Shrinking the proton: Researchers confirm the small value of the proton radius determined from muonic hydrogen

October 6, 2017 by Olivia Meyer-Streng
This photo shows the vacuum chamber used to measure the 2S-4P transition frequency in atomic hydrogen. The purple glow in the back stems from the microwave discharge that dissociates hydrogen molecules into hydrogen atoms. The blue light in the front is fluorescence from the ultraviolet laser that excites the atoms to the 2S state. The turquoise blue glow is stray light from the laser system used to measure the frequency of the 2S-4P transition. Credit: MPQ

It was one of the breakthroughs of the year 2010: Laser spectroscopy of muonic hydrogen resulted in a value for the proton charge radius that was significantly smaller, by four standard deviations, than previous determinations using regular hydrogen. This discrepancy and its origin have attracted much attention in the scientific community, with implications for the so-called Standard Model of physics.

Now, a team of scientists from the Laser Spectroscopy Division of Professor Theodor W. Hänsch at the Max Planck Institute of Quantum Optics in Garching has made a new spectroscopic measurement of regular hydrogen (Science, 6 October 2017). The resulting values for the Rydberg constant and the radius are in excellent agreement with the muonic results (Nature 466, 213 (2010)), but disagree by 3.3 standard deviations with the average of the previous determinations from regular hydrogen.

Hydrogen is the simplest of all chemical elements. According to the model proposed by Niels Bohr in 1913, it consists of a single proton and an electron orbiting around it. The theory of quantum electrodynamics predicts the energy levels of this system with 12 digits of precision. Because of this, hydrogen plays a key role in our understanding of nature. Its study allows the determination of fundamental constants such as the Rydberg constant and the proton charge radius.

Hydrogen is thus the ideal subject for testing the laws of nature. This is why a measurement on muonic hydrogen, resulting in a surprisingly small value for the proton charge radius, made big waves in 2010. In that experiment, done at the Paul Scherrer Institute in Villingen, Switzerland, the electron of the hydrogen atom is replaced with its sister particle, the 200-times heavier and short-lived muon. Laser spectroscopy of this muonic hydrogen resulted in a value of the proton radius that was extremely precise, but four percent smaller than previous measurements on regular hydrogen. "Since the muon is 200-times heavier than the electron, it orbits much closer to the proton and 'feels' its size," explains Prof. Randolf Pohl (now at Johannes Gutenberg-Universität Mainz), a member of the MPQ team. "Because of this, the proton radius has a seven orders of magnitude larger influence on the spectral lines than in regular hydrogen. This allows us to determine the proton radius with such a high precision."

The large discrepancy between the measurements of regular hydrogen and its exotic cousin has sparked many debates about its origin. "However, some of the previous measurements in fact agree with the muonic value. The influence of the proton radius on the energy levels in regular hydrogen is tiny, and even very high precision measurements struggle to resolve it. The discrepancy only becomes significant when all measurements are averaged," explains Lothar Maisenbacher, one of the graduate students working on the project. "This is why, to solve this 'proton radius puzzle', new individual measurements with high precision, and, if possible, using different experimental approaches are necessary."

In order to determine both the Rydberg constant and the proton charge radius from spectroscopy of regular hydrogen, two different transition frequencies need to be measured. The by far sharpest resonance, the so-called 1S-2S transition, serves as a corner stone in this determination. Its frequency has been measured, in 2011, to 15 digits by the MPQ team (Phys. Rev. Lett. 107, 203001 (2011)). This high precision was made possible not least by the invention of the frequency comb, for which Professor Hänsch was awarded the Nobel Prize in Physics in 2005. For the second frequency measurement needed, the MPQ team chose the so-called 2S-4P transition, which connects the metastable 2S state with the much shorter lived 4P state.

