The size of the helium nucleus measured to femtometer accuracy

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An international research team managed by the Swiss Paul Scherrer Institute (PSI

An international research team managed by the Swiss Paul Scherrer Institute (PSI) has measured the radius of the atomic nucleus of helium five times more accurately than before. An important part of the collaboration was a complex laser system, which was developed with the participation of the Institute of Laser Technologies at the University of Stuttgart. [ Picture: ETH Zurich, K. Schumann]

Helium is the second most abundant element in the universe after hydrogen. Helium nuclei consist of four components, namely two protons and two neutrons. Knowing the properties of the helium nucleus is crucial for fundamental physics, for example, in order to understand the processes in atomic nuclei that are heavier than helium. What we know so far about the helium nucleus comes from experiments with electrons. The researchers at the PSI have now developed a novel measurement method for the first time that allows five times higher accuracy. According to these measurements, the so-called mean charge radius of the helium nucleus is 1.67824 femtometers (1 quadrillion femtometers are equal to 1 meter).

The scientists worked with exotic atoms or ions, in which both electrons were replaced by one single muon. Although a muon resembles an electron, it is about 200 times heavier than an electron and much more strongly bound to the atomic nucleus. Furthermore, it can also reside in the nucleus itself with much higher probability.

Slow muons and a complex laser system

The muons are produced at the PSI using a particle accelerator. The specialty of the machine: it creates low-energy muons. These particles are slow and can be stopped in the apparatus to conduct experiments. Only in this way can the exotic muonic helium ions be formed, in which a muon throws the electrons out of their orbits and replaces them. The muons move through a small chamber that is filled with helium gas. If the conditions are right, muonic helium will be produced, where the muon is in an energy state in which it frequently resides in the atomic nucleus.

This is where the laser system comes into play, where the Institute of Laser Technologies at the University of Stuttgart was involved in the development of important components (pump laser and amplifier). The complex system shoots a laser pulse at the muonic helium ion. If the laser has the right frequency, the muon is excited and transferred to a higher energy state. When the muon returns from this excited state to the ground state, it emits X-ray light. Detectors register these X-ray signals.

In the experiment, the laser frequency is varied until many X-ray signals arrive. Physicists then speak of the so-called resonant frequency. With the help of this frequency, the difference between the two energy states of the muon in the atom can be determined. According to theory, this measured energy difference is dependent on the size of the atomic nucleus. Therefore, the radius of the helium nucleus can be determined from theoretical equations using the measured resonant frequency.

A cooperation that has a long tradition

The research findings are the result of 20 years of proven cooperation between internationally renowned institutes such as the PSI, the ETH Zurich, the Max Planck Institute of Quantum Optics in Garching near Munich, the Institute of Laser Technologies at the University of Stuttgart, the Johannes Gutenberg University of Mainz as well as the Laboratoire Kastler Brossel and the CNRS in Paris, the University of Coimbra and the University of Lisbon in Portugal, and the National Tsing Hua University in Taiwan.

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