A New Nuclear ‘Magic’ Number in Exotic Calcium Isotopes
Author: David Steppenbeck
Affiliation: Center for Nuclear Study, University of Tokyo, Japan
Physicists have come one step closer to understanding unstable atomic nuclei. A team of researchers from the University of Tokyo and RIKEN, among other institutions in Japan and Italy, has provided direct evidence for a new nuclear ‘magic’ number in the radioactive calcium isotope 54Ca (a bound system of 20 protons and 34 neutrons). In an article published in the journal 'Nature' , they show that 54Ca is the first known nucleus where N = 34 is a magic number.
The atomic nucleus, a quantum system composed of protons and neutrons, exhibits shell structures analogous to that of electrons orbiting in an atom. In stable, naturally occurring nuclei, large energy gaps exist between ‘shells’ that fill completely when the number of protons or neutrons is equal to 2, 8, 20, 50, 82 or 126 . These are commonly referred to as the nuclear ‘magic’ numbers. Nuclei that contain magic numbers of both protons and neutrons are dubbed ‘doubly magic’ and these systems are more inert than others since their first excited states lie at relatively high energies.
However, recent studies have indicated that the traditional magic numbers (listed above) are not as robust as was once thought and may even change in nuclei that lie far from the stable isotopes on the Segrè chart. It is now known that while some magic numbers can disappear, other new ones can present themselves . A few noteworthy examples of such phenomena are the vanishing of the N = 28 (neutron number 28) traditional magic number in 42Si and the appearance of a new magic number at N = 16 in very exotic oxygen isotopes, one that is not observed in stable isotopes.
The explanation for such behaviour lies in the interplay between nucleons (protons and neutrons) in the nucleus and the ‘shuffling’ of nucleonic orbitals relative to one another, which is often referred to as ‘shell evolution’. In radioactive isotopes with extreme proton-to-neutron ratios, these orbitals may shuffle around so much to the extent that previously large energy gaps between orbitals can become rather small (causing the traditional magic numbers to disappear) while new enlarged energy gaps can sometimes appear (the onset of new magic numbers).
Nuclei around exotic calcium isotopes on the Segrè chart have also received much recent attention and experiments on 52Ca, 54Ti and 56Cr have provided substantial evidence for a new magic number at N = 32. Another new magic number has been predicted to occur at N = 34 in the very exotic calcium isotope 54Ca, but difficulties in producing this isotope in the laboratory have hindered experimental input—that is, until now. Owing to the world’s highest intensity radioactive beams being produced at the Radioactive Isotope Beam Factory  in Japan, the team of researchers was able to study the structure of the 54Ca nucleus for the first time.
Figure 1: Detectors in the DALI2 γ-ray detector array used in the experimental study of 54Ca. [Photo credit: Satoshi Takeuchi]
A primary beam of 70Zn30+ ions at an energy of 345 MeV/nucleon and an intensity of 6 X 1011 ions per second was fragmented to produce a fast radioactive beam that contained 55Sc and 56Ti. These radioactive nuclei were directed onto a 1-cm-thick Be target to produce 54Ca by removing one proton from 55Sc or two protons from 56Ti. The 54Ca nuclei were produced either in their ground states or in excited states. In the case of the latter, the excited states decayed rapidly by emitting γ-ray photons to shed their excess energy. The energies of the γ rays were measured using an array of 186 sodium iodide detectors (Fig. 1) that surrounded the Be target. In turn, the Doppler-corrected γ-ray energies were used to deduce the energies of the nuclear excited states, which provide information on the nuclear structure.
The results of the study  indicate that the first excited state in 54Ca lies at a relatively high energy, which not only highlights the doubly magic nature of this nucleus but confirms the presence of a new magic number at N = 34 in very exotic systems for the first time, ending over a decade of debate on the matter since its first prediction . From a more general standpoint, understanding the nucleon-nucleon forces and evolution of nuclear shells in unstable nuclei plays a key role in the understanding of astrophysical processes such as nucleosynthesis in stars.
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