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REVIEW 3 major objections 5 minor 62 references

Spectroscopy of $^{52}$K

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

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Pith's one-line read First spectroscopy of potassium-52 finds a 2− ground state and single-particle excitations at 293, 536, and 1076 keV.

desk verdict First spectroscopy of 52K with a clean level scheme and honest theory comparison, but the Jπ assignments partly lean on model ordering and the 536-keV 0− is tentative despite the conclusions. read the letter →

arxiv 2412.03602 v1 pith:WVP3FODM submitted 2024-12-03 nucl-ex

M. Enciu , A. Obertelli , P. Doornenbal , M. Heinz , T. Miyagi , F. Nowacki , K. Ogata , A. Poves
show 73 more authors
A. Schwenk K. Yoshida N.L. Achouri H. Baba F. Browne D. Calvet F. Château S. Chen N. Chiga A. Corsi M.L. Cortés A. Delbart J.-M. Gheller A. Giganon A. Gillibert C. Hilaire T. Isobe T. Kobayashi Y. Kubota V. Lapoux H.N. Liu T. Motobayashi I. Murray H. Otsu V. Panin N. Paul W. Rodriguez H. Sakurai M. Sasano D. Steppenbeck L. Stuhl Y.L. Sun Y. Togano T. Uesaka K. Wimmer K. Yoneda O. Aktas T. Aumann L.X. Chung F. Flavigny S. Franchoo I. Gašparić R.-B. Gerst J. Gibelin K.I. Hahn D. Kim Y. Kondo P. Koseoglou J. Lee C. Lehr P.J. Li B.D. Linh T. Lokotko M. MacCormick K. Moschner T. Nakamura S.Y. Park D. Rossi E. Sahin P.-A. Söderström D. Sohler S. Takeuchi H. Toernqvist V. Vaquero V. Wagner S. Wang V. Werner X. Xu H. Yamada D. Yan Z. Yang M. Yasuda L. Zanetti
This is my paper · ORCID
classification nucl-ex
keywords potassium-52knockoutreactionsgamma-rayspectroscopymomentumdistributionsspin-parityassignmentshellmodelVS-IMSRGN=32closure
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

The paper reports the first spectroscopy of $^{52}$K, an odd-odd nucleus with one proton below the $Z=20$ shell closure and one neutron outside the $N=32$, $34$ closures. Using one-proton and one-neutron knockout at about 230 MeV per nucleon, it builds the level scheme from $\gamma$-ray coincidences and assigns spins and parities by comparing exclusive momentum distributions with distorted-wave impulse approximation (DWIA) calculations. It concludes that $^{52}$K has a $2^-$ ground state and excited states at $293(3)$ keV ($1^-$), $536(6)$ keV ($0^-$), and $1076(14)$ keV (listed as $1^-$ in the body and Table II, although the conclusion says $1/2^-$, an apparent typo). These four states are interpreted as one-particle–one-hole configurations: a $p_{1/2}$ neutron coupled to either a $d_{3/2}$ or an $s_{1/2}$ proton hole. If this is right, the proton $s_{1/2}$ and $d_{3/2}$ orbitals keep their normal ordering near $N=32,34$, with an energy gap close to that of the odd-mass neighbors $^{51,53}$K.

What carries the argument

The load-bearing tool is the exclusive momentum distribution measured for each final state after $(p,2p)$ knockout, compared with DWIA calculations: the width of the parallel-momentum distribution identifies whether the removed proton came from a $d_{3/2}$ orbital or an $s_{1/2}$ orbital. That orbital tag is combined with the angular-momentum coupling identity $p_{1/2}\otimes d_{3/2}\to 2^-,1^-$ and $p_{1/2}\otimes s_{1/2}\to 0^-,1^-$ to propose the four states. Since the momentum data cannot fix the order of the two members of each doublet, the ordering is taken from the theoretical spectra (SDPF-Umod and VS-IMSRG), and the exclusive cross-section ratios serve as a consistency check on the single-particle interpretation.

