Conjuring up calcium’s inner magic

Every naturally occurring heavy element on Earth has its origins in the stars of the Universe. Through a process known as nucleosynthesis, nuclear collisions inside massive celestial bodies fuse together lightweight atoms such as hydrogen and helium to produce heavier and heavier elements, such as carbon and silicon. The natural abundance of elements and their isotopic variants—atoms with an unbalanced number of protons and neutrons—is determined by the stability of the nucleus, which governs whether an astrophysical isotope will be long-lived or susceptible to rapid radioactive decay.

One way that physicists gauge the stability of atomic nuclei is with the concept of ‘magic numbers.’ Similar to the way that electrons travel in tightly defined ‘shells’ around a central nucleus, protons and neutrons also occupy distinct orbits inside the nucleus. When the number of protons or neutrons completely fills a particular shell, corresponding to 2, 8, 20, 28, 50, 82 or 126 particles (the magic numbers), the isotope gains exceptional stability. Such nuclei take on a spherical shape and are difficult to excite due to a significant energy gap that must be overcome before the nucleus can accept new protons and neutrons.

Now, a research team led by David Steppenbeck from the University of Tokyo and Hiroyoshi Sakurai and Satoshi Takeuchi from the RIKEN Nishina Center for Accelerator-Based Science has uncovered evidence of a new magic number of 34 neutrons in the calcium-54 (⁵⁴Ca) isotope¹. The finding is significant because the isotope displays surprising stability despite its seemingly volatile nuclear structure.

When the theory of magic numbers was developed over a half-century ago, researchers believed that nuclear shells were robust and constant. These notions began to change, however, with studies into short-lived exotic nuclei that have quite different properties from those of natural isotopes, which have balanced numbers of protons and neutrons. In exotic nuclei with significantly more neutrons than protons, the excess neutrons begin to fill normally empty orbital shells, producing extra forces not seen in stable isotopes. “These attractive and repulsive forces cause the orbitals to shuffle about,” explains Steppenbeck. “In some cases, the large energy gaps associated with the magic numbers of standard stable nuclei can disappear and new energy gaps—the onset of new magic numbers—can materialize.”

In order to better understand how changes in shell structure—or ‘shell evolution’—occur, researchers are increasingly turning to calcium isotopes. This element has a magic number of 20 protons, and evidence has emerged that an exotic calcium isotope with 32 neutrons (⁵²Ca) has a substantial energy gap and therefore forms a relatively inert nuclear core. Theoretical calculations have also suggested that ⁵⁴Ca, which has 20 protons and 34 neutrons, should show magic-number stability, while other studies have cast doubt on this proposition.

“Prior to our experiment, we simply did not know whether the magic number of 34 neutrons would exist in calcium or not,” says Steppenbeck. “There are a great number of theories that predict different characteristics of the ⁵⁴Ca excited states. Some predict a shell closure with 34 neutrons that is just as large as the traditional one seen with 28 neutrons, while others predict no shell closure at all. Clarifying which theories are correct was a major motivation behind our work.”