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Nuclear physics

Unexpected doubly magic nucleus

Nature volume 459, pages 10691070 (25 June 2009) | Download Citation


Nuclei with a 'magic' number of both protons and neutrons, dubbed doubly magic, are particularly stable. The oxygen isotope 24O has been found to be one such nucleus — yet it lies just at the limit of stability.

Physicists often state that nuclear shell structure — the way in which protons and neutrons are arranged within a nucleus — is the cornerstone of any satisfactory description of an atomic nucleus. But over the past decade it has become apparent that the exact number of particles required to fill a particular shell is not as fixed as was once thought. The results of two experiments, one by Kanungo et al.1 reported in Physical Review Letters, and the other by Hoffman et al.2 in Physics Letters B, add significantly to the discussion. They demonstrate that 24O, the oxygen isotope with proton number Z = 8 and neutron number N = 16, is a doubly magic nucleus. This result is all the more surprising because 24O is also the heaviest oxygen isotope to exist.

The concept of nuclear shell structure is akin to that of atomic shell structure, in that shell closure results in enhanced stability. That is, there are certain nuclei — those that have a 'magic' number of protons and/or neutrons (2, 8, 20, 28, 50 and 82) — that have a full outer shell and are characterized by a large energy gap to the next available shell. As a result, they are more tightly bound than nuclei that have just one more proton or neutron. For neutrons, there is an additional such number: 126. Nuclei that have either the proton or the neutron number equal to one such magic number are thus termed magic nuclei; doubly magic nuclei are those with shell closures for both protons and neutrons.

The existence of nuclear magic numbers has been called into question as a result of studies of nuclei that — in terms of their proton and neutron numbers — are far from the region of stable, naturally occurring isotopes. It seems that the large energy gaps that give rise to the extra stability of magic nuclei are not all that robust and can change with proton and neutron number. In other words, there is experimental proof that some of these rather exotic nuclei, which are expected to be magic, are not particularly tightly bound, and other nuclei seem to signal the presence of new magic numbers3.

The first indications of an unexpected shell closure at N = 16 — with the inference that 24O might be a doubly magic nucleus — came from experiments investigating the binding energy of the neutron that can be most easily removed, and of the radioactive (β) decay properties of nuclei close to 24O (refs 3, 4). However, the main properties associated with enhanced stability had thus far not been observed. Two things were lacking. First, a demonstration that the shell closure of 24O has a spherical shape, as expected for a tightly bound nucleus. And second, that 24O is especially difficult to excite — that is, its first excited state is located at a high energy. This is where Kanungo et al.1 and Hoffman et al.2 check in with their experiments.

Both experiments used 'secondary' beams to probe the properties of 24O. They started from a high-energy primary beam of the calcium isotope 48Ca, which was made to interact with a beryllium target to produce a multitude of nuclear fragments. Fragment separators were then used to identify and select the species of interest, collect them into a beam — the secondary beam — and send them on to a reaction target. Kanungo et al.1 studied the interaction of the very few (barely 3 particles per second) 24O fragments produced in this way with a carbon reaction target. Specifically, they focused on the properties of 23O products obtained from the direct removal of a neutron.

At the high energies involved, the 24O secondary-beam particles undergo peripheral, grazing collisions with the target nuclei, where only the surfaces interact, and there is a simple relation between the physical descriptions, known as wavefunctions, of the incoming and outgoing nuclei5. From the momentum distribution of 23O products, Kanungo and colleagues1 were able to show unambiguously that the neutron removed from 24O occupied, with a very large probability, the 2s1/2 energy level rather than the higher-energy 1d3/2 level (Fig. 1a). Because the wavefunction associated with the 2s1/2 state is spherical, this is an indication that the shell closure is a spherical one. Hence, the first of the two criteria for a doubly magic nucleus is fulfilled.