What would settle it

Measure the 536-keV state's momentum distribution with enough statistics to distinguish $s_{1/2}$ from $d_{3/2}$ removal, or directly determine the ground-state spin through $\gamma$-ray angular correlations or a transfer reaction. Finding $J\neq 2$ for the ground state, or $J^\pi\neq 0^-$ for the 536-keV state, would falsify the proposed level scheme and the normal-ordering conclusion.

Watch

Extended reading notes

Core claim

The central discovery is the first complete low-lying level scheme of $^{52}$K: a $2^-$ ground state, a $1^-$ state at $293(3)$ keV, a $0^-$ state at $536(6)$ keV, and a fourth state at $1076(14)$ keV assigned $1^-$ in the body (the conclusion writes $1/2^-$, which the stated coupling scheme cannot produce). The assignments come from matching the parallel- and perpendicular-momentum distributions of the knockout residue to DWIA calculations, which identify the removed proton as $d_{3/2}$ for the ground and 293-keV states and $s_{1/2}$ for the 536- and 1076-keV states. Because the momentum width tags the orbital but not the total angular momentum $J$, the ordering of the $2^-$/$1^-$ doublet and the tentative $0^-$ assignment are guided by the level ordering from the SDPF-Umod shell-model Hamiltonian and from VS-IMSRG ab initio calculations. The single-particle nature of all four states is supported by exclusive cross sections whose relative values match theory, and whose overall quenching factor of 0.66 agrees with $(e,e'p)$ knockout results.

Load-bearing premise

The assignments assume the theoretical ordering of the two states in each proton-hole–neutron doublet is correct, because the measured momentum distributions identify only which proton orbital was removed, not the total angular momentum of the final state; the 536-keV state's $0^-$ label has no momentum constraint at all.

Editorial extensions

If this is right

  • The $s_{1/2}$ and $d_{3/2}$ proton orbitals keep their normal ordering in $^{52}$K, with a gap similar to $^{51}$K and $^{53}$K, so the inversion observed in $^{47,49}$K does not extend to $N=33$.
  • The four low-lying states are essentially single-particle 1p-1h excitations, making $^{52}$K a clean benchmark for shell-model and ab initio methods near the $N=32$ and $N=34$ closures.
  • VS-IMSRG(3) corrections move the predicted ground state from $0^-$ to $2^-$, matching experiment, so fully converged three-body normal-ordered calculations should settle the remaining $0^-$/$2^-$ ordering sensitivity.
  • The measured quenching factor $\sigma_{\rm exp}/\sigma_{\rm th}=0.66$ is consistent with $(e,e'p)$ knockout on stable nuclei, supporting the single-particle cross-section interpretation.
  • The $(p,pn)$ channel feeds mainly the ground and 293-keV states, confirming that those states share the proton configuration of the $^{53}$K projectile.

Reading between the lines

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

  • If the normal $s_{1/2}/d_{3/2}$ ordering holds, measuring heavier potassium isotopes such as $^{55}$K could map where monopole drift reverses the ordering again, using the K chain as a one-proton-hole laboratory.
  • The 536-keV $0^-$ assignment rests entirely on theory because its momentum distribution could not be analyzed; a higher-statistics measurement of that state's momentum distribution or a transfer reaction would be the most direct test.
  • The conclusion's $1/2^-$ for the 1076-keV state is internally inconsistent with the body's $1^-$ assignment and with the stated $p_{1/2}\otimes s_{1/2}$ coupling, which only permits $0^-$ and $1^-$; it should be read as a typographical slip.
  • The close agreement between the empirical SDPF-Umod interaction and the ab initio VS-IMSRG spectrum suggests that ab initio methods are now precise enough at $A\sim50$ to guide spin-parity assignments when knockout momentum distributions are ambiguous.
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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 paper reports the first spectroscopy of 52K, produced at the RIKEN RIBF via (p,2p) knockout from a 53Ca beam and (p,pn) knockout from a 53K beam on the MINOS liquid-hydrogen target, with de-excitation gamma rays measured in DALI2+ and fragments identified in SAMURAI. The gamma-ray singles and coincidence analysis establishes three transitions at 243(5), 293(3), and 540(13) keV forming a 1076 -> 536 -> 293 -> 0 keV cascade, and hence excited states at 293(3), 536(6), and 1076(14) keV. Exclusive momentum distributions analyzed with DWIA identify the knocked-out proton orbital as d3/2 for the ground and 293-keV states and s1/2 for the 1076-keV state; the 536-keV state is too weak for a momentum analysis. Guided by SDPF-Umod shell-model and VS-IMSRG calculations, and by comparison of exclusive cross sections, the states are assigned 2-, 1-, (0-), and 1-_2 (second 1-), leading to the conclusion that the low-lying spectrum of 52K consists of one-particle one-hole states with normal d3/2-below-s1/2 proton orbital ordering.

