INSIGHTS | PERSPECTIVES
sured with an accuracy of just a few kHz.
This means they had to resolve the line
center with an accuracy 1/10,000 the width
of the line. To achieve this, they had to understand possible line-shifting mechanisms
with that accuracy.
Two frequencies are needed to accurately
determine both the proton radius rp and the
Rydberg constant R∞, relying on the highly
accurate quantum electrodynamics (QED)
theory of the hydrogen atom. One of these
is the frequency of the 1S-2S transition. This
transition is extremely narrow because of the
small linewidth of the 2S state (1.3 Hz), and
its frequency was measured with a tantalizing 10-Hz accuracy in the lab of the authors
some years ago ( 4). All other transitions
one can use are inherently broad, with linewidths of several MHz. As a second transition, Beyer et al. chose the 2S-4P Balmer-b
line, which has a 12.9-MHz natural linewidth
(see the figure).
In the experiment, a cryogenic beam of
atoms in only one of the two 2S hyperfine
states was produced by two-photon ex-
citation of 1S ground-state atoms. The 2S
atoms were subsequently excited to both
the 4P1/2 and 4P3/2 fine structure states us-
ing a single blue photon. Much effort was
put into exciting the atoms at an angle of
90°, as the tiniest deviation of the angle between the atomic and laser beams would
shift the line center by the Doppler effect. It
is this first-order Doppler effect that determines the final accuracy of the experimental measurement.
Another crucial effect that Beyer et al. had
to cope with is quantum interference be-
tween the neighboring resonances ( 5). Even
though both 4P fine structure states are sep-
arated by more than 100 natural linewidths,
it was found, and studied thoroughly, that
tiny shifts of the line center of each occur as
a result of the presence of the other. This ap-
parent shift amounts to tens of kHz, to be
compared with a much smaller 8.9-kHz shift,
which is the proton-radius discrepancy they
wanted to resolve. After a thorough analysis,
Beyer et al. do not claim to have solved
the proton-size puzzle. After all, it is only
one measurement, and the data analysis was
very complicated. Moreover, one would need
to understand why other measurements in
hydrogen are so far off or, possibly, exhibit
a systematic shift in the same direction.
There is presently no explanation for that.
Also, the proton size deduced from electron-
proton scattering disagrees. Thus, more
measurements are what is needed. Several
experiments in hydrogen spectroscopy as
well as on electron-proton and muon-proton
scattering are on the way (2). Experiments
with heavier nuclei may also shed light on
the puzzle. In recent experiments with mu-
onic deuterium, the hydrogen isotope with
one proton and one neutron in its nucleus,
a smaller deuteron size compared to that of
normal deuterium was found using spec-
troscopy ( 6), reinforcing the original puz-
zle. Interestingly, with the shifted Rydberg
constant as determined by Beyer et al., the
muonic and electronic deuterium data now
also seem to be reconciled. Spectroscopy
on muonic 4He and 3He ions was recently
performed and will soon, when theory is
finalized, provide the size of the a particle
(the 4He nucleus) and the helion (the 3He
nucleus), which will then be compared with
spectroscopy on 4He and 3He atoms ( 7) and
ions ( 8, 9). QED theory for molecules like
H2+, HD+, D2+ ( 10), and H2 ( 11) has recently
become so accurate that the radii of the
nuclei that constitute these molecules can
be extracted from precision spectroscopy
as well ( 12), thereby allowing yet another
means to determine nuclear sizes. j
1. R. Pohl et al., Nature466, 213 (2010).
2. R. J. Hill, EPJ Web of Conferences 137, 01023 (2017).
3. A.Beyer et al., Science 358, 79(2017).
4. C. G. Parthey et al ., Physical Review Letters 107, 203001
5. M. Horbatsch, E. A. Hessels, Physical Review A 82, 052519
6. R. Pohl et al., Science353, 669 (2016).
7. R.P. M.J.W.Notermans, R.J.Rengelink, W.Vassen,
Physical Revie w Letters 117, 213001 (2016).
8. M. Herrmann et al ., Physical Review A 79, 052505 (2009).
9. R. K. Altmann, S. Galtier, L. S. Dreissen, K. S. E. Eikema,
Physical Revie w Letters 117, 173201 (2016).
10. V. I. Korobov, L. Hilico, J.-Ph. Karr, Physical Review Letters
118, 233001 (2017).
11. M. Puchalski, J. Komasa, P. Czachoro wski, K. Pachucki,
Physical Review Letters 117, 263002 (2016).
12. J. Biesheuvel, J.-Ph. Karr, L. Hilico, K. S. E. Eikema, W.
Ubachs, J. C. J. Koelemeij, Nature Communications 7,
The 2S-4P transition is
excited by one photon at
a wavelength of 486 nm
(Balmer-b). Its excitation
is monitored by observing
decay of the 4P state via
primarily 97-nm Lyman-g
The 1S-2S transition is excited by
two photons at 243 nm. Its excitation
is monitored by observing 121.6-nm
Lyman-a radiation from the 2P state,
populated from the 2S state in an
spectroscopy Electron scattering
Beyer et al. hydrogen spectroscopy Earlier hydrogen spectroscopy
The proton radius (1 fm = 10–15 m) is measured by various techniques. The Beyer et al. value agrees with the more
accurate result from muonic hydrogen spectroscopy and not with electron-proton scattering data and earlier laser
spectroscopy in regular hydrogen.
0.83fm 0.84 0.85 0.86 0.87 0.88 0.89
“…the muonic and electronic
deuterium data now
also seem to be reconciled.”
40 6 OCTOBER 2017 • VOL 358 ISSUE 6359
Proton size from
Tiny shifts of level energies occur when
an electron spends some of its time
inside the nucleus, providing a handle
on the proton radius rp. The shift is
largest for low S states. To measure rp
accurately, two transition frequencies