Figure 1: Until now, physicists thought that all heavy nuclei deformed from spheres are elongated in one direction like rugby balls (top), but RIKEN researchers have shown that virtually all of such nuclei have triaxial symmetry with oval cross-sections like almonds (bottom). © 2025 RIKEN Nishina Center for Accelerator-Based Science
Many heavy atomic nuclei are shaped more or less like squashed rugby balls than fully inflated ones, a theoretical study by RIKEN nuclear physicists has found1. This unexpected finding overturns the consensus held for more than half a century.
Illustrations of atoms often depict the nucleus as a round blob made up of neutrons and protons. Physicists initially assumed that nuclei were spherical like soccer balls.
But in the 1950s, Aage Bohr and Ben Mottelson developed a theory that predicted that many heavy nuclei are elongated in one direction, being shaped like a rugby ball.
Following in the footsteps of his father Niels Bohr, who was awarded the 1922 Nobel prize in physics for his model of the structure of atoms, Aage Bohr shared the 1975 Nobel prize for physics for this discovery.
But Takaharu Otsuka, a visiting scientist at the RIKEN Nishina Center for Accelerator-Based Science, always had niggling doubts about this. In particular, he wondered why heavy nuclei should be shaped like rugby balls, which are round in cross section, and not have a more general, almond-like shape that is oval in cross section. It struck him that the lower symmetry shape would be more natural for nuclei to adopt (Fig. 1).
"When Aage Bohr's model was proposed it produced some simple calculations, but they appeared overly simplistic to me," he recalls. "And there was no convincing general argument why the nucleus should be deformed in such a symmetric way."
Over the decades, this doubt nagged at the back of Otsuka's mind, and he increasingly began to question whether most large nuclei were actually rugby-ball shaped. But when he started proposing at conferences that nuclei with almond-like shapes are common, he experienced a lot of skepticism and even opposition from other nuclear physicists.
Now, Otsuka has been vindicated, showing in a theoretical study with co-workers that virtually all heavy elliposoidally deformed nuclei actually have triaxial shapes resembling almonds rather than biaxial shapes like rugby balls.
"This work represents a major shift in the fundamental description of nuclear structure that was entrenched for nearly 70 years," says Otsuka.
One thing that was indispensable for Otsuka's team was having access to Fugaku computer-one of the most powerful supercomputers in the world.
This finding about the shape of nuclei affects how nuclei rotate since it means they can rotate about two axes instead of just one. It also has implications for the search for new superheavy nuclei that are heavier than currently known nuclei.
Takaharu Otsuka and Yusuke Tsunoda, co-author of the paper © 2025 RIKEN
