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REVIEW 3 major objections 5 minor 61 references

Competition of the shell closure and deformations across the doubly magic $^{78}$Ni

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The review argues that recent proton-knockout experiments provide the first experimental evidence that $^{78}$Ni, long assumed rigidly doubly magic, also hosts a deformed band coexisting with its spherical ground state.

desk verdict Solid review of the 78Ni campaign, but the abstract overstates the shape-coexistence evidence that the body itself hedges. read the letter →

arxiv 2412.16972 v1 pith:ODGGUV2S submitted 2024-12-22 nucl-ex nucl-th

Ryo Taniuchi This is my paper · ORCID
classification nucl-exnucl-th PACS 21.10.-k25.40.-h27.50.+j23.20.Lv
keywords 78Nidoublymagicnucleusshapecoexistenceshellclosureprotonknockoutin-beamgamma-rayspectroscopyN=50isotonesevolution
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This review argues that the long-postulated doubly magic nucleus $^{78}$Ni is both a shell closure and a site of shape coexistence. The experimental basis is in-beam gamma-ray spectroscopy after relativistic proton knockout: the first excited $2^+$ state lies at 2.6 MeV, a standard signature of double magicity, while a second $2^+$ state at 2.9 MeV appears in the two-proton knockout channel and is interpreted as the first experimental sign of a deformed band coexisting with the spherical ground state. If this reading is correct, the $Z=28$ and $N=50$ shell gaps survive at the neutron-rich extreme even though deformed configurations are energetically close, and descriptions of very neutron-rich nuclei and r-process nucleosynthesis must include both spherical and deformed degrees of freedom. The review consolidates the experimental results and compares them with large-scale shell-model and first-principles calculations, most of which reproduce the dual-band structure only when neutron orbitals above $N=50$ are included.

What carries the argument

The load-bearing object is the level scheme of $^{78}$Ni: a $0^+$ ground state, a first $2^+$ state at 2.6 MeV, and a second $2^+$ state at 2.9 MeV. Shape coexistence is the mechanism invoked to explain both numbers at once, meaning a spherical ground-state configuration and a deformed (prolate) excited band live in the same nucleus. Experimentally the states are produced by one- and two-proton knockout from a fast secondary beam on a thick liquid hydrogen target with vertex reconstruction, with de-excitation gamma rays detected by a high-efficiency NaI(Tl) array; theoretically the decisive tool is the PFSDG-U large-scale shell-model interaction, which includes the full $pf$ shell for protons and the full $sdg$ shell for neutrons and predicts two close-lying bands. The comparison with models that lack neutron $sdg$ orbitals, and with vibrational-only approaches, is what turns the second $2^+$ state into evidence of coexistence.

What would settle it

A higher-statistics, higher-resolution measurement of the 2.9 MeV peak, using gamma-ray tracking or germanium detectors to obtain angular distributions and gamma-gamma coincidences, would settle the issue: if the peak resolves into two close-lying transitions, or the angular distribution rules out a $2^+$ assignment, the deformed-band assignment fails. A missing-mass experiment that searches for the expected $0^+_2$ band head near 2.9 MeV and does not find it would similarly remove the direct experimental support for coexistence.

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Extended reading notes

Core claim

The review's central claim is that recent proton-knockout experiments provide the first experimental evidence for shape coexistence at $^{78}$Ni and its immediate neighbours. The measured first excited state of $^{78}$Ni sits at 2.6 MeV, confirming the doubly magic character expected from the $Z=28$ proton gap and the $N=50$ neutron gap. The additional $2^+$ state at 2.9 MeV, populated in the two-proton knockout channel, is interpreted as the deformed partner of the spherical ground state; large-scale shell-model calculations with the PFSDG-U interaction and an extended Monte Carlo shell model predict exactly such a low-lying prolate band, while calculations without neutron $sdg$ orbitals do not. The same calculations show the spherical and deformed configurations nearly degenerating in $^{76}$Fe and predict deformed ground states for lighter $N=50$ isotones, marking $^{78}$Ni as the northern edge of the $N=40$ island of inversion. The review also reports that the inclusive proton-knockout cross section to $^{78}$Ni is about five times smaller than for neighbouring isotopes, consistent with a weakly bound but shell-closed core.

Load-bearing premise

The load-bearing assumption is that the 2.9 MeV transition observed in the two-proton knockout channel is a single $2^+$ state belonging to a deformed band; the review does not show an angular distribution or spin-parity analysis, and if the state is an unresolved doublet or has different quantum numbers the experimental case for shape coexistence reduces to theoretical prediction alone.

