Deutschland Rundfunk April 23, 2015
FORSCHUNG AKTUELL / Beitrag vom 14.04.2015
Germany Broadcast April 23, 2015
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Eva Raisig (translated by Horst Meyer and corrected by Haiyan Gao)
Hydrogen is not only the most abundant element of the universe, but it is also the simplest. One would think that no other atom has been so thoroughly investigated. But in spite of this, many questions remain. Experiments yield quite different values for the charge radius of the proton, which cannot be explained through the uncertainties in the measurements. So the proton paradox was a topic at the recent meeting of the American Physical Society.
The proton gives problems. For many physicists, this is nothing new, but even recognizing this widely does not alleviate the situation. This time, it is the size of the proton that gives problems to physicists. This proton charge radius, or the size weighted by the charge distribution inside the proton, is completely different as obtained from different experiments. Its size is smaller than a femtometer, hence less than a millionth of a millionth of a millimeter.
“The question is: Why does this actually worry us? For us, the charge radius of the proton, hence the distribution of its charge, is important because it gives information about the inner structure of the proton. With the help of the charge radius we can, for instance, learn to understand better one of the fundamental forces of Nature, the strong force.”
So Haiyan Gao, the nuclear physicist from Duke University in North Carolina, is also interested in this problem to resolve the discrepancies of the proton size.
Apparently these discrepancies emerged nearly five years ago when scientists at the Paul Scherrer Institute (PSI) in Switzerland investigated the proton charge radius with an accuracy never reached before. Actually, so they stated later, they only wanted to add to the accepted value one or more digits at the end, after the

dot. For this purpose, they investigated very small displacements in the energy levels of hydrogen, which are closely related to the size of the proton. There have been such experiments before, but this time the physicists at PSI used a special form of hydrogen. They replaced the electron of the atom by a muon - an elementary particle, which resembles the electron in almost all properties, but actually is 200 times heavier. The small energy displacements can be observed especially well in this muonic hydrogen. But instead of more new digits in the radius value, the physicists recorded a completely different and much lower value than in the other experiments: only 0.84 instead of the well accepted 0.88 femtometer – a huge discrepancy taking into account the accuracy of this new measurement. The probability that a mistake in the measurement was the reason for this result is extremely small, namely one in four billion.
“Nuclear or particle physics experiment can never surpass the precision of atomic experiments. On the other hand, one still has some doubts when a result is so very different from all the other measurements. The researchers have again checked their results by investigating another energetic displacement, but the results remained the same. The measurement was even more precise than their previous one. There is no reason to doubt these results, but this is why one asks the question: What is the reason for this discrepancy?”
There are no reasons to have any doubts about the previous experiments. In order to solve this basic problem, Haiyan Gao and collaborators are following a different direction than physicists at PSI did. With a particle accelerator in the Jefferson Lab near the U.S. East Coast, they shoot electrons on hydrogen atoms. From the change of direction of the scattered electron beam, they deduce information about the inner structure and the size of the proton. The special accelerator design at the Jefferson Lab should give much more accurate results than the earlier scattering experiments and in the design there are provisions to guard against unforeseen problems:
“We shoot the electrons onto hydrogen gas. The electron beam does not get scattered only by the proton, which we actually want to observe, but also by the electron of the hydrogen atom. This electron-electron scattering can be calculated very well, and in this case this is the reference for the actual scattering, which we investigate. This way, many systematic problems can be minimized - for example, that we cannot say accurately how many electrons there are in the beam.”
The success of the measuring method depends critically on the accuracy, with which the hit impact of electrons on protons can be regulated. This is because in

order to determine most accurately the charge radius, the electrons should not be scattered by the protons by more than a tiny amount from their original direction.
This is no small challenge even for a highly precise experimental set up. But with the scattering experiments at the Jefferson Lab, scientists could well come closer to their goal than all the previous teams. This is one more reason to wait impatiently for the results.
“The deciding factor is really getting new data – whether now through our scattering experiments or through other experimental arrangements such as those of the physicists at the PSI. If, after these measurements, the discrepancies still remain, we will in fact have some reason to assume that we have found something
exciting, which we do not understand. Perhaps there will be some new physics.”