Evidence for Efimov Quantum States in an Ultracold Gas of Caesium Atoms
Nature, 2006 · paper · Physics
Reports an Efimov resonance in an ultracold cesium gas, seen as a giant loss of atoms through three-body recombination at large negative scattering lengths. A recombination minimum at positive scattering lengths is also found, confirming central predictions of Efimov physics.
Checked: PDF from arxiv.org, fetched 5 Oct 2026. Page numbers are those of that PDF.
1 finding
Wording The a<0 expression "C(a) = 4590 sinh(2η−)/(sin²[s0 ln(|a|/a−)] + sinh² η−)" takes |a| over the signed a−, but the paper reports "a− = −850(20) a0" and writes "a+/|a−|", so the logarithm's argument is negative as printed; it should be a/a− or |a|/|a−|.
- p. 4 last lines, analytic expression for C(a) for a<0
sin2 [s0 ln (|a|/a−)] + sinh2 η−
- p. 5 first line and fit result
a−= −850(20) a0
- p. 8 discussion, ratio of fit parameters
ratio a+/|a−|
Judge's note: Page 4 image shows the absolute-value bars around a only, with a− bare. Page 5 image prints a− = −850(20) a0, the Fig. 2 caption text gives a− = −850 a0, and page 8 image prints a+/|a−|, so a− is a negative quantity throughout. At the resonance, |a|/a− = 850/(−850) = −1, which has no real logarithm. This is a notation slip with an evident fix; the fitted values are unaffected.
Second check: another model agreed
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6 minor (typos and the like; most checked by the judge only)
Wording "An infinite series of such Efimov states is found when scattering lengths and energies are increased in powers of universal scaling factors e^{π/s0} ≈ 22.7 and e^{2π/s0} ≈ 515 (s0 = 1.00624), respectively": both quantities are said to be 'increased', whereas the binding energy of successive states shrinks in magnitude by 515 as the scattering length grows by 22.7.
- p. 3 paragraph on Efimov's scenario, last sentence
scattering lengths and energies are increased in powers of universal scaling factors
Judge's note: Read on the page 3 image; the wording is as quoted. The same paragraph calls the quantity a 'binding energy' with E_b = −ħ²/(ma²), so its magnitude falls as a grows. The sentence can be read loosely ('scaled in powers of', or the signed negative energy rising toward zero), so this is an ambiguity in wording, not a wrong number. The factors themselves are not in dispute.
Second check: another model agreed
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Typo "in a range between −2500 a0 to 1600 a0" mixes 'between … and' with 'from … to'.
- p. 5 second paragraph
in a range between −2500 a0 to 1600 a0
Judge's note: Confirmed on the page 5 image. Purely grammatical. The endpoints agree with the Methods fit formula on page 9 evaluated at 0 G and 150 G.
Second check: none (judge only)
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Typo "we have already benefitted of this loss minimum": wrong preposition; should be 'benefitted from'.
- p. 7 paragraph on Fig. 3, penultimate sentence
we have already benefitted of this loss minimum
Judge's note: Confirmed on the page 7 image; the wording is as quoted. Cosmetic.
Second check: none (judge only)
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Typo "Here we in particular raise question how the regions of positive and negative scattering lengths are connected": missing article; should be 'raise the question'.
- p. 8 first paragraph, line 5
Here we in particular raise question how the regions
- p. 8 discussion paragraph, line 5
Here we in particular raise question how the regions of positive
- p. 8 para 1
we in particular raise question how the regions
Judge's note: Confirmed on the page 8 image; the wording is as quoted. Cosmetic.
Second check: none (judge only)
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Typo Reference 25 prints the year without parentheses, "Appl. Phys. B 79, 1013–1019 2004.", unlike the other entries, which use '(year)'.
- p. 14 Reference 25
B 79, 1013–1019 2004.
- p. 14 Refs 25 and 30
Appl. Phys. B 79, 1013–1019 2004.
Judge's note: Confirmed on the page 14 image: refs 24 and 26–29 give the year in parentheses, ref 25 does not. Cosmetic formatting inconsistency. The same defect in ref 30 is handled under C008. I did not check the reviewer's side remark about ref 15.
Second check: none (judge only)
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Typo Reference 30 prints the year without parentheses, "Nature 412, 295–299 2001.", unlike the other entries, which use '(year)'.
- p. 14 Reference 30
Nature 412, 295–299 2001.
Judge's note: Confirmed on the page 14 image. Cosmetic formatting inconsistency; a distinct entry from the ref 25 case in C007.
Second check: none (judge only)