Institut de recherche sur les lois fondamentales de l'Univers

The magic nuclei

An atomic nucleus is made up of protons and neutrons. It is qualified as magic if its number of protons Z or neutrons N is equal to 2, 8, 20, 28, 50, 82, 126. Magic stable nuclei have well-known characteristics: thus, the energy of its first excited state of spin 2⁺ is higher than its neighboring isotopes, so more energy is required to excite it. A magic nucleus has more stability than its neighbours. In Figure 1, the usual magic numbers for N or Z are displayed with the dashed lines and we can clearly see the "peaks" corresponding to magic nuclei.

The measurement of the energy of the first excited state of spin 2⁺ can therefore reveal the "magic" character of a nucleus. Beyond the indication of magic numbers, systematic measurements of the energies of the first 2+ states provide us with information on the properties of the strong interaction within the atomic nucleus. These properties are currently under-determined due to theoretical uncertainties. The evolution of the shell effects far from the valley of stability is one of the major issues in nuclear physics. Nuclei that are very neutron- rich or neutron-deficient are unstable (radioactive) and described as "exotic".
Physicists want to know if the properties associated with the known magic numbers persist in exotic nuclei or if new phenomena may appear, associated with still unknown magic numbers. Some have already been highlighted, such as the appearance of a new magic number at N=16 and the disappearance of N=20 in oxygen isotopes.

The experiment

For the reactions induced by beams of a few particles per second on the proton target, unstable nuclei are produced with a very low counting rate. MINOS was designed to increase the luminosity by combining a thick liquid hydrogen target (with thickness ranging between 10 to 15 cm; target is in blue in Fig. 2) with a vertex tracking detector, which is a Time Projection Chamber (TPC) built with the Micromegas technique (in grey in Fig. 2).

To study ⁷⁸Ni, the thick hydrogen target of MINOS was bombarded with a beam of copper 79 (and of zinc 80) which induced nuclear reactions on the target protons, producing nickel 78 and two protons (three protons respectively). ⁷⁸Ni can be produced in an excited state; we study the deexcitation of this state by gamma-ray emission. Since only a few ⁷⁹Cu or ⁸⁰Zn nuclei are produced per second, the Minos device was essential to increase the number of particles produced by the reactions.

Results and interpretation

The figure 3 shows the measured spectrum of ⁷⁸Ni produced removing one proton from ⁷⁹Cu. The transition at 2.6 MeV is identified with the decay of the first excited 2⁺ state.

The energy of the measured 2⁺ (2.6 MeV) is comparable to that (2.7 MeV) of the doubly magic ⁵⁶Ni nucleus (Z=N=28). In Figure 4, we observe an increase of the 2⁺ energy compared to the last measured Ni isotopes, which directly proves that the numbers  N=50 and Z=28 remain magic in ⁷⁸Ni. The systematics of the 2⁺ energies of the Ni isotopes can then be used as a benchmark to select the models.
This effect is well predicted by several recent developments of the theoretical approaches ranging from shell-models (LSSM, MCSM) to ab initio calculations (CC and IM-SRG) and also by the QRPA (Quasi-Particle Random Phase Approximation) calculations done at CEA-DAM using the Gogny effective interaction (in its D1M version).

In Figure 1, we can see the "peaks" of the doubly magic nuclei dominating: ⁴He, ¹⁶O, ^40,48Ca and ²⁰⁸Pb among the stable ones; those already highlighted among the exotic ones are ²⁴O (with the new magic number N=16), ⁶⁸Ni and ¹³²Sn. It is now proven with the study of the Nature article that ⁷⁸Ni is part of this group!

To go further…
Additionally, a second 2⁺ state is observed when ⁷⁸Ni is populated from ⁸⁰Zn (Fig. 5). This observation provides evidence for a second deformed band and suggests a collapse of Z=28 and N=50 beyond N=50 and below Z=28. In this sense, ⁷⁸Ni acts as doubly magic stronghold before deformation prevails in more exotic nuclei.

And beyond ⁷⁸Ni?
By studying nuclei even richer in neutrons, deformed and weakly bound isotopes could be found, the deformation leading to a shift of the dripline (the nuclear binding limit) to heavier isotopes. To make progress and conclude on the expected disappearance of traditional shell closures, it will therefore be necessary to study the shell evolution in the vicinity of the dripline for nickel isotopes and for neighboring isotope chains (Z=27 cobalt, Z=29 copper). This will require measurements of the masses (i.e. binding energies) of the most exotic nuclei. These observables will be used as benchmarks for ab initio calculations and will thus validate our understanding of interactions and binding mechanisms far from the valley of stability.