Einsteinium-255, produced through irradiation in ILL’s high-flux reactor, provided a continuous supply of fermium-255, facilitating high-resolution laser spectroscopy in Mainz.

Where does the periodic table of elements end, and what processes give rise to heavy elements? An international research team has conducted experiments at the GSI/FAIR accelerator facility and Johannes Gutenberg University (JGU) in Mainz to explore these questions. Their study focused on the atomic nuclei of fermium (element 100), examining variations with different neutron counts. The findings, which provide new insights into nuclear structure, have been published in Nature.

“Using a laser-based method, we investigated fermium atomic nuclei, which possess 100 protons, and between 145 and 157 neutrons. Specifically, we studied the influence of quantum mechanical effects on the size of their atomic nuclei,” explains Sebastian Raeder, the head of the experiment at GSI/FAIR.

Producing Fermium for Study

An international collaboration of 27 institutes across seven countries investigated fermium isotopes with lifetimes ranging from a few seconds to over 100 days. This study used multiple production methods tailored to different isotopes. Short-lived fermium isotopes were synthesized through fusion reactions at the GSI/FAIR accelerator facility. In contrast, neutron-rich, long-lived isotopes such as 255Fm and 257Fm were produced in trace amounts (picograms) through irradiation in high-flux research reactors.

The initial irradiation took place at the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory (ORNL), USA, generating isotopes up to 257Fm. From this irradiated mixture, radiochemists at Mainz University isolated the neighboring element einsteinium (element 99), which was then irradiated in the high-flux reactor at Institut Laue-Langevin (ILL) in Grenoble, France. This process produced 255Es, which has a half-life of nine months and continuously decays into 255Fm, a much shorter-lived isotope with a half-life of only 20 hours. To ensure a steady supply for laser spectroscopy, 255Fm was repeatedly extracted through radiochemical techniques at Mainz University—a process radiochemists refer to as “milking” a fermium cow.

“Interestingly these elements’ names are well-deserved eponyms for the production process: the famous E=mc2 relation by Albert Einstein is the foundation of energy generation in nuclear reactors, while Enrico Fermi is the creator of the first man-made nuclear reactor and fermium is the heaviest element directly reachable by reactor irradiations,” points out Ulli Köster, ILL scientist and one of the authors of the publication.

“This study demonstrates impressively the synergy of different production methods: accelerators are best suited to produce neutron-deficient isotopes (less neutrons than usual) while research reactors are best suited to produce neutron-rich isotopes. Extending such studies to superheavy elements often requires a combination of both techniques, namely accelerator-irradiation of reactor-produced targets,” Köster adds.

Using forefront laser spectroscopy techniques, subtle changes in the atomic structure can be analyzed, which in turn provide information about nuclear properties such as the nuclear charge radius, i.e. the distribution of protons in the atomic nucleus. Laser light of a suitable wavelength lifts an electron in the fermium atom to a higher-lying orbital, and then removes it from the atom altogether, forming a fermium ion, which can be detected efficiently. The exact energy required for this stepwise ion-formation process varies with neutron number. This small change in excitation energy was measured to obtain information about the change in charge radius of the atomic nuclei.

Understanding Nuclear Stability and Shell Effects

The investigations provided insight into the changes of the nuclear charge radius in fermium isotopes across the neutron number 152 and showed a steady, uniform increase. The comparison of the experimental data with various calculations performed by international collaboration partners using modern theoretical nuclear physics models allows an interpretation of the underlying physical effects.

“Our experimental results and their interpretation with modern theoretical methods show that in the fermium nuclei, nuclear shell effects have a reduced influence on the nuclear charge radii, in contrast to the strong influence on the binding energies of these nuclei,” says Jessica Warbinek, who was a doctoral student at GSI and JGU at the time of the experiments and is first author of the publication. “The results confirm theoretical predictions that local shell effects, which are due to few individual neutrons and protons, lose influence when the nuclear mass increases; instead, effects dominate that are to be attributed to the full ensemble of all nucleons, with the nuclei rather seen as a charged liquid drop.”

