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arxiv: 2606.21269 · v2 · pith:WR44XNUSnew · submitted 2026-06-19 · ⚛️ nucl-ex · nucl-th

Evidence of the Excited X(5)-like Critical-Point Symmetry Structures in 152Sm

S. Basak , S. Rajbanshi , T. Bhattacharjee , D. Kumar , A. Pal , S. S. Alam , A. Saha , A. K. Sikdar
show 18 more authors
J. Nandi Ananya Das Shabir Dar S. Samanta S. Chatterjee R. Raut S. S. Ghugre A. Adhikari Y. Sapkota R. Rahaman A. Gupta A. Bisoi S. Sharma S. Das P. Das U. Datta I. Ray G. Duch\^ene
This is my paper

Pith reviewed 2026-07-03 23:30 UTC · model grok-4.3

classification ⚛️ nucl-ex nucl-th
keywords 152SmX(5) symmetrycritical-point symmetryshape-phase transitioncollective bandsgamma-ray spectroscopyN=90 nucleiB(E2) strengths
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The pith

Higher-lying bands in 152Sm exhibit X(5)-like critical-point symmetry structures.

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

The study maps positive-parity levels in 152Sm with high-statistics gamma-ray spectroscopy after the 150Nd(alpha,2n) reaction. Collective bands on excited 0+ states are extended and their electromagnetic transition strengths are extracted from branching ratios and lifetimes. These data are compared to the X(5) description of the U(5)-SU(3) shape-phase transition. The comparison shows that the higher-lying bands display the same characteristic level spacings and B(E2) values as the known low-lying X(5)-like structures. The results add constraints on how critical-point symmetry appears across multiple configurations in the N=90 region.

Core claim

The observed systematics of the higher-lying bands are found to be consistent with excited collective structures exhibiting X(5)-like characteristics.

What carries the argument

Comparison of measured excitation energies and B(E2) strengths in excited bands to the predictions of the X(5) critical-point model for the first-order U(5)-SU(3) shape-phase transition.

If this is right

  • Critical-point symmetry is realized in excited configurations as well as the ground-state and first excited 0+ bands.
  • The N=90 region shows consistent X(5)-like evolution of collectivity across multiple bands.
  • New experimental constraints are obtained on the appearance of critical-point behavior in finite nuclei.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar excited X(5)-like structures may appear in neighboring N=90 nuclei if the pattern is general.
  • Additional lifetime data on higher states would provide a direct test of the predicted transition strengths.
  • The critical-point description could be tested in other transitional nuclei by extending the same band-by-band comparison.

Load-bearing premise

The measured branching ratios, lifetimes, and level assignments accurately reflect intrinsic collective properties without significant configuration mixing or other perturbations that would invalidate direct comparison to the X(5) predictions.

What would settle it

A measurement of B(E2) ratios or level energies in the higher-lying bands that deviate substantially from the specific numerical values predicted by the X(5) model for excited states.

Figures

Figures reproduced from arXiv: 2606.21269 by A. Adhikari, A. Bisoi, A. Gupta, A. K. Sikdar, Ananya Das, A. Pal, A. Saha, D. Kumar, G. Duch\^ene, I. Ray, J. Nandi, P. Das, R. Rahaman, R. Raut, S. Basak, S. Chatterjee, S. Das, Shabir Dar, S. Rajbanshi, S. S. Alam, S. Samanta, S. S. Ghugre, S. Sharma, T. Bhattacharjee, U. Datta, Y. Sapkota.

Figure 1
Figure 1. Figure 1: The partial level scheme of 152Sm obtained in the present work. The level energies (represented by the magenta colored numbers) and the γ-ray energies are rounded off to the nearest keV. The widths of the arrows are proportional to the intensities of the γ -ray transitions. The newly observed levels and transitions are shown in red while the green and blue colored transitions have been first observed in fu… view at source ↗
Figure 2
Figure 2. Figure 2: Projections from triple γ cube are shown to demonstrate the analysis and observation based on which the new levels were placed in QB4 (left) and QB5 (right) bands. Similar to QB2 and QB3, parity changing γ transitions were found that connect these levels to the negative parity states of the octupole band, as also shown in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The level scheme of 152Sm obtained from (a) the X(5) critical-point solution (for s = 1, 2, 3, and 4 family of bands) and (b) the present experiment. The level energies, both for the experimental and calculated scheme, are rounded off to the nearest keV (represented by the magenta-colored numbers). The label (blue in (a) and colored red in (b)) associated with the transitions represents the B(E2) values in… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the experimental energy ratios (red squares) with [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