Figure 1: Doubly magic nature of 24O.
Figure 1

Experiments by Kanungo et al.1 and Hoffman et al.2 provide evidence that 24O (proton number Z = 8 and neutron number N = 16) is a doubly magic nucleus — that is, both its protons and neutrons are arranged into complete energy shells, and so have large energy gaps to the next available shell. a, In this representation of the nuclear shell structure of 24O, only the last 2 of the 8 protons are shown: they occupy the 1p1/2 level, which is separated from higher-lying levels by a large gap, as 8 is indeed a magic number; similarly, the last 2 of the first 8 neutrons reside in the 1p1/2 neutron level, whereas the remaining 8 fill the 1d5/2 and 2s1/2 levels. Hoffman et al.1 demonstrate that the first excited state of 24O is a doublet of levels, termed 1+ and 2+, separated by a large energy gap from the 2s1/2 level. (In this notation, the subscripts 1/2, 3/2 and 5/2 correspond to energy-level multiplicities — or the maximum number of particles allowed per level — of 2, 4 and 6 respectively.) b, The variation of the energy of the 2+ excited state with neutron number for different oxygen isotopes (Z = 8, N = 6−16) illustrates the sensitivity to shell closure: complete shells at N = 8 and N = 16 lead to an increase in energy. (Energies are given in megaelectronvolts (MeV); plot based on Fig. 4 of Hoffman et al.2.)

Hoffman et al.2 focused instead on the second criterion: the energy of the first excited state of 24O. In their experiment, fluorine 26F (Z = 9, N = 17) fragments were selected and turned into a secondary beam that was subsequently sent on to a beryllium target, removing a proton and a neutron from the fluorine fragments and thus leaving behind excited 24O. The latter decayed promptly into 23O and a neutron, for 24O has no excited states bound to particle decay.

Hoffman and colleagues' detection2 of both 23O and a neutron represents a real tour de force: the 23O ions had to be deflected from the direction of the secondary beam by a superconducting magnet, so that they could be detected without interfering with the forward-moving neutrons; these were measured using the modular neutron array (MoNA)6 at Michigan State University. From approximately 400 23O–neutron coincidence events, Hoffman et al. showed that the neutron energy spectrum is best reproduced by simulations of the reaction that postulate the presence of a doublet of unbound excited states in 24O, termed 1+ and 2+ states (Fig. 1a).

The authors2 compared the energies of the first excited 2+ states in all the Z = 8 oxygen isotopes that have an even neutron number N and showed how they vary markedly with N (Fig. 1b). As neutrons fill the 1d5/2 shell beyond the magic number N = 8, which corresponds to the doubly magic nucleus 16O, the energy drops by a factor of about three on reaching N = 12 before increasing at N = 14, a manifestation that full 1d5/2 occupation is reached at that neutron number. A complete 2s1/2 shell at N = 16 leads to an even more dramatic increase in energy — a clear signature of the doubly magic character of 24O.

As shown by Hoffman et al.2, most theoretical shell-structure calculations are unable to reproduce the observations satisfactorily. The task is far from trivial, as several puzzling observations need to be reconciled. Experiments have demonstrated that oxygen isotopes such as 25O or 26O, which are heavier than 24O, do not exist in nature — that is, they are unbound. Therefore, 24O is truly remarkable because it is hard to excite, implying that it is doubly magic and very tightly bound. But it is located at the very limits of nuclear existence, as the addition of even a single neutron is not possible.

Equally surprising is the fact that the addition of a single proton, when moving from oxygen to fluorine, enables at least six additional neutrons to bind: observations indicate that even 31F (Z = 9, N = 22) is bound7. Thus, the shell structure in Figure 1a changes drastically with proton and neutron number: it seems that, as soon as protons occupy the 1d5/2 orbital (as happens when going from O to F), the gap between the neutron 2s1/2 and 1d3/2 shells decreases significantly, an indication that a tensor force — an especially attractive, spin-dependent force between protons and neutrons — is providing the additional binding8. The full characterization of this force remains a challenge.

Experiments such as those of Kanungo et al.1 and Hoffman et al.2 highlight aspects of the physics of nuclei that are not readily apparent from the structure of stable nuclei, yet are essential for addressing the most fundamental challenge of nuclear physics — that of deciphering the exact nature of the nuclear force that binds protons and neutrons together in the nucleus and that defines the limits of the nuclear landscape.


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  1. Robert V. F. Janssens is in the Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA.

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