Editorial extensions

If this is right

  • If the claim is correct, $^{78}$Ni is the first doubly magic nucleus with experimental evidence of shape coexistence, and the $Z=28$ and $N=50$ shell closures persist at the neutron-rich extreme.
  • The $N=40$ island of inversion extends to $N=50$: lighter isotones such as $^{76}$Fe, $^{74}$Cr, $^{72}$Ti, and $^{70}$Ca are predicted to become progressively more deformed, with deformed ground states in the lighter systems.
  • Models that include neutron orbitals above $N=50$ reproduce the two bands, while models restricted to the $pf$ shell or to vibrational degrees of freedom do not, so the observation discriminates between theoretical approaches.
  • The inclusive proton-knockout cross section to $^{78}$Ni is about five times smaller than those of neighbouring isotopes, which the review attributes to the low neutron separation energy and significant feeding of unbound states.
  • Further spectroscopy of $^{79,80}$Ni, $^{77}$Co, and $^{76}$Fe, plus mass and charge-radius measurements, will test whether deformed configurations grow as one moves away from $^{78}$Ni.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the 2.9 MeV state is a genuine deformed $2^+$ member, a $0^+_2$ band head should lie nearby; a dedicated missing-mass or two-neutron transfer search for it would be a direct test that the experiments summarized here do not yet provide.
  • The emphasis on neutron $sdg$ orbitals implies a quantitative prediction: adding neutrons beyond $N=50$ should rapidly increase deformation, so measuring $B(E2)$ values and quadrupole moments in $^{79,80}$Ni would distinguish this picture from one in which the $N=50$ gap simply weakens.
  • The same knockout-plus-gamma technique could be applied to other doubly magic nuclei near the drip line, where deformed intruder bands are predicted but rarely observed, to test whether coexistence of a closed shell and deformation is a general phenomenon.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This manuscript is a review article by R. Taniuchi surveying recent experimental and theoretical studies of the region around the doubly magic nucleus 78Ni. It summarizes the first in-beam gamma-ray spectroscopy campaigns using the MINOS liquid-hydrogen target and DALI2 array, including the spectroscopy of 79Cu and 78Ni via proton-knockout reactions, and it compares the experimental level scheme of 78Ni with large-scale shell-model, Monte Carlo shell-model, coupled-cluster, IM-SRG, 5DCH, and QRPA calculations. The paper's central claim, stated in the abstract, is that proton-knockout reactions have provided the first experimental evidence of shape coexistence at 78Ni and its vicinity, while the body also emphasizes the doubly magic character of 78Ni inferred from E(2+_1) = 2.6 MeV and a candidate second 2+ state at 2.9 MeV.

Significance. If the strong claim were fully supported, the coexistence of a doubly magic spherical ground state with deformed excited configurations in 78Ni would be an important touchstone for shell evolution, for the extension of the N=40 island of inversion, and for r-process nucleosynthesis. The review is valuable as a concise synthesis of a coherent body of recent RIBF results, and it has the strength of bringing together experimental data and multiple theoretical predictions in a single comparison (Fig. 6). It also usefully identifies limitations of current instrumentation, such as the modest resolution of DALI2 and the lack of firm spin-parity assignments for several newly observed transitions. However, the significance of the paper as a review is diminished by the mismatch between the abstract's categorical claim of 'first experimental evidence' for shape coexistence and the more cautious language used in the body.

major comments (3)
  1. [Abstract and Section 2.2] The abstract states that proton-knockout reactions 'have provided the first experimental evidence of shape coexistence at the cornerstone nucleus 78Ni and its vicinity,' but Section 2.2 only says that the 2.9-MeV 2+ state 'suggests the presence of shape coexistence.' The body does not present the spectra, angular distributions, spin-parity analysis, transition strengths, or lifetimes that would be needed to elevate this to 'evidence,' and Section 3.4 explicitly describes the supporting argument as 'indirect.' This overstatement is load-bearing because the claimed first observation of shape coexistence is the central novelty of the review. The abstract should be tempered (e.g., 'evidence consistent with shape coexistence' or 'suggestive evidence') or the body should include a detailed justification of the strong claim.
  2. [Section 2.2 and Figure 6] The interpretation that the 2.9-MeV state is the 2+ member of a deformed band rests on the premise that a second 2+ state in 78Ni can be taken as a shape-coexistence signature. A second 2+ state can also arise from spherical seniority or two-phonon excitations, and the review provides no discriminating observable beyond the excitation energy itself. Because this assumption is the basis for the paper's central shape-coexistence claim, the text should explicitly acknowledge this ambiguity and state what experimental information (e.g., B(E2), lifetime, or a rotational band sequence) would distinguish a deformed bandhead from a spherical intrinsic excitation.
  3. [Section 3.4] The sentence stating that 'the absence of the 2+_2 state in QRPA calculations ... indirectly supports the existence of shape coexistence' is a logical non sequitur. A model's failure to produce a state does not by itself constitute evidence for a particular alternative interpretation; it may simply reflect the model's restricted configuration space. This should be rephrased as a limitation of the QRPA approach rather than as supporting evidence for shape coexistence.
minor comments (5)
  1. [Section 2.2] The energies '2.6 MeV' and '2.9 MeV' are quoted without uncertainties. Since the original data in ref. [26] presumably report uncertainties, these should be included so that the quantitative comparison in Figure 6 is meaningful.
  2. [Figure 6] The experimental level labels in Figure 6 are crowded and the distinction between the 2.60-MeV and 2.91-MeV states is difficult to read; the placement of the 'Sn' label and the 'CCSD' label is also unclear. Please improve the figure's readability and add a legend explaining all labels and lines.
  3. [Section 4.2] The paragraph states that 'highly excited states around 4 MeV were identified' and then that 'three new transitions' were found with spins and parities 'yet to be identified.' Please clarify whether the three transitions are the same states and whether any spin-parity constraints exist.
  4. [Acknowledgment] There is a typographical error: 'On be half of the conference organizers' should read 'On behalf of the conference organizers.'
  5. [Section 3.3] The term 'first-principle calculations' should be 'first-principles calculations'; the same correction applies to the section title and the first sentence of Section 3.3.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the review compiles independent prior measurements and external theory comparisons, with no fitted parameter, definitional reduction, or self-citation chain forcing the central claim.

