Nuclear physics

Doubly magic tin

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  • A Correction to this article was published on 02 June 2010

By swapping the roles of the target and beam in an experiment that is otherwise impossible to implement, researchers have confirmed the doubly magic nature of the neutron-rich radioactive tin isotope 132Sn.

Among the thousands of atomic nuclei studied to date, 'doubly magic' nuclei form a very small and exclusive club. Nuclear magic numbers were identified1 by Maria Goeppert-Mayer in 1948 as being the numbers of protons or neutrons that form closed (full) outer shells in an atomic nucleus, just as do magic numbers of electrons in noble-gas elements such as helium and neon. Nuclei that have magic numbers of both protons and neutrons — thus termed doubly magic isotopes — are the best examples of nuclear systems that are rigidly spherical. To date, six nuclei have had their membership in the doubly magic club confirmed through observation of their rigid sphericity. Five of them are among the 256 stable isotopes found in nature. A sixth is radioactive and is proton rich — it would need two more neutrons to be stable.

In an experiment performed at Oak Ridge National Laboratory and reported on page 454 of this issue, Jones et al.2 demonstrate that the neutron-rich radioactive tin isotope tin-132 (132Sn, with a half-life of 39.7 seconds) belongs to the doubly magic club. It becomes the seventh isotope — and the first neutron-rich radioactive isotope — to join the club. The result also promises to provide insight into an astrophysical reaction known as the 'r-process', in which heavy elements are produced through a complex combination of nuclear reactions, involving rapid (hence the 'r') neutron capture, during stellar explosions called supernovae.

The nuclear magic numbers (2, 8, 20, 28, 50, 82 and 126) are shown in the chart of nuclides in Figure 1. In this chart, isotopes are arranged with their numbers of protons on the vertical axis and their neutron numbers on the horizontal axis. It shows stable isotopes, the 3,000 radioactive isotopes already produced, radioactive isotopes that may exist but have not yet been observed, and isotopes thought to be produced in the r-process. The isotopes to the right of the 'valley of stability' — formed by the stable isotopes (black in the figure) — are each said to have a 'neutron excess' that is defined as the difference between the number of neutrons in the isotope and the number of neutrons in the heaviest stable isotope of the same element. According to this definition, the farther to the right of the valley of stability an isotope is, the greater its neutron excess. The figure shows how close 132Sn is to the r-process nuclei and therefore how important Jones and colleagues' result with this isotope is for achieving a more accurate picture of how the r-process produces heavy elements in the cosmos. Points at which the 'magic' lines intersect are thought to correspond to doubly magic isotopes. The confirmation of their doubly magic nature is an important test of the nuclear-shell model, for which Goeppert-Mayer and J. Hans D. Jensen won a share of the 1963 physics Nobel prize.

Figure 1: Chart of nuclides.

The diagram plots the number of protons (Z) against the number of neutrons (N) for stable isotopes (black), radioactive isotopes that have been produced (yellow), radioactive isotopes that may exist but have not yet been observed (green), and isotopes that are thought to be produced in a succession of nucleosynthesis reactions called the r-process (blue). The dashed lines denote the nuclear 'magic numbers', which correspond to nuclei that are generally more stable against decay than other isotopes. Jones and colleagues2 show that the neutron-rich radioactive tin isotope 132Sn (Z = 50, N = 82), which had been anticipated to be a 'doubly magic' isotope (it lies at the intersection of two 'magic' lines), is indeed doubly magic.

The doubly magic stable isotopes, which are helium-4 (4He; 2 protons and 2 neutrons), oxygen-16 (16O; 8 protons and 8 neutrons), calcium-40 (40Ca; 20 protons and 20 neutrons), calcium-48 (48Ca; 20 protons and 28 neutrons) and lead-28 (28Pb; 82 protons and 126 neutrons), have been studied extensively for the past 60 years. The sphericity of the radioactive proton-rich doubly magic nucleus nickel-56 (56Ni; 28 protons and 28 neutrons, half-life 5.9 days) was confirmed3 in 1998. However, until now, candidates for being radioactive, neutron-rich and also doubly magic have not been accessible to the types of experiment necessary to confirm their rigidly spherical nature. Such experiments are particularly important because changes in magic numbers have already been observed in some neutron-rich nuclei. For example, Bastin et al.4 found that the 28-neutron shell closure has disappeared in silicon-42, which has 12 excess neutrons.

The experiment devised by Jones et al.2 to test the doubly magic character of radioactive 132Sn (50 protons and 82 neutrons) was a technical tour de force. One way of identifying the doubly magic character of a stable isotope is with a 'neutron-stripping reaction', which is performed by placing a thin foil holding the doubly magic isotope (the target) in a beam of nuclei of deuterium (2H), an isotope of hydrogen that has one proton and one neutron. The experimental set-up includes detectors that determine when a single deuterium nucleus drops its neutron off into an orbit around a nucleus in the target. However, the short half-life of 132Sn made it impossible to produce a foil target of the type used in neutron-stripping experiments on stable doubly magic isotopes. Instead, the researchers turned the experiment around.

They used a foil target of deuterated polyethylene (that is, thin plastic in which hydrogen is in the form of 2H, instead of 1H, which makes up 99.99% of naturally occurring hydrogen) and a beam of 132Sn nuclei that had been produced in violent collisions of protons with uranium carbide at Oak Ridge's Holifield Radioactive Isotope Beam Facility (HRIBF). The 132Sn nuclei were accelerated to a kinetic energy of 630 megaelectronvolts — corresponding to a velocity of about 10% of the speed of light — and then focused on the deuterated polyethylene target. In this way, the experimenters did the neutron-stripping measurement in reverse, with the 132Sn nucleus 'picking up' a neutron as it passed by a deuterium nucleus. The experiment's success depended not only on the quality of the 132Sn beam produced by the HRIBF, but also on the advanced detection system ORRUBA, the Oak Ridge Rutgers University Barrel Array, named after the institutions that constructed it.

The experiment determined quantities called spectroscopic factors — essentially, measurements of the purity of quantum states — for four orbitals of the nuclear-shell model. In a rigidly spherical doubly magic nucleus, the spectroscopic factors should each be close to 1.0, which indicates a perfectly pure orbital quantum state. All four spectroscopic factors measured by Jones and collaborators2 were consistent with the value 1.0, given the experiment's statistical uncertainties.

ORRUBA demonstrates the technological advances that will be necessary to study isotopes that have even greater neutron excesses. These will be produced at the Facility for Rare Isotope Beams (FRIB) at Michigan State University, which will begin experimental operations in around 2019. FRIB will join the facilities already operating at the German laboratory GSI and at RIKEN in Japan in performing experiments with nuclei that have the greatest neutron excesses ever produced. Together, these laboratories should illuminate the cosmological origins of the heavy elements.


  1. 1

    Mayer, M. G. Phys. Rev. 74, 235–239 (1948).

  2. 2

    Jones, K. L. et al. Nature 465, 454–457 (2010).

  3. 3

    Rehm, K. E. et al. Phys. Rev. Lett. 80, 676–679 (1998).

  4. 4

    Bastin, B. et al. Phys. Rev. Lett. 99, 022503 (2007).

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Cottle, P. Doubly magic tin. Nature 465, 430–431 (2010) doi:10.1038/465430a

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