Research Article

A measurement of the atomic hydrogen Lamb shift and the proton charge radius

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Science  06 Sep 2019:
Vol. 365, Issue 6457, pp. 1007-1012
DOI: 10.1126/science.aau7807
  • Fig. 1 Energy levels of hydrogen relevant to our experiment.

    Shown are the 2S1/2 and 2P1/2 energy levels, indicating the Lamb shift, as well as the hyperfine (|FmF) states of atomic hydrogen. The green arrow indicates the transition measured in this work; the transitions marked with red and blue arrows are used to remove populations from the 2S1/2 (F = 1) states. Here, F and mF are the total angular momentum and its projection along the direction of the rf fields.

  • Fig. 2 The measurement apparatus.

    Metastable 2S1/2 atoms are created by colliding a beam of protons with H2 molecules. Deflector plates remove the protons, and rf cavities (red and blue) remove 2S1/2 (F = 1) atoms. The 2S1/2 (F = 0) atoms are driven to the 2P1/2 (F = 1) state in a pair of FOSOF regions (green), which have rf frequencies that are offset from each other. The number of surviving 2S1/2 (F = 0) atoms is measured by mixing them in an electric field and observing the resulting Lyman-α photons via an efficient gas-ionization detector. Key to the success of the measurement is the fact that the entire FOSOF system (generator, amplifiers, monitors, and in-vacuum FOSOF waveguides) can be rotated by 180°, so that the atoms can encounter the two fields in the reverse order. The additional 910-MHz cavities shown (brown) are used to test for systematic effects. The relative phase of the rf going to and reflecting back from the FOSOF regions is measured by rf combiners C1 and C2.

  • Fig. 3 The FOSOF signal.

    (A and B) The FOSOF technique measures the phase difference Δθ between the atomic signal [red and blue in (A) and (B), respectively] and the reference signal (purple). The sign of Δθ depends on whether the atoms first encounter the f + δf or f − δf rf fields. In particular, in (A) the atoms first travel through the rf field region of frequency f − δf and then through the field region of frequency f + δf. For the plot in (B), the order of the encountered frequencies is reversed. |Δθ(A)| is larger than |Δθ(B)| because of a phase offset caused by the limited bandwidth of the detection system. (C) The average of Δθ(A) and −Δθ(B) cancels this phase offset and is shown versus f for the two orientations of the FOSOF regions. (D) Average of Δθ(0°) (brown) and −Δθ(180°) (gray). The straight-line fit determines the f0 at which Δθ = 0. (E) The residuals from the fit in (D) show that the data are fit well [χ2(39) = 29.1] by a simple straight line.

  • Fig. 4 Observed values for the atomic resonant frequency, f0.

    (A) Consistent centers are found for the 18 (v, d, Erf) parameter sets used. Circles, squares, triangles, and diamonds represent d = 4, 5, 6, and 7 cm, respectively. (B) Averaged f0 values for each v, d, and Erf also agree, as do f0 values obtained with the use of different frequency ranges. The pink band shows the 1σ uncertainty range for the current measurement. Numbers above the data points in (B) give the value of the parameters listed below the data points.

  • Fig. 5 Summary of proton radius data.

    Shown are values for the proton RMS charge radius from our measurement, muonic hydrogen, CODATA 2014, and the measurements of Beyer et al. (18) and Fleurbaey et al. (19) combined with that of Parthey et al. (20). Also shown in gray is the value from Lundeen and Pipkin (6, 16).

  • Table 1 Systematic corrections.

    Shown are systematic corrections and corrected centers for the 18 parameter sets (d, v, Erf) used in our measurement. Systematic effects for Doppler shift (ΔDop), ac Stark shift (Δac), and phase error (Δϕ) are listed with their uncertainties. The rightmost column provides the corrected line center along with the total statistical and systematic uncertainties. The bottom row indicates weighted averages.

    d (cm)v (mm/ns)Erf (V/cm)weight (%)ΔDop (kHz)Δac (kHz)Δϕ (kHz)f0[corrected] (kHz)
    weighted average:−51.6(1.0)29.5(2.3) 0.0(1.5)909,871.7(1.4)(2.9)
  • A measurement of the atomic hydrogen Lamb shift and the proton charge radius

    N. Bezginov, T. Valdez, M. Horbatsch, A. Marsman, A. C. Vutha, E. A. Hessels

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

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    • Figs. S1 to S3
    • Tables S1 to S4 
    • References 

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