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REVIEW 1 major objections 4 minor 89 references

Reduction in nuclear size and quadrupole deformation of high-spin isomers of 127,129In

T0 review · 1 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Collinear laser spectroscopy finds that the fully aligned 23/2− isomer of 129In has a smaller charge radius and quadrupole moment than its 9/2+ ground state, a result no single nuclear model consistently reproduces.

desk verdict The charge-radius result for 129In is solid and new, but the quadrupole-deformation reduction rests on a rotor assumption the paper never tests. read the letter →

arxiv 2505.14977 v1 pith:ZUVY7IAZ submitted 2025-05-20 nucl-ex nucl-thphysics.atom-ph

A.R. Vernon , C.L. Binnersley , R.F. Garcia Ruiz , K.M. Lynch , T. Miyagi , J. Billowes , M.L. Bissell , T.E. Cocolios
show 24 more authors
J.P. Delaroche J. Dobaczewski M. Dupuis K.T. Flanagan W. Gins M. Girod G. Georgiev R.P. de Groote J.D. Holt J. Hustings Á. Koszorús D. Leimbach J. Libert W. Nazarewicz G. Neyens N. Pillet P.-G. Reinhard S. Rothe B.K. Sahoo S.R. Stroberg S.G. Wilkins X.F. Yang Z.Y. Xu D.T. Yordanov
This is my paper
classification nucl-exnucl-thphysics.atom-ph PACS 21.10.Ft21.10.Ky27.60.+j
keywords laserspectroscopynuclearchargeradiihigh-spinisomersindiumisotopesquadrupolemomentsisomershiftdeformationshellclosure
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 collinear laser spectroscopy of the neutron-rich indium isotopes 127In and 129In and their high-spin isomers, extracting changes in charge radius and electromagnetic moments from hyperfine spectra. The central result is that the fully aligned Iπ = 23/2− isomer of 129In has a mean-squared charge radius smaller by −0.0512(17)[9] fm² and an intrinsic quadrupole moment reduced from 893(24) to 768(41) mb relative to the 9/2+ ground state. This provides simultaneous measurements of charge radius and moments for a high-spin multi-quasiparticle isomer near the doubly magic 132Sn core. A similar reduction is not observed for the 127In isomer, and none of the three families of nuclear-structure calculations consistently reproduces the data.

What carries the argument

The measurement chain is: hyperfine spectra from collinear resonance ionization spectroscopy give magnetic ($A$) and quadrupole ($B$) hyperfine constants and isomer shifts; atomic field-shift and mass-shift constants convert the isomer shift into $\delta\langle r^2\rangle$; the ratio $B_{\mathrm{hf}}/Q_S$ from relativistic coupled-cluster theory converts $B$ into the spectroscopic quadrupole moment $Q_S$; and the strong-coupling formula $Q_0=\frac{(I+1)(2I+3)}{I(2I-1)}Q_S$ converts $Q_S$ into the intrinsic quadrupole moment. The state of interest is the maximally aligned 23/2− three-hole configuration in 129In, a proton $g_{9/2}$ hole plus neutron $d_{3/2}$ and $h_{11/2}$ holes, whose simple structure is meant to isolate the effect of full spin alignment. These outputs are compared with three complementary theoretical frameworks: valence-space in-medium similarity renormalization group, multiconfiguration self-consistent field, and energy-density-functional theory.

What would settle it

Measure the E2 transition strength connecting the 23/2− isomer of 129In to lower states (for example by Coulomb excitation or γ-ray timing) to extract the intrinsic quadrupole moment without the strong-coupling conversion, and compare it with the ground-state value of 893(24) mb; if it matches that value rather than 768(41) mb, the claimed deformation reduction is an artifact of the rotor assumption.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that forming the maximally aligned three-hole configuration in 129In—a proton $g_{9/2}$ hole plus neutron $d_{3/2}$ and $h_{11/2}$ holes—makes the nucleus smaller and less deformed than its ground state. The isomer shift gives $\delta\langle r^2\rangle_{g,m} = -0.0512(17)[9]\,\mathrm{fm}^2$, and the quadrupole hyperfine constant gives a spectroscopic quadrupole moment of 598(32)[4] mb, corresponding through the strong-coupling formula to $Q_0 = 768(41)$ mb against 893(24) mb in the ground state. For 127In, the measured isomer shift is about three times smaller, and the spin assignment (21/2− versus 23/2−) remains open, with magnetic-moment comparisons mildly favoring 23/2−. The data also show that the charge-radius reduction cannot be fully explained by reduced quadrupole collectivity alone, since models with similar $Q_0$ reductions predict different radius shifts, and no single calculation reproduces the isomeric radii and moments simultaneously.

Load-bearing premise

The quadrupole-deformation part of the claim rests on converting the measured spectroscopic quadrupole moment to an intrinsic moment with the strong-coupling rotor formula, which assumes these soft, near-spherical isomers behave as rigid axially symmetric rotors.