In the experiment, this transition is excited by a laser with a wavelength of 486 nm and the collected fluorescence from the decay of the 4P state serves as a signal. The apparatus used previously for the 1S-2S measurement serves as a source of atoms in the 2S state. Compared to previous experiments, which used room temperature atoms, the atoms probed here have a substantially lower temperature of 5.8 Kelvin and, consequently, a much lower velocity. This, together with especially developed techniques, strongly suppresses the Doppler shift, which constitutes the largest source of uncertainty for this measurement.

"Another source of uncertainty in this experiment is the so-called quantum interference," explains Lothar Maisenbacher. "If we could probe a single, isolated transition, the shape of the resulting spectral line would be symmetric. However, in our case there are two other upper states that can be excited by the laser, called 4P1/2 und 4P3/2. This results in a slightly asymmetric shape of the spectral lines, making the determination of the line center more challenging. While this is a very small effect, it plays a big role for us because we determine the line center with such a high precision of almost one part in 10,000 of the line width."

To describe the influence of the quantum interference, the scientists performed sophisticated numerical simulations, which are in very good agreement with the experimental results. "In our case, however, a specially derived, simple fit function is sufficient to remove the effects of ," emphasizes Vitaly Andreev, also a graduate student on the project. "We use this fit function for our data evaluation. In this way, the simulation is only needed for small corrections on the order of 1 kHz."

With this, the MPQ team managed to determine the frequency of the 2S-4P transition with an uncertainty of 2.3 kHz. This corresponds to a fractional uncertainty of 4 parts in 1012, making this the second-best spectroscopy measurement of hydrogen after the aforementioned 1S-2S transition measurement. Combining these results, the Rydberg constant and the proton size are determined to be R = 10973731.568076(96) m-1 and rp = 0.8335(95) fm, respectively.

"Our measurement is almost as precise as all previous measurements on regular hydrogen combined," summarizes Prof. Thomas Udem, the project leader. "We are in good agreement with the values from muonic hydrogen, but disagree by 3.3 standard deviations with the world data, for both the Rydberg constant and the . To find the causes of these discrepancies, additional measurements with perhaps even higher precision are needed. After all, one should keep in mind that many new discoveries first showed up as discrepancies."

Explore further: Physicists confirm surprisingly small proton radius

More information: Axel Beyer et al. The Rydberg constant and proton size from atomic hydrogen, Science (2017). DOI: 10.1126/science.aah6677

Related Stories

Physicists confirm surprisingly small proton radius

January 24, 2013

International team of physicists confirms surprisingly small proton radius with laser spectroscopy of exotic hydrogen. The initial results puzzled the world three years ago: the size of the proton (to be precise, its charge ...

Proton radius puzzle may be solved by quantum gravity

November 26, 2013

(Phys.org) —Officially, the radius of a proton is 0.88 ± 0.01 femtometers (fm, or 10-15 m). Researchers attained that value using two methods: first, by measuring the proton's energy levels using hydrogen spectroscopy, ...

Most precise measurement of proton mass

July 20, 2017

What is the mass of a proton? Scientists from Germany and Japan have made an important step toward better understanding this fundamental constant. By means of precision measurements on a single proton, they were able to improve ...

Recipe for muon pair creation, in theory

January 19, 2016

A true-muonium only lives for two microseconds. These atoms are made up one positively and one negatively charged elementary particle, also known as muons. Although they have yet to be observed experimentally, a Japanese ...

Particle physics: 'Honey, I shrunk the proton'

July 7, 2010

Scientists lobbed a bombshell into the world of sub-atomic theory on Wednesday by reporting that a primary building block of the visible Universe, the proton, is smaller than previously thought.

Recommended for you

Single-photon detector can count to four

December 15, 2017

Engineers have shown that a widely used method of detecting single photons can also count the presence of at least four photons at a time. The researchers say this discovery will unlock new capabilities in physics labs working ...

Complete design of a silicon quantum computer chip unveiled

December 15, 2017

Research teams all over the world are exploring different ways to design a working computing chip that can integrate quantum interactions. Now, UNSW engineers believe they have cracked the problem, reimagining the silicon ...

