Charge radii as benchmark for state-of-the-art nuclear models

To date, 118 elements are known, of which only six have a “magic” number of protons: In helium, oxygen, calcium, nickel, tin and lead, the shells on which protons are arranged are fully occupied, which gives them a special stability. These elements are to nuclear physics what the noble gases are to chemistry and atomic physics. The element nickel with 28 protons is one of these elements. Information about the course of the nuclear charge radii along the isotope chain – as a measure of the “size” of the nucleus of an isotope – is extremely attractive for the development of a common theoretical framework in which all nuclei, from the lightest to the heaviest, can be consistently described.

Interplay between two models of nuclear physics

An important part of this project is the connection of ab initio theories with density-functional theory (DFT). The ab initio theory describes nuclei on the basis of individual protons and neutrons and the forces prevailing between them. Density-functional theory is based on continuous density and current distributions of the nucleons. Ab initio calculations used to be limited to lighter nuclei, as the computational effort increased dramatically for heavier elements due to the growing number of nucleons. In the meantime, their application could be extended beyond the nickel region due to a great progress in the treatment of many-body systems. Density-functional theory, on the other hand, was developed in order to be able to apply it to nuclei of the heaviest known elements. However, it is limited in the description of very light nuclei. Nickel is currently the heaviest magic element to which both models can be applied and is therefore an ideal test field.

Playing to individual strengths through international cooperation

Laser spectroscopy is the technique with which charge radii along an isotope chain can be determined with the highest precision. Now, two experiments involving nuclear physicists from TU Darmstadt from Professor Wilfried Nörtershäuser's group have determined charge radii of nickel isotopes. One of the experiments took place at the ISOLDE isotope separator at CERN and the other at the National Superconducting Cyclotron Laboratory at Michigan State University (NSCL), with each of the two facilities exploiting its specific strength in the production of short-lived isotopes. At ISOLDE, an entire isotope chain was studied from the lightest stable isotope 58Ni to the neutron-rich 70Ni. As part of his dissertation, Simon Kaufmann evaluated the data from the experiment. At MSU, the researchers concentrated on the neutron-poor and very short-lived isotope 54Ni. The Nörtershäuser group was also involved here.

Deviation between calculations and experiments becomes smaller and smaller

The precise calculation of nuclear charge radii is a major challenge in theoretical nuclear physics. Both ab initio and DFT calculations on neutron-rich isotopes of the lighter magic element calcium have had discrepancies with their experimental values. Since then, both approaches have been improved. The now published agreement of the experimental data for 58-70Ni with the DFT results and those of three independent ab initio calculations, among others with the participation of the group of Professor Achim Schwenk (Institute for Nuclear Physics), with deviations of at most one percent, shows that a precise nuclear theory based on fundamental principles of nuclear power is getting closer.

The result of the measurement of the 54Ni nuclear charge radius at MSU was already published a few weeks ago in the journal Physical Review Letters. The researchers compared it with the already known charge radius of the 54Fe nucleus, in which the proton and neutron numbers are just reversed. This comparison allows conclusions to be drawn about a thin layer of pure neutron matter that extends beyond the protons. The thickness of this so-called neutron skin is closely related to neutron stars and allows a better estimation of the radii of these extremely compact objects, which are hardly accessible to other observations. More details about this experiment and its results can be found in an article on the Michigan State University website.

The experiments at ISOLDE were funded by the German Federal Ministry of Education and Research (BMBF), while the experiments at MSU are part of the DFG-funded Collaborative Research Centre “From Fundamental Interactions to Structure and Stars” (SFB 1245).