Editorial extensions

If this is right

  • For 129In, the fully aligned 23/2− isomer has a charge-radius shift of −0.0512(17)[9] fm², about three times larger than in 127In and comparable to the isotopic change between the 127In and 129In ground states.
  • The intrinsic quadrupole moment of 129mIn is 768(41) mb versus 893(24) mb for the ground state, so full alignment reduces the isomer's quadrupole deformation.
  • Because models with similar $Q_0$ reductions predict different radius shifts, the charge-radius reduction cannot be attributed solely to a shape change; pairing-blocking and gradient surface terms must play a role.
  • No single nuclear-structure method (valence-space IMSRG, multiconfiguration self-consistent field, or DFT) consistently reproduces both isomeric charge radii and electromagnetic moments; the first two underestimate quadrupole moments, and only one tested functional captures the magnitude of the 129In radius reduction.
  • The measured magnetic moments favor the Iπ = 23/2− assignment for 127mIn, but the isomer shift changes little between the two spin assumptions, leaving the assignment open.

Reading between the lines

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

  • If the 129In result survives a model-independent deformation probe, it would establish full angular-momentum alignment as a mechanism for shrinking the nuclear volume near a doubly magic core, giving a sharper test of pairing-blocking and of gradient terms in energy functionals.
  • The same technique applied to high-spin isomers near 56Ni, 100Sn, or 208Pb could show whether the effect is specific to N = 80 or a general feature of maximally aligned configurations.
  • Because the strong-coupling $Q_0$ conversion is questionable for soft nuclei, the true uncertainty on the 129In deformation reduction may exceed the quoted 41 mb; a direct measurement of the isomer's $B(E2)$ strength would settle this.
  • The spin ambiguity of 127mIn could be resolved by a spin-independent probe of its quadrupole moment or by a more precise g-factor measurement; the current data only mildly favor 23/2−.
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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

1 major / 4 minor

Summary. The manuscript reports collinear laser spectroscopy measurements of the high-spin isomers of 127In and 129In, extracting changes in mean-squared charge radii, magnetic dipole moments, and electric quadrupole moments relative to the ground states. The central experimental finding is a significant reduction of the mean-squared charge radius for the 23/2- isomer of 129In, with a smaller effect for 127In. The paper also extracts intrinsic quadrupole moments Q0 from the measured spectroscopic moments QS using the strong-coupling rotor formula, and compares all results with three families of nuclear structure calculations (VS-IMSRG, MPMH/DFT, and several DFT functionals).

Significance. This is a technically demanding measurement that provides the first charge-radius and electromagnetic-moment data for high-spin multi-quasiparticle isomers near 132Sn. The charge-radius reduction in 129In is robust: it is consistently observed in two independent atomic transitions, with the atomic field- and mass-shift factors taken from independent prior calculations, and the underlying raw data are openly available. The comparison against multiple ab initio and phenomenological models is valuable and shows a clear theoretical spread, giving the community a sharp new benchmark. The main limitation is that the claimed reduction in the intrinsic quadrupole moment, a headline conclusion, rests entirely on the strong-coupling rotor conversion of the measured spectroscopic moments; the measured QS actually increases in the isomer, so the Q0 reduction is produced by the I-dependent conversion factor. This model dependence needs to be acknowledged or validated before the quadrupole-deformation part of the claim can be considered an experimental observation.

major comments (1)
  1. [Discussion, Table II] The intrinsic quadrupole moments Q0 in Table II are obtained from the measured spectroscopic moments QS using the rigid-rotor, strong-coupling formula Q0 = (I+1)(2I+3)/(I(2I-1)) QS, cited to Ref. [54]. For 129In, QS increases from 487(13) mb in the 9/2+ ground state to 598(32) mb in the 23/2- isomer, while Q0 decreases from 893(24) mb to 768(41) mb because the conversion factor changes from 1.833 to 1.285 between I = 9/2 and I = 23/2. The manuscript states this conversion in one sentence without testing the rotor assumption, and the Supplemental Material reports that constrained HFB calculations show 'axial softness around sphericity with a small intrinsic prolate deformation' for both 127In and 129In ground states. For such soft, near-spherical nuclei, K is not rigorously a good quantum number and the strong-coupling formula need not be valid; if it is not, the reported ~14% reduction in Q0 is an artifact of the I-dependent conversion rather than a measured property. Because the abstract and conclusions present the reduction of the intrinsic quadrupole moment as an observed fact, the authors should either justify the strong-coupling conversion for these states (for example, by using the quadrupole sum rule from the IMSRG or HF calculations to show a stable intrinsic deformation) or explicitly separate the model-dependent Q0 from the directly measured QS and qualify the wording in the abstract and conclusions.
minor comments (4)
  1. [Table I] In Table I, the uncertainties in parentheses and square brackets are labeled as statistical and atomic-theory, respectively, but the text does not specify how these two components are combined when reporting the weighted averages; please state the combination rule.
  2. [Abstract] The abstract states that the high-spin isomers have 'nuclear spin suggested to be I >= 21/2', but the body of the paper adopts I = 23/2 for 129In and considers both 21/2 and 23/2 for 127In; this ambiguity is relevant to the interpretation of Q0 and should be mentioned in the abstract or the spin assignment explicitly stated.
  3. [Fig. 1 caption] In Fig. 1, the experimental values are described by 'vertical lines' with a 'shaded area' for the uncertainty, but the caption does not explain what the vertical lines represent; please clarify the graphical elements.
  4. [Discussion near Fig. 2] The sentence 'A similar structure of the ground states in the neighboring isotopes will partially cancel systematic uncertainties in their charge radius differences' is unclear; it could be rephrased to specify which systematic uncertainties are meant and how the cancellation occurs.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the isomer charge radii and moments are extracted with independent atomic factors, and the theoretical comparisons are unadjusted benchmarks against new data.