Significance. If correct, this measurement provides the first spectroscopic information on 52K, a nucleus situated between the N=32 and N=34 shell closures and the Z=20 closure, and offers a direct benchmark for the proton d3/2-s1/2 single-particle splitting in the potassium isotopic chain. The strengths of the manuscript are its careful treatment of systematic uncertainties (DALI2+ response benchmarked at the 5% level, explicit error budgets for the cross sections), the self-consistent cascade-based level scheme, and the full tabulation in Table II of experimental cross sections, DWIA single-particle cross sections, and shell-model C2S values, which allows the reader to reconstruct the assignment logic independently. The authors also deserve credit for labeling the 0- assignment as tentative in the body and for disclosing that VS-IMSRG(2) at its converged truncation level prefers a 0- ground state, with the supporting VS-IMSRG(3) result explicitly unconverged.

major comments (3)
  1. [Sec. III.D-III.E, Table II] The momentum distributions determine only the orbital angular momentum of the knocked-out proton; within the p1/2(x)d3/2 doublet (2-/1-) and the p1/2(x)s1/2 doublet (0-/1-_2), the total-J ordering is taken from the SDPF-Umod and the explicitly unconverged VS-IMSRG(3) calculations. The body is transparent about this, but the claim in Sec. III.E that the exclusive cross sections 'further confirm' the spin-parity assignments is never backed by an explicit test of the swapped J orderings, even though Table II contains all numbers needed for such a test: sigma(g.s.)/sigma(293) = 3.21/1.45 = 2.2(4) versus the C2S ratio 2.352/1.303 = 1.8 (the (2J+1) sum-rule limit gives 5/3), while the swapped assignment would predict a ratio of about 0.55, a discrepancy of roughly 4 sigma; likewise sigma(536)/sigma(1076) = 0.38/0.81 = 0.47(16) versus 0.402/1.244 = 0.32, while the swapped assignment would predict about 3.1, excluded at many sigma. I ask that this quantitative comparison be added to Sec. III.E, with the caveat that it is conditional on the SDPF-Umod C2S values, and that the sentence 'It is shown that 52K has a 2- ground state' be made consistent with the demonstrated level of certainty; this matters because the theory guidance alone is ambiguous, with VS-IMSRG(2) predicting a 0- ground state.
  2. [Sec. IV Conclusions; Sec. III.D] The Conclusions state 'It is shown that 52K has a 2- ground state and three excited states at 293(3) keV (1-), 536(6) keV (0-), and 1076(14) keV', listing the 536-keV state without the tentative qualifier used in Sec. III.D ('it is tentatively assigned Jpi=0-') and in Table II ('(0-)'). Since no momentum distribution exists for this state (Sec. III.B), the Conclusions overstate the certainty of a member of the central claim. The Conclusions should also note that the only fully converged ab initio result reported, VS-IMSRG(2), places the 0- below the 2-, so that the ground-state ordering rests on the shell model and the unconverged VS-IMSRG(3) calculation rather than on a settled ab initio prediction. The qualification and the caveat should be restored in the Conclusions.
  3. [Sec. III.E, Table II] The agreement between experimental and theoretical relative exclusive cross sections is described as 'excellent', but the 1076-keV 1-_2 state shows a measured value of 14(3)% versus 22% (method a) or 25% (method b), a deviation at the 2-3 sigma level, and the comparison for the four states is only marginally acceptable as a whole (roughly chi2/ndf of order 8/3 if the ratios are treated as independent). In addition, the 160-fm uncertainty on the fitted radial parameter for the s1/2 orbital (r0 = 1.416(160) fm) is not propagated into the DWIA single-particle cross sections sigma_sp used to build the theoretical cross sections, and the quoted inclusive quenching factor is 0.66 with the optimum r0 but 1.01 with the Bohr-Mottelson value of 1.27 fm, a factor of 1.5 variation. The spin-parity conclusions rely on the relative cross sections, which are robust to this normalization ambiguity, but the text should either quote sigma_sp with its uncertainty or restrict the 'excellent agreement' claim to the relative pattern and state the normalization ambiguity explicitly.
