from the measured momenta of the ground- and excited-state mixture by filtering out the structures with higher KERs (for details, see the supplementary materials). Experimental distributions have been reconstructed from the measured momenta, using Newtonian mechanics to invert the Coulomb explosion. The theoretical pair distance distribution of the excited He trimer is shown in purple.

  • Fig. 4

    Structures of the He trimer. (A and B), respectively ,show the theoretical and experimental excited-state structure; (C) shows the theoretical ground state. Note the different scale for the ground state structure. For the plots, the center of mass of the trimer was shifted to the origin. The structures were rotated so that the principal axis with the smallest moment of inertia lay along the y axis. Additionally, if required, the structure was mirrored with respect to the x or y axis in order to get one He atom in the first quadrant and the other two in the third and fourth quadrants. The corresponding normalized structures are plotted in (D to F). The structures are normalized to the largest pair distance and subsequently located so that the two atoms with the largest pair distance get coordinates (–0.5,0) and (0.5,0) and the position of the third atom is plotted. The gray rectangle in (E) relates to structures that were cut during the reconstruction (see the supplementary materials for details). The linear color scale encodes the number of entries. The typical structure of the excited state of the He3 is sketched in the upper right corner of (D).

Supplementary Materials

  • Observation of the Efimov state of the helium trimer

    Maksim Kunitski, Stefan Zeller, Jörg Voigtsberger, Anton Kalinin, Lothar Ph. H. Schmidt, Markus Schöffler, Achim Czasch, Wieland Schöllkopf, Robert E. Grisenti, Till Jahnke, Dörte Blume, Reinhard Dörner

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

    Download Supplement
    • Materials and Methods
    • Figs. S1 to S7
    • References (30–32)

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