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arxiv: 2606.21269 · v1 · pith:WR44XNUSnew · submitted 2026-06-19 · ⚛️ nucl-ex · nucl-th

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

S. Basaka , 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 2026-06-26 12:51 UTC · model grok-4.3

classification ⚛️ nucl-ex nucl-th
keywords 152SmX(5) symmetrycritical-point symmetryshape-phase transitiongamma-ray spectroscopycollective bandsN=90 regionB(E2) strengths
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The pith

152Sm shows X(5)-like symmetry in excited collective bands.

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

The paper uses high-statistics gamma-ray spectroscopy after the 150Nd(alpha,2n) reaction to map positive-parity levels in 152Sm. New transitions and levels are added to bands built on excited 0+ states, with spins and parities fixed by directional-correlation and polarization data. Branching ratios combined with known lifetimes yield B(E2) values that indicate strong collectivity. These energies and strengths are compared to the X(5) critical-point model for the U(5)-SU(3) shape-phase transition. The higher bands follow the same systematic patterns already seen in the ground-state and first-excited 0+ structures.

Core claim

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.

What carries the argument

The X(5) critical-point description of the first-order U(5)-SU(3) shape-phase transition, which supplies predicted energy ratios and B(E2) strengths for nuclei at the spherical-to-deformed boundary.

If this is right

  • The N=90 region contains multiple realizations of X(5)-like behavior at different excitation energies.
  • Critical-point symmetry can appear in excited configurations as well as in the ground-state band.
  • Collectivity in 152Sm follows the X(5) pattern across several bands, tightening constraints on shape-phase models.
  • Similar excited X(5) sequences may occur in neighboring nuclei near the same phase transition.

Where Pith is reading between the lines

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

  • Comparable excited-band studies in 150Nd or 154Gd could test whether the pattern repeats across the N=90 isotones.
  • The results suggest the U(5)-SU(3) transition may support replicated critical points at higher energies, a feature not usually included in standard calculations.
  • If the pattern holds, models of nuclear collectivity would need explicit provisions for X(5)-like structures above the lowest bands.

Load-bearing premise

The spin-parity assignments and B(E2) values derived from branching ratios and lifetimes correctly identify pure collective motion without important mixing from other configurations.

What would settle it

A new lifetime or branching-ratio measurement that places the B(E2) values of the higher bands far from X(5) predictions while matching a rigid-rotor or pure-vibrator limit.

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. Basaka, 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 / 3 minor

Summary. The manuscript reports high-statistics γ-ray spectroscopy of 152Sm following the 150Nd(α,2n) reaction at 26 MeV. New levels and transitions in positive-parity collective structures built on excited 0+ states are identified, with J^π assignments from directional-correlation and linear-polarization data. B(E2) values are deduced from branching ratios combined with known lifetimes, revealing collectivity. The level scheme is compared to the X(5) critical-point symmetry of the U(5)-SU(3) transition; in addition to the established low-lying X(5)-like features, the systematics of higher-lying bands are reported as consistent with excited X(5)-like structures, yielding new constraints on critical-point behavior in the N=90 region.

Significance. If the quantitative comparisons hold, the work extends X(5) descriptions beyond the ground-state and first-excited 0+ bands to higher collective configurations, supplying additional experimental constraints on the realization of critical-point symmetries in finite nuclei and on collectivity evolution near N=90. The use of conventional γ-spectroscopy techniques (DCO, polarization, branching ratios + lifetimes) applied to extended bands is a standard approach in the field and, when the data tables are complete, adds to the existing body of N=90 studies without introducing new methodological assumptions.

major comments (2)
  1. [Results and Discussion sections] The central claim of X(5)-like behavior in the higher-lying bands rests on the comparison of excitation energies and B(E2) values; the manuscript should provide explicit tables or figures showing the numerical experimental values (with uncertainties) alongside the X(5) predictions, including any parameter choices (e.g., the ratio of moments of inertia or effective charges) used for the excited bands, so that the degree of agreement can be assessed independently.
  2. [Electromagnetic transition strengths subsection] The deduction of B(E2) strengths from branching ratios and known lifetimes assumes negligible mixing or contamination; the paper should quantify possible effects of configuration mixing on the assigned collective character of the higher bands, citing specific levels or transitions where this could affect the X(5) comparison.
minor comments (3)
  1. [Abstract] The abstract would be strengthened by inclusion of at least one or two representative numerical B(E2) ratios or energy ratios that support the X(5)-like claim for the higher bands.
  2. [Introduction and Experimental details] Notation for the reaction should follow standard nuclear-reaction format throughout (e.g., consistent use of 150Nd(α,2n)152Sm).
  3. [Introduction] Ensure all cited previous X(5) studies on 152Sm and neighboring nuclei are referenced in the introduction for context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and constructive comments on our manuscript. We address each major comment below and will revise the manuscript accordingly to improve clarity and transparency of the comparisons.

read point-by-point responses

  1. Referee: [Results and Discussion sections] The central claim of X(5)-like behavior in the higher-lying bands rests on the comparison of excitation energies and B(E2) values; the manuscript should provide explicit tables or figures showing the numerical experimental values (with uncertainties) alongside the X(5) predictions, including any parameter choices (e.g., the ratio of moments of inertia or effective charges) used for the excited bands, so that the degree of agreement can be assessed independently.

    Authors: We agree that explicit numerical comparisons will allow independent assessment. In the revised manuscript we will add a dedicated table (and associated figure) in the Results and Discussion sections listing experimental excitation energies and B(E2) values (with uncertainties) for the higher-lying bands next to the X(5) predictions. All model parameters, including the ratio of moments of inertia and effective charges adopted for the excited bands, will be stated explicitly. revision: yes

  2. Referee: [Electromagnetic transition strengths subsection] The deduction of B(E2) strengths from branching ratios and known lifetimes assumes negligible mixing or contamination; the paper should quantify possible effects of configuration mixing on the assigned collective character of the higher bands, citing specific levels or transitions where this could affect the X(5) comparison.

    Authors: We will expand the Electromagnetic transition strengths subsection to include a quantitative discussion of possible configuration mixing. For the specific levels and transitions where mixing could influence the extracted B(E2) values, we will cite the relevant data and estimate its potential impact on the X(5) comparison. The current analysis is based on the observed systematics supporting dominant collective character, but we will explicitly note the assumptions and limitations. revision: partial

Circularity Check

0 steps flagged

No significant circularity; comparison to external X(5) model

full rationale

The paper reports experimental gamma-ray spectroscopy results from the (150Nd(α,2n)) reaction, including new level extensions, spin-parity assignments via DCO and polarization, and B(E2) values from branching ratios plus known lifetimes. These data are then compared to the pre-existing X(5) critical-point symmetry (an external theoretical framework from the literature). No derivation chain, equation, or fitted parameter is shown to reduce by construction to the paper's own inputs; the X(5) comparison is not generated from the present dataset via self-definition or self-citation load-bearing steps. The analysis follows standard nuclear-structure methods without internal circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the X(5) critical-point symmetry to both ground and excited bands and on the accuracy of experimental spin-parity and lifetime inputs; no free parameters or invented entities are visible in the abstract.

axioms (1)
  • domain assumption The X(5) critical-point symmetry provides a valid description of the U(5)-SU(3) shape-phase transition in finite nuclei.
    The paper explicitly examines the data within the X(5) framework.

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