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A new Frontier of Unstable Doubly Magic Nuclei
Ryo Taniuchi, Pieter Doornenba
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DOI: 10.22661/AAPPSBL.2019.29.5.13

A new Frontier of Unstable Doubly Magic Nuclei



The doubly magic character of the isotope 78Ni was demonstrated experimentally. To accomplish this, a newly developed target and detector system was created to measure the de-excitation gamma rays following proton-knockout reactions. While the high energy of the first excited state of 78Ni manifests its closed-shell nature, a second state found at a similar energy questions the nuclear shell robustness for nuclei with larger neutron-to-proton ratios. This result triggers further comprehensive studies to delineate the evolution from spherical to deformed nuclei at the extremes of the nuclear chart.


Atomic nuclear systems have finite numbers of two types of fermions, i.e., protons and neutrons, interacting with each other via nuclear forces or, in general, by strong interaction. It can be approximated by a mean-field in which protons and neutrons are independently arranged in shells. This approximation is justified by the experimental observation that a completely filled shell results in greater stability of the nucleus. More than a half century ago, the empirical numbers of completely filled closed shells, 2, 8, 20, 28, 50, 82, 126, also known as magic numbers, were explained by introducing a strong spin-orbit interaction to a (Woods-Saxon type) mean-field potential [1].

The concept of the nuclear shell model was able to well reproduce properties of stable nuclei and isotopes in their vicinity. However, innovations in accelerator facilities have been able to produce extremely neutron rich isotopes, which has led to the discovery that the canonical magic numbers may disappear, while new numbers can emerge [2].


Fig. 1: Chart of experimental first 2+ excitation energies for even-even nuclei. This energy is a measure for shell closures. Because the energies of 4He, 14C, and 14,16O are extremely high, their lengths are trimmed. Energies of the doubly magic nuclei are more than twice the energy of neighboring semi magic nuclei. The theoretically estimated two-neutron drip line and its associated errors are also drawn with a blue line and hatched area.

The measurement of 2+ excitation energies of nuclei is a powerful tool to reveal their magic nature. Figure 1 shows the distribution of these excitation energies across the nuclear chart, which is arranged in two dimensions by the proton and neutron numbers. While more than 3000 isotopes are known to exist [3], doubly magic nuclei, for which both proton and neutron numbers correspond to shell closures, such as 4He, 16O, 40Ca, 48Ca, are rare across the nuclear chart.

The isotope 78Ni, which was studied in our work [4], has drawn immense interest from both experimental and theoretical nuclear physicists. As indicated in Fig.1, it is an anticipated doubly magic nucleus with 28 protons and 50 neutrons. However, it is located in a very neutron-rich region of the nuclear chart and in proximity to the two-neutron drip line, where isotopes cease to be bound. Whether the doubly magic features of 78Ni are preserved has been a topic of long-standing discussion. Several studies in the vicinity of 78Ni supported the picture of a typical shell closure [5-8]. Others suggested a breakdown of the neutron shell gaps around this region [9-12]. To settle this long-standing question, a direct measurement of the 2+ excitation energy of 78Ni is required.

Production of exotic neutron-rich nuclei

Since 78Ni does not exist naturally, the best way is to produce it from fission reactions from uranium or transuranium nuclei. At present, the Radioactive Isotope Beam Factory (RIBF), operated by the RIKEN Nishina Center and the Center for Nuclear Study of the University of Tokyo, is the only place in the world to produce sufficient amounts of 78Ni [13]. Here, 238U particles are accelerated by four coupled cyclotrons up to 70% of the speed of light (corresponding to an energy of 345 MeV per nucleon) to induce in-flight fission reactions. During our 6-day experiment, the average intensity of the primary 238U beam was 7.5 횞 1010 particles per second.


Fig. 2: Schematic layout of the experiment. The final two cyclotron stages, IRC and SRC, of the RIBF along with the BigRIPS and ZeroDegree fragment separators are shown. In the inset, a schematic picture of MINOS, the 10 cm-thick liquid hydrogen secondary target system with a vertex reconstruction system, and DALI2, the gamma-ray array, are illustrated. The blue and red arrows show the secondary beam from BigRIPS and the reaction residue heading to the ZeroDegree spectrometer, respectively. Protons recoiling from the target penetrating into the TPC are shown as green arrows in the figure. The protons ionize the gas in the TPC chamber along their tracks. An electric field in the chamber was applied to collect the drifting electrons induced along the tracks with a certain drift velocity.

Figure 2 displays a schematic view of the experimental setup. After the acceleration process, including the final two cyclotron stages IRC (intermediate stage ring cyclotron) and SRC (superconducting ring cyclotron), a 3-mm-thick beryllium production target was placed at the F0 focus to produce fission fragments and followed by the BigRIPS in-flight separator to identify those fragments [14, 15]. In front of the second spectrometer, ZeroDegree, the 10-cm thick liquid hydrogen target system MINOS (Magic Numbers Off Stability) [16], and the gamma-ray detector array DALI2 (Detector Array for Low Intensity radiation 2) [17] were placed at F8 (illustration in Fig. 2 and picture in Fig. 3) to populate excited states of 78Ni by one- and two-proton knockout reactions. This required the identification of 79Cu and 80Zn with BigRIPS. ZeroDegree identified reaction products exiting MINOS, in particular 78Ni.