minor comments (5)
  1. [Sec. IV; Table II] The notation '1-_2' (a subscript 2 on the 1-) for the second 1- state is rendered ambiguously; in the Conclusions it appears as '1- 2', which can be misread as the half-integer '1/2-', an impossible spin for the odd-odd nucleus 52K. Please use an unambiguous notation (for example '1-_2' or 'second 1-') everywhere and verify the final PDF rendering.
  2. [Sec. III.D] The sentence 'The SDPF-Umod interaction reproduces the E(3/2+ - 1/2+) exactly for 51K' uses the wrong parity superscripts; the states in question are 3/2- and 1/2-.
  3. [Sec. III.A] The sentence 'The ratio of the 243-keV and 540-keV transitions in coincidence with the 293-keV transition implies that the 243-keV transition feeds directly the 293-keV transition' is easy to misread; the intended point is that the 293-keV level is fed both by the 243-keV transition from the 536-keV level and directly by the knockout reaction, which is why the 243-keV coincidence yield exceeds the 540-keV one.
  4. [Sec. III.E, Table II] The (p,pn) exclusive yields are listed for the 2-, 1-, and 0- states but not for the 1076-keV state; since the pattern of (p,pn) population is quoted as supporting the level scheme, please state explicitly that the 1076-keV yield is consistent with zero and give an upper limit.
  5. [Fig. 3] In the experimental level scheme in panel (a), please clarify how the color coding applies to the 536-keV level, whose orbital assignment is inferred from the models and the cascade rather than measured from a momentum distribution.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the measured level scheme is independent; the model-guided Jpi assignments are acknowledged extrapolations rather than definitional reductions.

full rationale

The paper's central measurement is the gamma-ray spectrum of 52K: transition energies, coincidence relationships, and level energies at 293(3), 536(6), and 1076(14) keV are extracted directly from data (Section III.A) and are not derived from the theoretical models. The spin-parity assignments are model-guided, but this is a standard inference with the model playing the role of an external hypothesis, not a definitional identity. The momentum distributions identify the knocked-out orbital (d3/2 vs s1/2) from the DWIA shapes, with wrong-orbital curves visually failing (Fig. 4 and Section III.C), so this identification is not forced by a fitted parameter that already encodes the answer. The radial parameter r0 is fitted to the momentum distributions, but the s/d distinction is robust to that fit, and the cross-section comparison is reported for both the fitted r0 and the fixed Bohr-Mottelson value (Table II). The exclusive cross sections use C2S values from SDPF-Umod, the same interaction that also provides the level ordering, so the cross-section agreement is a consistency check of the model rather than an independent confirmation of the J ordering; however, it is not a fit to the 52K data and the model itself is anchored to external measurements of 51,53K cited from the same collaboration. The paper also explicitly flags the limitations that would matter if one wanted to call the assignments forced: the 536-keV state "could not be analyzed" and is "tentatively assigned Jpi=0-" (Section III.D), and the VS-IMSRG(3) calculation is explicitly said to use a model space "insufficient to fully converge the effects of three-body operators" (Section III.D). These caveats are model-dependence and correctness risks, not circular reasoning. The Conclusions state the assignments without repeating the tentative qualifier, which is an overstatement, but the underlying experimental chain is self-contained. No equation or parameter is defined in terms of the claimed result, and no load-bearing argument reduces to a self-citation. Score 0, no significant circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central measurement is a set of gamma-ray energies and coincidence relations, which require no free parameters. The model-dependent part (orbital assignment and spin-parities) relies on two fitted radial parameters in the DWIA analysis and on the theoretical level ordering from SDPF-Umod and VS-IMSRG. No new particles, forces, or conserved quantities are introduced.

