Prediction made by Noble Prize laureates confirmed

In the world of science, predictions sometimes precede the discovery by several decades. The physicists in Darmstadt are thus especially excited that they have been able to prove the existence of atomic nuclei with unusual symmetries, as was predicted 45 years ago by the Nobel Prize laureates Aage Bohr and Ben Mottelson. “These types of atomic nuclei are extremely difficult to observe”, says Tobias Beck from the Institute of Nuclear Physics at the Technical University of Darmstadt. The team headed by Norbert Pietralla has now achieved this using new analysis and measurement methods that can very precisely map the decay of excited nuclei. The researcher’s work was supported by an experiment carried out under the guidance of Dr. Volker Werner, who is also a researcher in Pietralla’s work group. The State of Hesse provided support for the project as part of the “Nuclear Photonics” research cluster funded by the LOEWE programme. Support was also provided by teams in the USA, Russia, Great Britain and Romania, while the project received additional financial assistance from the German Federal Ministry for Education and Research. Yet the researchers also had some luck.

Atomic nuclei are extremely useful, for example in medical imaging technology such as nuclear magnetic resonance imaging. A great deal is already known about them in nuclear physics but these tiny particles are still shrouded in some mystery. One mystery is the question of what spatial form atomic nuclei can take. Laymen often imagine them as being spherical but most nuclei take on a different form. For example, the sphere can be distorted along one axis to form a sort of cigar shape and thus has a much less symmetrical structure.

As atomic components, they are subject to the laws of quantum mechanics – which state that a spherical object cannot rotate because no new, distinguishable state would exist as a result. A cigar-shaped nucleus cannot rotate around its longitudinal axis because this would not change its state. However, the “cigar” can certainly rotate around an axis which is perpendicular to the longitudinal axis. Yet in this case, it is also possible to observe both higher and lower symmetry. Quantum mechanics describes objects using a mathematical function – the so-called wave function. This can be positive or also negative at different locations. If you imagine the signs of the wave function of a nucleus to be red (positive) and blue (negative), it can occur that the “cigar” changes its “signs” as it rotates around 180 degrees. The red and blue colours will thus swap sides. It is only after further rotation around a full 360 degrees that the initial state is restored. It is also possible for both sides to be blue (or red) and a 180 degree rotation is then sufficient to achieve congruency. The specialist jargon for these two cases is R-symmetry. They are described using the values +1 (identical to the initial state after a 180 degree rotation) and -1 (a 360 degree rotation is required).

An atomic nucleus cannot only be symmetrical with respect to its axial rotation but also its reflection about its centre point. Roughly speaking, a point lying on the bottom left is reflected in the top right or vice versa. This type of symmetry is called parity in physics. There are also two types of parity defined as +1 and -1.

States of atomic nuclei in which R-symmetry and parity have the same sign have been well studied. “However, there is a lack of information on states with different signs”, says Tobias Beck. Although these states had been predicted by the Nobel Prize laureates Bohr and Mottelson, they are extremely difficult to observe directly. To detect the rotating state of a nucleus, the nuclei have to be given energy, for instance in the form of gamma radiation. Different states can then be excited energetically. As the nuclei return to their ground states, each one emits a characteristic gamma ray signature with different energy. Special forms of nuclei are difficult to detect because they are only rarely excited in comparison to other forms.

“While investigating atomic nuclei of dysprosium, we were lucky enough to find unusually favourable conditions in the isotope ¹⁶⁴Dy”, says Beck. In this isotope, there is a mix of states with different values for the R-symmetry. It would be like having a cigar with a red and a blue half but where the red half also has a blue tip. In this type of situation, the high probability of being excited by gamma radiation is inherited from the symmetrical configuration (two blue tips). “This makes them easier to observe”, says Beck.

The team from Darmstadt achieved this thanks to a very precise measurement method that was developed using the High Intensity Gamma Ray Source at Duke University in Durham, North Carolina, USA. It produces gamma radiation that can target individual excited states of the atomic nuclei. The research cluster “Nuclear Photonics” is dedicated to this kind of precise manipulation of nuclear states and Darmstadt is a world leader in the further development of this field of research. The scientists at TU Darmstadt were thus able to excite mixed states that should contain the desired quantum state of positive parity and negative R-symmetry.

Their model predicted that this previously unobserved state would emit its excitation energy in the form of gamma radiation with two different energies, whereby one would be twice as intensive as the other. In the more familiar state with the same signs for parity and R-symmetry, the relationship between the two intensities is reversed. The researchers were able to determine the different intensities of the two types of radiation in an experiment. They discovered that there was a mix of two intensity ratios. The contributions made by the investigated state with different signs for parity and R-symmetry proved to be 125 times weaker than for the known state. “This explains why such a quantum state had never been previously observed”, says Beck.

“In the future, we want to specifically investigate other atomic nuclei in which we expect to find deviations in the decay behaviour”, adds the physicist. He hopes that this work will be helped above all by the planned commissioning of the “Variable Energy Gamma-ray System” at the European research facility “Extreme Light Infrastructure – Nuclear Physics” in Bucharest, Romania, in 2022. The nuclear physicists in Darmstadt have made decisive contributions to the design of this facility and it will allow the energy to be focused even more precisely into a narrow frequency band. It is something that Tobias Beck is looking forward to: “It will take our research into nuclear photonics and its scientific and technical applications to a whole new level.”