Record precision achieved in measuring muonic helium-3 nucleus radius

An international research team led by the Paul Scherrer Institute PSI has measured the radius of the nucleus of muonic helium-3 with unprecedented precision. The results are an important stress test for theories and future experiments in atomic physics.

1.97007 femtometer (quadrillionths of a meter): That’s how unimaginably tiny the radius of the atomic nucleus of helium-3 is. This is the result of an experiment at PSI that has now been published in the journal Science.

More than 40 researchers from international institutes collaborated to develop and implement a method that enables measurements with unprecedented precision. This sets new standards for theories and further experiments in nuclear and atomic physics.

This demanding experiment is only possible with the help of PSI’s proton accelerator facility. There Aldo Antognini’s team generates so-called muonic helium-3, in which the two electrons of the helium atom are replaced by an elementary particle called a muon. This allows the nuclear radius to be determined with high precision.

With the measurement of helium-3, the experiments on light muonic atoms have now been completed for the time being. The researchers had previously measured muonic helium-4 and, a few years ago, the atomic nucleus of muonic hydrogen and deuterium.

Muonic helium-3: Twice as slimmed-down

Helium-3 is the lighter cousin of ordinary helium, helium-4. Its atomic nucleus has two protons and two neutrons (hence the 4 after the abbreviation for the element); in helium-3, one of the neutrons is missing. The simplicity of this slimmed-down atomic nucleus is very interesting to Aldo Antognini and other physicists.

The helium-3 that PSI physicist and ETH Zurich professor Antognini is using in the current experiment lacks not only a neutron in the nucleus, but also both electrons that orbit this nucleus. The physicists replace the electrons with a negatively charged muon—hence the name muonic helium-3.

The muon is around 200 times heavier and gets close to the nucleus. Thus, the nucleus and the muon “sense” each other much more intensely, and the wave functions overlap more strongly, as they say in physics.

That makes the muon the perfect probe for measuring the nucleus and its charge radius. This indicates the area over which the positive charge of the nucleus is distributed. Ideal for the researchers, this charge radius of the nucleus does not change when the electrons are replaced by a muon.

Antognini has experience in measuring muonic atoms. A few years ago, he carried out the same experiment with muonic hydrogen, which contains only one proton in the nucleus and whose one electron was replaced by a negatively charged muon. The results caused quite a commotion at the time, because the deviation from measurements based on other methods was surprisingly large. Some critics even considered them wrong. It has now been confirmed many times over: The results were correct.

Worldwide-unique facility enables experiments

This time Antognini will not need to exercise as much persuasive power. For one thing, he has established himself as the leading expert in this area of research. Another factor is that there was no big surprise this time. The current results from muonic helium-3 fit well with those from previous experiments in which other methods were used. However, the PSI team’s measurements are around 15 times more precise.

Negatively charged muons, and plenty of them, are the most important ingredient for the experiment. These must have a very low energy—that is, they must be very slow, at least by the standards of particle physics.

At PSI, around 500 muons per second with energies of one kiloelectron-volt can be generated. This makes the PSI proton accelerator facility, with its beamline developed in-house, the only one in the world that can deliver such slow negative muons in such large numbers.

Laser developed in-house was crucial for success

A crucial share of the success is due to a laser system that the researchers themselves developed. There the challenge is that the laser must fire immediately when a muon flies into the experimental setup.

To make this possible, Antognini and his team installed an extremely thin foil detector in front of the airless experimental chamber. This detects when a muon passes through the foil and signals the laser to emit a pulse of light immediately and at full power.

The researchers determine the charge radius indirectly by measuring the frequency of the laser light. When the laser frequency precisely matches the resonance of a specific atomic transition, the muon is briefly excited to a higher energy state before decaying to the ground state within picoseconds; at that point it will emit a photon in the form of an X-ray.

Finding the resonance frequency at which this transition occurs requires a lot of patience, but the reward is an extremely accurate value for the charge radius of the nucleus.

New benchmark for theoretical modeling

The charge radii obtained from muonic helium-3 and helium-4 serve as important reference values for modern ab initio theories—that is, physical models that calculate the properties of complex physical systems directly from the fundamental laws of physics, without resorting to experimental data.

In the context of nuclear physics, these models offer detailed insights into the structure of light atomic nuclei and the forces between their building blocks, the protons and neutrons.

Precise knowledge of these nuclear radii is also crucial for comparisons with ongoing experiments on conventional helium ions with one electron and on neutral helium atoms with two electrons. Such comparisons provide stringent tests of quantum electrodynamics (QED) in few-body systems—the fundamental theory that describes how charged particles interact through the exchange of photons. They allow researchers to test the predictive power of our most fundamental understanding of atomic structure.

These efforts could lead to new insights into QED in for bound systems—that is, in systems such as atoms, in which particles are not free but bound to each other by forces—or perhaps even to indications of physical effects outside beyond the Standard Model of Particle Physics.

Follow-up experiments are currently being conducted by research teams in Amsterdam, Garching, and China, as well as in Switzerland by the Molecular Physics and Spectroscopy group led by Frédéric Merkt at ETH Zurich.

Antognini also has additional ideas for future experiments aimed at testing the theories of atomic and nuclear physics with even greater precision. One idea is to measure hyperfine splitting in muonic atoms. This refers to energy transitions between split energy levels that reveal deeper details about effects in the atomic nucleus that involve spin and magnetism.

An experiment with muonic hydrogen is currently being prepared, and an experiment with muonic helium is planned. “Many people who work in nuclear physics are very interested in it and are eagerly awaiting our results,” Antognini says.

But the energy density of the laser must be increased significantly, which will require an enormous advance in laser technology. This development is currently under way at PSI and ETH Zurich.