The experimental enhancements of this method enable more precise laser spectroscopic studies of heavy elements, particularly those near and beyond neutron number 152. These advancements contribute to a deeper understanding of stabilization processes in heavy and superheavy elements. Nuclei with fully filled nuclear shells, known as “magic” numbers of nucleons, exhibit increased stability, making them less reactive. As a result, these nuclei have higher binding energies and longer lifetimes.

Additional info: heavy elements, quantum mechanical effects and the nuclear shell model

• Elements beyond uranium (element 92) do not occur naturally in the Earth’s crust. To be studied, they thus have to be produced artificially.
• Elements like fermium (element 100) form a bridge between the heaviest naturally occurring elements and the so-called superheavy elements.
• Superheavy elements, which start at element 104, owe their existence to stabilizing quantum mechanical shell effects, which add about two thousandths of the total nuclear binding energy; albeit a small contribution, it is decisive in counteracting the disruptive forces acting between the many positively charged protons, which all repel each other.
• Quantum mechanical effects induced by the building blocks of atomic nuclei (protons and neutrons) are explained by the nuclear shell model. Similarly as for atoms, where those with completely filled electron shells are chemically stable and thus unreactive, nuclei with filled nuclear shells (containing so-called “magic” numbers of nucleons) exhibit an increased stability. Consequently, their nuclear binding energies and their lifetimes increase.
• In lighter nuclei, filled nuclear shells are known to also influence trends in the nuclear radii. Indeed, studies of several atomic nuclei of the same element, but with different neutron numbers, have revealed a steady increase in this radius, unless a magic number is crossed. Then, a kink is observed, as the slope of the radial increase changes at the shell closure. This effect was found for lighter, spherical atomic nuclei up to lead.

Reference: “Smooth trends in fermium charge radii and the impact of shell effects” by Jessica Warbinek, Elisabeth Rickert, Sebastian Raeder, Thomas Albrecht-Schönzart, Brankica Andelic, Julian Auler, Benjamin Bally, Michael Bender, Sebastian Berndt, Michael Block, Alexandre Brizard, Pierre Chauveau, Bradley Cheal, Premaditya Chhetri, Arno Claessens, Antoine de Roubin, Charlie Devlin, Holger Dorrer, Christoph E. Düllmann, Julie Ezold, Rafael Ferrer, Vadim Gadelshin, Alyssa Gaiser, Francesca Giacoppo, Stephane Goriely, Manuel J. Gutiérrez, Ashley Harvey, Raphael Hasse, Reinhard Heinke, Fritz-Peter Heßberger, Stephane Hilaire, Magdalena Kaja, Oliver Kaleja, Tom Kieck, EunKang Kim, Nina Kneip, Ulli Köster, Sandro Kraemer, Mustapha Laatiaoui, Jeremy Lantis, Nathalie Lecesne, Andrea Tzeitel Loria Basto, Andrew Kishor Mistry, Christoph Mokry, Iain Moore, Tobias Murböck, Danny Münzberg, Witold Nazarewicz, Thorben Niemeyer, Steven Nothhelfer, Sophie Péru, Andrea Raggio, Paul-Gerhard Reinhard, Dennis Renisch, Emmanuel Rey-Herme, Jekabs Romans, Elisa Romero Romero, Jörg Runke, Wouter Ryssens, Hervé Savajols, Fabian Schneider, Joseph Sperling, Matou Stemmler, Dominik Studer, Petra Thörle-Pospiech, Norbert Trautmann, Mitzi Urquiza-González, Kenneth van Beek, Shelley Van Cleve, Piet Van Duppen, Marine Vandebrouck, Elise Verstraelen, Thomas Walther, Felix Weber and Klaus Wendt, 30 October 2024, Nature.
DOI: 10.1038/s41586-024-08062-z