full rationale

This is a review article that compiles previously published experimental and theoretical results; it performs no new fit, no derivation, and no parameter extraction whose output could be compared with its input. The shape-coexistence claim for 78Ni rests on the 2.9 MeV second 2+ state reported in ref. [26] (Taniuchi et al., Nature 2019), whose first author is the present author; however, that citation is an independent, peer-reviewed measurement with its own raw data (in-beam gamma-ray spectroscopy after (p,2p)/(p,3p) knockout) and is cross-compared with external shell-model calculations from other groups (PFSDG-U, MCSM, CC, IM-SRG, 5DCH, QRPA) that are not derived from the present manuscript. The review does not redefine the experimental quantity in terms of the prediction: E(2+1) = 2.6 MeV and the 2.9 MeV state are quoted as measured results, and the theory curves in Fig. 6 are genuinely predictive comparisons. The abstract's 'first experimental evidence' wording is stronger than the body's 'suggests the presence of shape coexistence,' and the review itself flags the modest resolution of DALI2 as a limitation (Sec. 5), but overstatement and unresolved spin/parity evidence are evidentiary concerns, not circularity. No equation or definition in the paper is shown to be equivalent to its own input, and no fitted parameter is relabeled as a prediction. Therefore no significant circularity is present.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The review introduces no free parameters or invented entities. Its central claims rest on the reliability of the cited experimental data and theoretical models, which are treated as given. The key assumption is the spin-parity assignment of the 2.9 MeV state, which is not established in the review itself.

assumptions (3)
  • domain assumption The quoted experimental results (E(2+1)=2.6 MeV for 78Ni, the 2.9 MeV second 2+ candidate, cross sections, half-lives) are correctly extracted from refs. [26,30,50,53,54].
    The review builds its central narrative on these published measurements and does not reanalyze the raw data.
  • domain assumption Theoretical predictions (PFSDG-U, A3DA-m, LNPS, CCSD(T), IM-SRG, 5DCH, QRPA) reliably describe shape coexistence and shell evolution in this region.
    The review uses the agreement between calculations and data to support the shape-coexistence interpretation; these model spaces and interactions are not derived in the review.
  • ad hoc to paper A second 2+ excited state in 78Ni can be interpreted as the bandhead of a deformed band, indicating shape coexistence.
    This interpretation is the core of the shape-coexistence claim. It is consistent with PFSDG-U calculations but is not directly established by the data (no spin assignment is shown in the review).

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Cite this review

Pith. "Pith review of Competition of the shell closure and deformations across the doubly magic $^{78}$Ni." pith.science (2026). https://pith.science/paper/ODGGUV2S

@misc{pith2026241216972,
  author       = {Pith},
  title        = {Pith review of: Competition of the shell closure and deformations across the doubly magic $^78$Ni},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ODGGUV2S}},
  note         = {Machine review of arXiv:2412.16972}
}
abstract

The properties of the neutron-rich isotope $^{78}$Ni, long postulated to be doubly magic, have been extensively explored through recent experimental and theoretical studies. Confirmations of robust shell closures at $Z=28$ and $N=50$ as well as hints of competing deformations in neighboring isotopes have been obtained. Innovations of a thick liquid hydrogen target system with vertex reconstructions and the in-beam $\gamma$-ray spectroscopy technique have facilitated detailed investigations into the nuclear structure of these extreme systems. Proton knockout reactions conducted at relativistic energies have provided the first experimental evidence of shape coexistence at the cornerstone nucleus $^{78}$Ni and its vicinity. As the nuclear structure around $^{78}$Ni influences the description of very neutron-rich systems and r-process nucleosynthesis, these findings underscore the importance of further investigations. This review encapsulates the recent results concerning the nuclear structure at the vicinity of $^{78}$Ni on both experimental and theoretical aspects. It outlines prospective research directions that could further illuminate this complex and intriguing area of the nuclear chart.

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.