The mystery of nuclear 'magic numbers' has finally been resolved

A longstanding mystery in nuclear physics regarding the origin of “magic numbers” — specific numbers of protons and neutrons that confer exceptional stability to atomic nuclei — has been resolved by a team led by Jiangming Yao at Sun Yat-sen University in China. These magic numbers, first identified nearly 80 years ago by physicist Maria Goeppert Mayer, have been fundamental in explaining why certain elements are more stable and abundant in the universe. Yao and his colleagues used advanced quantum calculations starting from first principles to demonstrate how these numbers emerge naturally from the complex interactions between nuclear particles. Previous models, such as the shell model developed by Goeppert Mayer and others, treated nucleons as independent particles occupying discrete energy levels or shells. However, this approach did not fully incorporate the strong interactions between particles inside the nucleus, leaving a gap between theory and experimental observations. The new study bridges this gap by gradually transitioning from a high-resolution quantum description of particle interactions to a lower-resolution shell model, revealing how changes in the symmetry of quantum states lead to the formation of stable nuclear configurations at magic numbers. The researchers’ approach effectively acts as a “mathematical microscope,” allowing them to observe how nuclear structure evolves across different scales. This change in symmetry is linked to relativistic effects, integrating concepts from special relativity into nuclear theory and providing a more comprehensive understanding of nuclear stability. The team validated their theoretical framework by applying it to tin isotopes known to be doubly magic, containing 50 protons and 82 neutrons, confirming the robustness of their findings. This breakthrough not only resolves a fundamental question in nuclear physics but also enhances the predictive power of nuclear models, which has implications for understanding the formation of elements in the universe and could influence future research in nuclear energy and superheavy element synthesis. The work exemplifies how modern computational methods can unify disparate theoretical approaches and deepen insight into the quantum nature of atomic nuclei.