The positive-parity structure of 152Sm has been investigated through high-statistics {\gamma}-ray spectroscopy following the (150Nd({\alpha},2n)152Sm reaction at Elab = 26 MeV. Several collective structures built on excited 0+ states have been extended through the observation of new levels and {\gamma}-ray transitions, and spin-parity assignments have been established using directional-correlation and linear-polarization measurements. Electromagnetic transition strengths (B(E2)), deduced from measured branching ratios and known level lifetimes, reveal pronounced collectivity among the excited configurations. The resulting level scheme provides evidence for a sequence of excited collective bands extending beyond the well-known ground-state and first excited 0+ structures. The excitation energies and transition strengths are examined within the framework of the X(5) critical-point description of the first-order U(5)-SU(3) shape-phase transition. In addition to the established X(5)-like features of the low-lying spectrum, the observed systematics of the higher-lying bands are found to be consistent with excited collective structures exhibiting X(5)-like characteristics. The results provide new constraints on the realization of critical-point behavior in finite nuclei and on the evolution of collectivity in the N=90 region.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper reports new high-statistics gamma-ray spectroscopy data on the positive-parity levels of 152Sm populated via the 150Nd(α,2n) reaction at 26 MeV. New levels and transitions are identified in several bands built on excited 0+ states; spin-parity assignments are made from DCO ratios and polarization measurements; B(E2) values are extracted from branching ratios combined with known lifetimes. The excitation energies and transition strengths are compared to X(5) critical-point predictions, and the authors conclude that the higher-lying bands exhibit systematics consistent with excited X(5)-like collective structures, extending the known critical-point features of the ground-state and first-excited 0+ bands in the N=90 region.

Significance. If the quantitative comparisons hold, the work supplies new experimental constraints on the realization of critical-point symmetry in excited configurations of finite nuclei undergoing a U(5)–SU(3) shape-phase transition. The data on higher-lying bands and the reported collectivity provide a direct test of whether X(5)-like behavior persists beyond the lowest two bands, which is relevant for understanding the evolution of collectivity near N=90.

major comments (2)
  1. [Results and Discussion sections on higher-lying bands] The central claim of X(5)-like systematics for the higher-lying bands rests on the comparison of energies and B(E2) strengths, yet no table or figure in the results or discussion sections presents the numerical experimental values (with uncertainties) alongside the corresponding X(5) predictions for the excited 0+ structures. Without this explicit side-by-side quantification, the degree of consistency cannot be assessed independently.
  2. [Electromagnetic transition strengths subsection] The deduction of B(E2) values from branching ratios and lifetimes assumes that the measured quantities directly reflect the intrinsic collective matrix elements. A quantitative estimate of possible configuration mixing or other perturbations (acknowledged in the abstract) is needed to establish that such effects do not invalidate the direct comparison to pure X(5) predictions.
minor comments (2)
  1. List all newly observed levels, gamma-ray energies, intensities, and DCO/polarization results in a dedicated table for clarity.
  2. Specify the exact criteria (e.g., energy ratios, B(E2) ratio thresholds) used to classify a band as X(5)-like.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful review and for highlighting areas where the presentation of our comparisons can be strengthened. We address each major comment below and have made revisions to improve clarity and transparency without altering the core conclusions.

read point-by-point responses

  1. Referee: [Results and Discussion sections on higher-lying bands] The central claim of X(5)-like systematics for the higher-lying bands rests on the comparison of energies and B(E2) strengths, yet no table or figure in the results or discussion sections presents the numerical experimental values (with uncertainties) alongside the corresponding X(5) predictions for the excited 0+ structures. Without this explicit side-by-side quantification, the degree of consistency cannot be assessed independently.

    Authors: We agree that an explicit side-by-side tabulation is necessary for independent assessment. In the revised manuscript we have added a new Table IV that lists, for each higher-lying band, the experimental excitation energies (with uncertainties), the deduced B(E2) values (with uncertainties), and the corresponding X(5) predictions. This table is referenced in both the Results and Discussion sections and directly enables quantitative evaluation of the claimed consistency. revision: yes

  2. Referee: [Electromagnetic transition strengths subsection] The deduction of B(E2) values from branching ratios and lifetimes assumes that the measured quantities directly reflect the intrinsic collective matrix elements. A quantitative estimate of possible configuration mixing or other perturbations (acknowledged in the abstract) is needed to establish that such effects do not invalidate the direct comparison to pure X(5) predictions.

    Authors: The referee is correct that configuration mixing could in principle affect the extracted B(E2) values. We have expanded the Electromagnetic transition strengths subsection to include a more explicit statement of this assumption and a qualitative discussion of why mixing is expected to be limited (based on the small deviations already observed in the well-studied ground-state and first-excited 0+ bands). A full quantitative estimate, however, would require microscopic structure calculations that lie beyond the scope of the present experimental study; we therefore note this limitation while maintaining that the observed systematics remain consistent with X(5)-like behavior. revision: partial

Circularity Check

0 steps flagged

No significant circularity; experimental comparison to independent X(5) model

full rationale

The paper reports new experimental data (level energies, spin-parity assignments via DCO/polarization, branching ratios, and B(E2) values from lifetimes) obtained in the (α,2n) reaction on 152Sm. These observables are compared directly to the established X(5) critical-point symmetry predictions for energies and transition strengths. The claim of 'X(5)-like characteristics' for higher-lying bands is framed as consistency with an external theoretical framework (not derived or fitted from the present dataset). No equations reduce a prediction to a fitted input by construction, no self-citation chain bears the central claim, and the comparison remains falsifiable against the measured quantities without circular redefinition. The work is self-contained as data collection plus model comparison.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review provides minimal information on parameters or axioms; the central comparison rests on the applicability of the X(5) framework to excited states.

axioms (1)
  • domain assumption The X(5) critical-point symmetry provides a valid description for the level energies and transition strengths in the excited bands of 152Sm.
    The paper states that the data are examined within this framework and found consistent.

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