full rationale

The derivation chain is self-contained. The charge-radius changes are obtained from measured hyperfine isomer shifts via Eq. (1) using field- and mass-shift constants F and K_MS taken from independent atomic calculations (Refs. [20,26]), which are not fitted to the 127,129In isomer data. The spectroscopic quadrupole moments follow from measured Bhf values via Eq. (2) with the atomic factor Bhf/QS=576(4) MHz/b from relativistic coupled-cluster calculations (Refs. [19,31]); again, this factor is an independent atomic result and does not incorporate the new nuclear observables. The theoretical predictions from VS-IMSRG, MPMH, and DFT are genuine benchmarks: the paper states that no effective charges or effective g-factors were adjusted, and the models are compared with, not fitted to, the new isomer data. The conversion from spectroscopic to intrinsic quadrupole moment using Q0 = [(I+1)(2I+3)]/[I(2I-1)] QS is an explicit strong-coupling assumption, not a hidden fit or a fitted parameter renamed as a prediction; it can be debated on physical grounds, but it does not make the extraction circular. No load-bearing uniqueness result is imported from the authors' prior work, and no ansatz is smuggled in via self-citation. The self-citations that appear are to atomic calculations and previous ground-state measurements that are independent of the new isomer data and therefore do not raise the circularity score.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The paper's experimental extraction introduces no new fitted constants; it relies on atomic-structure factors and spin assignments from prior literature, plus a model formula for Q0. The only hand-adjusted model parameter mentioned is the UNEDF1 Landau parameter g'_0, which is not tuned to the new isomer data.

free parameters (1)
  • UNEDF1 Landau parameter g'_0 = Adjusted to reproduce the magnetic moment of 131In in Ref. [19]; value not quoted in this paper
    Mentioned in the Discussion as the adjustment that lets HF calculations reproduce magnetic moments. It is not fitted to the new isomer data and does not affect the charge-radius extraction.
assumptions (4)
  • domain assumption The field-shift and mass-shift factors F and K_MS from Refs. [20,26] accurately convert measured isomer and isotope shifts to changes in mean-squared charge radii via Eq. (1).
    Load-bearing for all delta<r2> values; uncertainties from atomic theory are quoted in square brackets in Table I, but the factors themselves are not independently re-derived in this paper.
  • domain assumption The strong-coupling formula Q0 = ((I+1)(2I+3))/(I(2I-1)) Q_S applies to these near-spherical, soft isomers.
    Used in Table II to convert spectroscopic quadrupole moments to intrinsic quadrupole moments; the paper labels these values as estimated.
  • domain assumption The previously reported spin and configuration assignments for 129mIn (Ipi=23/2-) and the candidate assignments for 127mIn are correct.
    Spins are taken from beta-gamma coincidence studies [21,27-29]; the interpretation of the 'fully aligned' structure depends on these assignments.
  • domain assumption The differential hyperfine anomaly is negligible within the quoted uncertainties.
    Eq. (3) omits delta with the justification that it is smaller than the experimental uncertainty.

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Cite this review

Pith. "Pith review of Reduction in nuclear size and quadrupole deformation of high-spin isomers of 127,129In." pith.science (2026). https://pith.science/paper/ZUVY7IAZ

@misc{pith2026250514977,
  author       = {Pith},
  title        = {Pith review of: Reduction in nuclear size and quadrupole deformation of high-spin isomers of 127,129In},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZUVY7IAZ}},
  note         = {Machine review of arXiv:2505.14977}
}
read the original abstract

We employed laser spectroscopy of atomic transitions to measure the nuclear charge radii and electromagnetic properties of the high-spin isomeric states in neutron-rich indium isotopes (Z = 49) near the closed proton and neutron shells at Z = 50 and N = 82. Our data reveal a reduction in the nuclear charge radius and intrinsic quadrupole moment when protons and neutrons are fully aligned in 129In(N = 80), to form the high spin isomer. Such a reduction is not observed in 127In(N = 78), where more complex configurations can be formed by the existence of four neutron-holes. These observations are not consistently described by nuclear theory.

Figures

Figures reproduced from arXiv: 2505.14977 by the authors.

Figure 1
Figure 1. FIG. 1. State-dependent charge radii of the neutron-rich [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Electromagnetic moments of the ground state and [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Hyperfine spectra obtained using the 5p [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Theoretical change in charge radii values (mark [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 4
Figure 4. Figure 4: FIG. 4. Hyperfine spectra obtained using the 5p [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Magnetic moments and (b) intrinsic quadrupole [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

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