Every particle transmitted by the spectrometers was identified by measuring their momentum, energy loss in gas detectors, and the velocity [15]. Figure 4 shows such particle-identification (PID) plots of the incoming and outgoing particles of MINOS. In order to analyze excited states of 78Ni, only the gamma-rays observed with DALI2, with the condition of 78Ni identified ZeroDegree, were analyzed.

Doppler-shift correction

As the 78Ni particles traveled at about 60% of the speed of light when emitting gamma-rays, it was necessary to correct for Doppler shift effects to determine the energies of the excited states [18]. To diminish the Doppler broadening of the gamma-ray spectra, DALI2 consisted of 186 scintillator boxes to resolve the gamma-ray emission angle of the reaction residues. In addition, MINOS contained a time projection chamber (TPC) to reconstruct the vertex position of every knockout reaction by tracking the knocked-out protons [16, 19].


Fig. 3: The liquid hydrogen target system, MINOS, and the gamma-ray detector array, DALI2, as seen from downstream.


Fig. 4: Particle identification (PID) plots of the radioactive beam accepted by BigRIPS and ZeroDegree. In the left panel, the PID plot obtained by BigRIPS is plotted, where events corresponding to 79Cu (red ellipse) and 80Zn (red dashed ellipse) are indicated. In the right panel, the PID plot of the ZeroDegree spectrometer is shown. Events corresponding to 78Ni are enclosed by the red circle.


Fig. 5: Doppler corrected gamma-ray spectra of 78Ni obtained from one-proton (top), and two-proton knockout reactions (bottom). To minimize events in which gamma-rays interacted with many detectors at the same time, constraints on the number of the detected hits, M, have been applied. The light-blue and dashed-blue lines are the simulated response functions for respective peaks and a double exponential background. Their sums for respective reactions are drawn with magenta lines.

Gamma-ray spectra

The Doppler-corrected gamma-ray spectra of 78Ni for the respective reaction channels from 79Cu and 80Zn are shown in Fig. 5. Limitations on the energy resolution and the numbers of observed events are reflected by the error bars of the obtained energy spectra. Statistical methods were applied to determine the observed gamma-ray transitions. The energy and intensity of each transition were deduced by a maximum likelihood estimation acquired by fitting the response functions of DALI2, which were obtained by the Monte Carlo based simulation toolkit Geant4 [20]. Significance levels for the existence of each peak were assessed by a likelihood ratio. In the spectrum of the one-proton knockout reaction, 79Cu(p,2p)78Ni, the 2,600-keV transition, which was the most intense peak after correcting the detection efficiency of DALI2, was evaluated as the transition from the first excited 2+ state to the ground 0+ state. At the same time, all other lower-energy transitions, which had weaker intensities, were evaluated as decaying to the first 2+ state. The large value of 2,600 keV for the 2+ state is the first direct evidence for the preservation of both magic numbers in 78Ni.

Unexpected gamma-ray transitions
Our findings for the two-proton knockout reaction, 80Zn(p,3p)78Ni, were much different. Most striking was the vast discrepancy in energy of the most intense (after efficiency correction) peak, 2,600 keV and 2,910 keV in the respective reactions. This observation leads to two consequences: First, the population of the states identified in the one-proton knockout spectrum were all small in the two-proton knockout spectrum. Second, the 2,910-keV transition, which was tentatively assigned as a second 2+ state, decays directly to the ground state, but not through the 2,600-keV 2+ state. This outcome was not anticipated prior the measurement, thus requiring additional theoretical studies discussed in the following section.

Two shapes coexist in one nucleus

Experimentally, two important results were obtained: the 2600-keV and 2900-keV transitions decay directly to the ground state in the respective reaction channels. As summarized in the left panel of Figure 6, the agreement between the experimentally measured and the theoretically predicted first 2+ excitation energy values along the nickel isotopic chain, showing a sudden increase at 78Ni with neutron number of 50, reinforces the preservation of the doubly shell closure in this isotope. This marks the first important result.

The 2,910-keV state has been interpreted through several theoretical approaches. Since no unified theory to describe such a quantum many-body system confined by a strong interaction exists, theoretical models rely on assumptions and simplifications. Thus, it is essential to test their validity and to depict the properties of the nuclei. The right panel of Figure 6 illustrates the energy levels of 78Ni deduced by several theoretical predictions confronted with our experimental results. Only the LSSM (large-scale shell-model) calculation [11] and the MCSM (Monte Carlo shell-model) calculation, developed based on Ref. [8], could reproduce the near degeneracy of the two 2+ states at 2.6 and 2.9 MeV, while the other frameworks, CC (coupled cluster) [21], IM-SRG (in-medium similarity renormalization group) [22], and QRPA (quasiparticle random-phase approximation) [23], could not replicate the observed phenomenon.