A shoe-box-sized chemical detector

December 15, 2017

A chemical sensor prototype developed at the University of Michigan will be able to detect "single-fingerprint quantities" of substances from a distance of more than 100 feet away, and its developers are working to shrink ...

Real-time observation of collective quantum modes

December 15, 2017

A cylindrical rod is rotationally symmetric - after any arbitrary rotation around its axis it always looks the same. If an increasingly large force is applied to it in the longitudinal direction, however, it will eventually ...

22 comments

Adjust slider to filter visible comments by rank

Display comments: newest first

EyeNStein
5 / 5 (2) Oct 06, 2017
It may be that the Muon is constantly "making a measurement" by feeling its nearer proton.
So the physicists measurement is a bit more "particle like" compared to the harder to measure, slightly more "wave like", and so marginally larger, proton of ordinary hydrogen.

If this is true: Then it could illuminate our understanding of the Copenhagen interpretation; by indicating a softer transition from 'wave like' to 'particle like' behaviour than we expected.
Whydening Gyre
4.5 / 5 (2) Oct 06, 2017
It may be that the Muon is constantly "making a measurement" by feeling its nearer proton.
So the physicists measurement is a bit more "particle like" compared to the harder to measure, slightly more "wave like", and so marginally larger, proton of ordinary hydrogen.

This begs the question.
Are the protons actually different in size? or is it just a difference in measurement acuity of muon vs electron...?

If this is true: Then it could illuminate our understanding of the Copenhagen interpretation; by indicating a softer transition from 'wave like' to 'particle like' behaviour than we expected.

Indeed.
EyeNStein
2 / 5 (2) Oct 06, 2017
The measurements are pretty clear. Muonic Hydrogen has a bigger proton at its centre. (Though not yet at 5 SD's certainty level)

Alternatively, the positively charged quarks could just be attracted outwards more, by the closer muon, making the composite proton bigger.
EyeNStein
3.5 / 5 (2) Oct 06, 2017
Alternatively, the positively charged quarks could just be attracted outwards more, by the closer muon, making the composite proton bigger.


Wrong: That would be the opposite result !
Whydening Gyre
5 / 5 (1) Oct 06, 2017
The measurements are pretty clear. Muonic Hydrogen has a bigger proton at its centre. (Though not yet at 5 SD's certainty level)

You have me confused...
Don't the measurements represent a smaller proton radii?
(at least, according to the article...)
Hyperfuzzy
1 / 5 (1) Oct 06, 2017
No they didn't; the proton has no boundary conditions. It's a Field Center! Go figure. Why you are here and glass is transparent.
Hyperfuzzy
2.5 / 5 (2) Oct 06, 2017
Anyway, QM is not precise by definition and is not causal so any measurement is questionable, i.e. it only defines wavelets. Our instrumentation is limited.
Ralph
not rated yet Oct 06, 2017
The article did not clarify whether the Standard Model makes a prediction of the proton charge radius, and if so, how that prediction compares with the new and old experimental values mentioned here.
Nik_2213
not rated yet Oct 06, 2017
"... some of the previous measurements in fact agree with the muonic value"
Kudos to them. But what did they do 'different' ??
Whydening Gyre
not rated yet Oct 06, 2017
"... some of the previous measurements in fact agree with the muonic value"
Kudos to them. But what did they do 'different' ??