free parameters (3)
  • radial parameter r0 for d3/2 proton knockout = 1.549(66) fm
    Fitted to the experimental ground-state momentum distribution in the DWIA analysis (Section III.C).
  • radial parameter r0 for s1/2 proton knockout = 1.416(160) fm
    Fitted to the 1076-keV state momentum distribution in the DWIA analysis (Section III.C).
  • Woods-Saxon diffuseness parameter = 0.67 fm (fixed)
    Adopted from the Bohr-Mottelson parametrization, not fitted; the paper refers to a separate study for sensitivity (Section III.C).
assumptions (4)
  • domain assumption DWIA describes one-nucleon knockout at approximately 230 MeV/nucleon with the Melbourne G-matrix interaction and Franey-Love NN interaction
    Invoked in Section III.C to compute momentum distributions and cross sections; no independent validation against other observables is given in this paper.
  • domain assumption The bound-state wavefunction of the knocked-out proton is a Woods-Saxon potential with adjusted depth and fitted radius
    Section III.C; the shape of the momentum distribution depends on this modeling choice.
  • domain assumption SDPF-Umod shell-model Hamiltonian and VS-IMSRG with the 1.8/2.0(EM) chiral interaction give the correct order and identity of low-lying states
    Section III.D; used to guide spin-parity assignments, especially for the 536-keV state, which has no momentum-distribution constraint.
  • domain assumption Neutrons from neutron evaporation are emitted isotropically and detected with 39(4)% efficiency in NeuLAND and NEBULA
    Section III.A; used to subtract the neutron-evaporation background from the (p,pn) channel.

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Pith. "Pith review of Spectroscopy of $^{52}$K." pith.science (2026). https://pith.science/paper/WVP3FODM

@misc{pith2026241203602,
  author       = {Pith},
  title        = {Pith review of: Spectroscopy of $^52$K},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WVP3FODM}},
  note         = {Machine review of arXiv:2412.03602}
}
abstract

The first spectroscopy of $^{52}$K was investigated via in-beam $\gamma$-ray spectroscopy at the RIKEN Radioactive Isotope Beam Factory after one-proton and one-neutron knockout from $^{53}$Ca and $^{53}$K beams impinging on a 15-cm liquid hydrogen target at $\approx$ 230~MeV/nucleon. The energy level scheme of $^{52}$K was built using single $\gamma$ and $\gamma$-$\gamma$ coincidence spectra. The spins and parities of the excited states were established based on momentum distributions of the fragment after the knockout reaction and based on exclusive cross sections. The results were compared to state-of-the-art shell model calculations with the SDPF-Umod interaction and ab initio IMSRG calculations with chiral effective field theory nucleon-nucleon and three-nucleon forces.

Figures

Figures reproduced from arXiv: 2412.03602 by the authors.

Figure 1
Figure 1. FIG. 1. The particle identification (PID) for the beam in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Doppler-shift-corrected [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The experimental (a) and calculated level scheme [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The momentum distributions of the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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