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Nuclear physics

Symmetrical tin

Nature volume 486, pages 330331 (21 June 2012) | Download Citation


The tin isotope 100Sn is the heaviest 'doubly magic nucleus' that has an equal number of protons and neutrons. It is now finally starting to give up its secrets, thanks to the persistent efforts of nuclear physicists. See Article p.341

On page 341 of this issue, Hinke et al.1 report how, after years of endeavour, they have achieved a significant leap forward in the study of the heaviest 'symmetrical doubly magic' nucleus — the tin isotope 100Sn. Composed of 50 protons and 50 neutrons, this nucleus is drawing the attention of nuclear physicists around the globe because of its unique location in the nuclear landscape.

Nuclei are complex and challenging quantum objects. In contrast to the structure of atoms, for which the fundamental interaction between the electrons and the nucleus — the electromagnetic force — is known with great precision, the interaction between the constituents of a nucleus, the strong nuclear force, is not so well known. This is due in part to the composite nature of the nuclear constituents, or nucleons, and the nature of the fundamental forces that bind nucleons together (quantum chromodynamics and the electroweak force).

As far as we know, nuclei are the smallest objects that can be split up into their constituents. They are therefore the smallest entities in which emergent properties — patterns that arise from complexity — can be studied. Nuclear scientists study these emergent phenomena and are using them to decipher the nature of the nuclear force. Magic numbers are numbers of protons or neutrons that form full shells in an atomic nucleus, and are perhaps the foremost emergent property of nuclei. Thought to have first been coined by the physicist Eugene Wigner, the term reflects the unexpected shell structure of nuclei, as opposed to the liquid-like behaviour expected for such densely packed and strongly interacting objects. In fact, the independent particle model used to describe atoms, in which electrons (the particles) are assumed to move independently of each other, also works remarkably well for nuclei. The model has been able to explain — at least for stable nuclei2 — the observed sequence of magic numbers: 2, 8, 20, 28, 50, 82 and 126, all of which, by virtue of their 'magic' nature, correspond to increased stability.

In recent years, however, as physicists have expanded their reach across the nuclear landscape, a different picture has emerged. The magic numbers observed in stable nuclei seem to be either vanishing or evolving, especially on the neutron-rich side of the nuclide chart3,4, which plots proton number against neutron number (Fig. 1).

Figure 1: Nuclear landscape.
Figure 1

The chart shows the location of all nuclei as a function of their neutron number (N) and proton number (Z). Dashed lines represent magic numbers, which correspond to full shells of protons or neutrons. Doubly magic nuclei lie at the intersections of magic-number lines. Symmetrical nuclei have an equal number of protons and neutrons. Hinke et al.1 have produced and studied 100Sn, the heaviest symmetrical doubly magic nucleus. Note that the calculation used to predict bound nuclei in this chart is limited to those with N less than 160.

Nuclei that have a magic number of neutrons or protons are more tightly bound than their non-magic counterparts, and their intrinsic simplicity makes them prime candidates for testing proposed models of nuclear structure. Particularly interesting are nuclei in which the number of both protons and neutrons reaches one of the magic numbers. These doubly magic nuclei have even greater binding energy than singly magic nuclei.

One would expect that symmetrical doubly magic nuclei, which have an equal magic number of protons and neutrons, would follow the magic number sequence, and this is indeed the case for light nuclei: those of helium (4He), oxygen (16O) and calcium (40Ca). However, because of the repulsion between protons, the line of stable nuclei in the nuclide chart veers away from the symmetry line, as ever more neutrons are required to bind heavier nuclei (Fig. 1). As a result, the only two other nuclei that follow the magic sequence are the nickel nucleus 56Ni and 100Sn. These nuclei are bound but unstable: they undergo β-decay, in which a positron (the antiparticle of an electron) is emitted to produce a daughter nucleus.

Although 56Ni is not too far from being a stable nucleus (58Ni is stable), 100Sn is very close to the edge of nuclear stability, where the nuclear force between nucleons can no longer bind them into a nucleus. The nucleus 100Sn has 12 neutrons fewer than the lightest stable isotope of tin, 112Sn. Therein lies the particular attraction of 100Sn: it is at the same time doubly magic and at the edge of the nuclear landscape. Many long-standing questions about this oddball are now beginning to be answered. For example, is it really doubly magic and simple in structure? How is the strength of its β-decay distributed across the energy levels of its daughter nucleus, indium-100? Does it have isomeric (metastable) states? The study of its β-decay is particularly interesting because of the large energy gap between the ground state of 100Sn and that of its daughter, a characteristic of nuclei that are close to the limits of nuclear binding.

Unfortunately, what makes this nucleus attractive is also what makes it difficult to study. It is so far away from stable isotopes that it is extremely difficult to produce. Two types of nuclear reaction have typically been used to attempt this feat. One, called fusion–evaporation5, is a bottom-up approach, in which two nuclei are fused together with minimum excitation energy, so as to minimize the subsequent loss of protons or α-particles (4He nuclei). The other reaction, called projectile fragmentation6, is more brutal but at present more effective. In this approach, a high-energy projectile that is heavier than 100Sn — the xenon nucleus 124Xe, at 1gigaelectronvolt per atomic mass unit in Hinke and colleagues' experiment1 — is sheared by making it collide with a target, leaving a residue that is composed of 50 protons and 50 neutrons. The chance of ending up with the desired nucleus is greater in the former approach than in the latter, but because of the underlying high energy involved, the latter method is more efficient at finding the 'needle in the haystack', and the experiment is actually feasible. To give a sense of the filtering (isolating the desired nuclei from the multitude of other species produced by the nuclear reaction) needed to pull this off, consider that, out of the 1.2×1015 124Xe projectiles accelerated during Hinke and colleagues' experiment at the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt, Germany, only 259 100Sn nuclei were identified.

The results of the authors' experiment represent a giant step compared with previous attempts to study 100Sn. Not only have the experimenters greatly improved the precision of the half-life measurement of this isotope, but they have, for the first time, also determined the end point of the energy spectrum of β-decay (the maximum energy of the emitted positrons) and have observed γ-ray transitions, which correspond to decays between states of the daughter nucleus. Their deductions are stunning: 100Sn seems to have the highest-known β-decay strength of all nuclei, and has been classified as a 'superallowed Gamow–Teller decay' (Gamow–Teller transitions allow the spin to change by 0 or ±1 between the initial state of the parent and the final states of the daughter). Usually, this label is reserved for Fermi decays (transitions that occur between states of the same spin), because they typically have the largest strengths.

As always happens with scientists, once they have been given a taste of a new delicacy, they crave more. Other laboratories have joined the race and are working to improve on the GSI 100Sn production rates. They include: the Radioactive Isotope Beam Factory in Wako, part of Japan's RIKEN national network of labs, which has recently synthesized 100Sn nuclei; SPIRAL2 at the heavy-ion accelerator GANIL in France; and the Facility for Rare Isotope Beams at Michigan State University. These facilities will produce this remarkable nucleus, as well as many others, in even larger quantities. Deciphering the emergent properties of 100Sn, and of other nuclei located far from the stability line on the nuclide chart, should lead scientists towards a fuller understanding of the nuclear force.


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  1. Daniel Bazin is at the National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824–1321, USA.

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Correspondence to Daniel Bazin.

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