Nik, My take is that the previous measurements were taken with an electron present, vs the heavier muon.
That said, if taking multiple measurements with electron presence resulted in a varying range of results,
might that not indicate the electron is a varying field around the proton....?
someone11235813
not rated yet Oct 07, 2017
@Whydening Gyre, how could it be possible to replace the electron on H with a particle with 200 times greater mass and not have it affect the size of the H atom?
Da Schneib
5 / 5 (3) Oct 07, 2017
The article did not clarify whether the Standard Model makes a prediction of the proton charge radius, and if so, how that prediction compares with the new and old experimental values mentioned here.
The proton charge radius has not so far been calculated ab initio from the SM, and can't be because we don't know enough yet about quark-gluon interactions to do so anywhere near the precision we can measure it to. Color force interactions are extremely complex and require enormous amounts of computer time; and that's only for an approximate simulation. Lattice QCD is possible for simpler simulations, but at that size and speed, we still don't have the math to do it.
Da Schneib
4.8 / 5 (5) Oct 07, 2017
In response to a few others, no, the muon does not increase (@Eyen made a mistake and immediately corrected it) or decrease the charge radius of a proton. The charge radius of a proton is what it is; this is just a new measurement method that's more exact and confirms data collected using muonic hydrogen with measurements of normal electronic hydrogen. The two measurements were previously in tension with one another (that is, they conflicted and are now resolved).
andyd
5 / 5 (3) Oct 07, 2017
Perhaps the old value is a classic case of false consensus effect, but now there is a new locus and the consensus will shift accordingly.
ursiny33
not rated yet Oct 07, 2017
Does an orbiting electron or muon have a tidal effect on radius as the moon has,on earth, but at the atomic level
swordsman
not rated yet Oct 07, 2017
These calculated figures may be (and probably are) incorrect. The electron and the proton are electrical charges and are therefore susceptible to Coulomb forces. The Coulomb force varies inversely with distance, so it acts like nonlinear spring that produces force of attraction (for unlike charges) and repulsion for like charges. The diameter of the hydrogen atom is 1.04 pm, so the radii of the electron and proton are much smaller. Measuring the size is quite difficult due to the effect of Coulomb force, and this makes these claims difficult to verify since the measurement affects the resulting data. The electrical properties of the muon will have similar effects, plus the differences in masses that produce the counter forces.
Hyperfuzzy
1 / 5 (2) Oct 07, 2017
Charge is dimensionless, it occupies all of space; it's a field!
Steve 200mph Cruiz
5 / 5 (4) Oct 07, 2017
Hyperfuzzy,

Protons are conglomerates of particles that add up to having a positive charge. They are not analogous to leptons.
They have 3 quarks and then you have additional gluons constantly getting exchanged between them.
Protons are more particle than wave, they are a stable state of the combination of a lot of forces, not simply charge.
Nik_2213
not rated yet Oct 07, 2017
"Perhaps the old value is a classic case of false consensus effect, but now there is a new locus and the consensus will shift accordingly."

It's certainly served notice that, despite best efforts, *some* of the workers were getting 'systematic' errors. Time to re-visit such, hopefully spot the source(s).
Whydening Gyre
not rated yet Oct 08, 2017
@Whydening Gyre, how could it be possible to replace the electron on H with a particle with 200 times greater mass and not have it affect the size of the H atom?

@Somone. Because I see the electron as more of an energy shell than particle that surrounds the proton.
The muon does the same thing but at a denser energy level.
By example... would an earth pressure atmosphere(less dense like an electron) on Venus make Venus bigger?
Whydening Gyre
5 / 5 (1) Oct 08, 2017
In response to a few others, no, the muon does not increase (@Eyen made a mistake and immediately corrected it) or decrease the charge radius of a proton. The charge radius of a proton is what it is; this is just a new measurement method that's more exact and confirms data collected using muonic hydrogen with measurements of normal electronic hydrogen. The two measurements were previously in tension with one another (that is, they conflicted and are now resolved).

Apologies, DS, I think I may have hit 4 instead of 5 ...
Whydening Gyre
5 / 5 (1) Oct 10, 2017
These calculated figures may be (and probably are) incorrect. The electron and the proton are electrical charges and are therefore susceptible to Coulomb forces. The Coulomb force varies inversely with distance, so it acts like nonlinear spring that produces force of attraction (for unlike charges) and repulsion for like charges. The diameter of the hydrogen atom is 1.04 pm, so the radii of the electron and proton are much smaller. Measuring the size is quite difficult due to the effect of Coulomb force, and this makes these claims difficult to verify since the measurement affects the resulting data. The electrical properties of the muon will have similar effects, plus the differences in masses that produce the counter forces.

Sword,
I don't think they are measuring the whole atom. Just the proton...

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.