Fig. 6: Systematics of experimental and theoretical 2+ excitation energies of the chain of nickel isotopes (left panel). A detailed comparison between the experimental levels from this work and theoretical calculations is provided on the right panel. While the states with solid lines in the predictions represent the spherical-shaped states of nuclei, the dashed lines correspond to states with large deformation, in this case, prolate spheroids, or cigar-shapes.

The essential difference between the former two and the latter three models is the occurrence of competing nuclear shapes at low energies. In the latter three models, shapes are spherical at low excitation energies, whereas the first two models can treat emerging deformation. In fact, LSSM and MCSM indicate the coexistence of both spherical and prolate-deformed states in the same nucleus. In particular, these two 2+ states have different shapes, one spherical and the other prolate deformed, competing with each other at similar excitation energies. Though the concept of a doubly magic nucleus is primarily and commonly interpreted as a rigid spherical body, this finding demonstrates the variety of nuclear structures in neutron-rich nuclei. Furthermore, both LSSM and MCSM predict a collapse of the neutron magic number 50 for more neutron rich isotones "below'' 78Ni [4]. This indication of the disappearance of magic numbers will be tested and confirmed by further studies.

Conclusion and outlook

The rearrangement of nuclear magic numbers in very neutron-rich nuclei is a hot topic in the field of nuclear physics. Our study investigated excited states of the isotope 78Ni and provided the first direct spectroscopic evidence for the double shell-closure of this very neutron-rich system. The combination of a high-intensity RI (radioactive isotope) beam at the RIBF, RIKEN; the newly implemented sophisticated thick liquid hydrogen system equipped with a vertex reconstruction system; and a high-efficiency, scintillator-based gamma-ray detector array was employed to observe the excited states of 78Ni. While the results support the double shell-closure of 78Ni, they also yield the possibility for a quenching of these shell-gaps beyond this anchor point nucleus. This region is a possible pathway for the early stage of the r-process, which is the process that generates most heavy elements in the universe beyond iron. Hence, the indication of a quenched neutron shell closure will enhance and improve our understanding of nucleosynthesis.

Acknowledgements: We thank the staff of the RIKEN Nishina Center accelerator complex for providing a stable and high-intensity uranium beam and the BigRIPS team for the smooth operation of the secondary beams. The development of MINOS (Magic Numbers Off Stability) and the core MINOS team have been supported by the European Research Council (ERC) through ERC grant number MINOS- 258567. The MCSM (Monte Carlo shell-model) calculations were performed on the K computer at RIKEN Advanced Institute for Computational Science (AICS) (hp160211, hp170230, hp180179) under 'Priority Issue on post-K computer' (Elucidation of the Fundamental Laws and Evolution of the Universe) and the Joint Institute for Computational Fundamental Science (JICFuS) of MEXT (Ministry of Education, Culture, Sports, Science and Technology), Japan. Taniuchi was supported by the JSPS (Japan Society for the Promotion of Science) Grant-in-Aid for JSPS Research Fellows JP14J08718 and UK STFC (Science and Technology Facilities Council) under contract number ST/P003885/1. This work was supported by several areas of funding and fellowships, including JSPS long-term fellowship L-13520; the IPA (International Program Associate) program at the RIKEN Nishina Center; the National Research Council of Canada and the Natural Sciences and Engineering Research Council of Canada (NSERC); the European Research Council (ERC) through grant number 307986 STRONGINT; the Deutsche Forschungsgemeinschaft (DFG) under grant SFB 1245 and the Cluster of Excellence PRISMA; the Federal Ministry of Education and Research of Germany (BMBF) under contract number 05P18RDFN1, 05P15RDNF1 and 05P12RDNF8; Grant-in-Aid for Scientific Research JP18K03639 and JP16K05352; Ministry of Economy and Competitiveness (Mineco, Spain) grants FPA2014-57916;Severo Ochoa Program SEV-2016-0597; Ministry of Science and Technology (MOST, Vietnam) through the Physics Development Program grant 횖T횖LCN.25/18; and the Economic Development and Innovation Operative Programme (GINOP, Hungary)-2.3.3-15-2016-00034 project.


Fig. 7: Talented collaborators in the Experimental hall.


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Ryo Taniuchi is a postdoctoral research associate at the Department of Physics, University of York, and a visiting scientist at the RIKEN Nishina Center for Accelerator-Based Science. He received his BS, MS, and PhD in physics from the University of Tokyo in 2012, 2014, and 2019, respectively. He joined Prof. Sakurai's group at RIKEN in 2012 as a student trainee and he became a research associate in 2018.

Pieter Doornenbal is a senior scientist of the RIKEN Nishina Center for Accelerator-Based Science. He obtained his PhD in 2007 at the University of Cologne, for which he studied the structure of the proton-rich calcium isotope 36Ca. After receiving his PhD, he became a postdoctoral fellow of the Japanese Society for the Promotion of Science, which was followed by a position as a Foreign Postdoctoral Researcher at RIKEN. In 2012, he became a staff member at the Nishina Center.

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