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arxiv: 2605.04841 · v1 · submitted 2026-05-06 · ⚛️ nucl-th

Recognition: unknown

Nuclear Structure and Shape Evolution of Nd Isotopes

P. Mohanty , C. Dash , A. Anupam , B. B. Sahu
Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:28 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords Nd isotopesshape evolutionrelativistic mean fieldnuclear deformationN=92 stabilitybinding energiespotential energy curvestwo-neutron separation energy
0
0 comments X

The pith

Relativistic mean field calculations show stability in Nd isotopes at neutron number 92 with shape transitions nearby.

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

The paper applies an axially deformed relativistic mean field model with two parametrizations to even-even neodymium isotopes from mass 126 to 188. It computes binding energies per nucleon, two-neutron separation energies and their derivatives, quadrupole deformations, charge radii, neutron skins, and single-particle levels, then compares the results to available data and the finite range droplet model. Potential energy curves versus deformation are examined specifically to trace shape evolution. These quantities together indicate a region of relative stability at N=92 accompanied by changes in nuclear shape. A reader would care because such patterns help locate where nuclear shells reorganize in heavy elements and set limits on how far isotopes can be pushed before they become unstable.

Core claim

Using the axially deformed RMF model with PK1 and NL-SH parametrizations, the structural properties of even-even Nd isotopes indicate a sign of stability at N=92 accompanied by shape transitions around it, as shown by the binding energies, separation energies, deformation parameters, and potential energy curves.

What carries the argument

Axially deformed Relativistic Mean Field (RMF) model with PK1 and NL-SH parametrizations, which self-consistently solves for proton and neutron densities to yield binding energies, separation energies, quadrupole deformations, radii, and potential energy surfaces as functions of the deformation parameter.

If this is right

  • Binding energy per nucleon and two-neutron separation energies exhibit features consistent with enhanced stability at N=92.
  • Quadrupole deformation parameters change across N=92, indicating a shift from one nuclear shape to another.
  • Potential energy curves display multiple minima whose locations move with neutron number, confirming the shape transition.
  • Bulk properties such as charge radii and neutron skin thickness follow smooth trends that match experimental trends where available.

Where Pith is reading between the lines

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

  • The same RMF approach could be applied to neighboring isotopic chains such as Sm or Ce to test whether the stability feature at N=92 is local to Nd or more general.
  • Adding explicit triaxial calculations might locate the precise boundary between prolate and oblate shapes in the transition region.
  • The predicted stability could affect estimates of neutron capture rates for nuclei near the r-process path in astrophysical environments.

Load-bearing premise

The axially deformed RMF model with the chosen PK1 and NL-SH parametrizations sufficiently captures the nuclear structure and shape evolution without requiring explicit inclusion of beyond-mean-field correlations or triaxial degrees of freedom.

What would settle it

Experimental values of two-neutron separation energies or quadrupole moments for Nd isotopes near N=92 that lack the predicted plateau in separation energy or the abrupt change in deformation would falsify the reported sign of stability and shape transitions.

read the original abstract

In this work, we have analyzed the structural properties of even-even $^{126-188}Nd_{60}$ isotopes. For this we have used axially deformed Relativistic Mean Field (RMF) model with PK1 and NL-SH parametrization. In structural properties, We have estimated and analyzed binding energy per nucleon (B.E./A), two neutron separation energy ($S_{2n}$), differential variation of two neutron separation energy ($dS_{2n}$), quadrupole deformation parameter ($\beta_{2}$), root mean square nuclear charge radius ($r_{ch}$), neutron skin thickness ($r_{np}$) and single particle energy (SPE) levels of Nd isotopes. Some bulk properties are also compared with experimentally accessible results and with results of Finite Range Droplet Model (FRDM). To understand the shape evolution around N = 92, the variation of the potential energy curves (PECs) with quadrupole deformation parameter are also investigated. From all the investigations, We observe some sign of stability at N = 92 and shape transitions around it.

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

1 major / 3 minor

Summary. The manuscript analyzes structural properties of even-even Nd isotopes (A=126-188) using an axially deformed relativistic mean field (RMF) model with PK1 and NL-SH parametrizations. It computes binding energy per nucleon, two-neutron separation energies S_{2n} and dS_{2n}, quadrupole deformation β_2, charge radii r_ch, neutron skin thickness r_np, and single-particle energies, comparing selected bulk properties to experiment and FRDM. Potential energy curves (PECs) versus quadrupole deformation are examined to assess shape evolution, with the conclusion that there are signs of stability at N=92 and shape transitions around it.

Significance. If the central interpretation holds, the work adds systematic RMF results for the Nd chain in the rare-earth region and identifies a possible stability point at N=92 that could be tested against future data. The comparisons to FRDM and experiment provide a useful benchmark, and the PEC analysis offers concrete, falsifiable predictions for shape evolution. However, the approach relies on standard RMF equations and literature parametrizations without new derivations or beyond-mean-field extensions, so the overall significance is incremental rather than transformative.

major comments (1)
  1. [PECs and shape evolution analysis] The central claim of stability at N=92 and shape transitions around it rests on PECs computed under the axial symmetry constraint (see abstract and the section investigating variation of PECs with quadrupole deformation). In the A≈150 region, triaxial softness is known to lower energies, shift or smooth prolate-oblate transitions, and alter barrier heights; the manuscript performs no triaxial relaxation or estimate of its effect. This assumption is load-bearing for the reported minima, barriers, and inferred transition point, and could qualitatively change the location or character of the features used to support the N=92 stability conclusion.
minor comments (3)
  1. [Abstract] Abstract contains inconsistent capitalization ('We observe', 'We have estimated') that should be standardized to lowercase 'we'.
  2. [Methods/Computational details] The manuscript would benefit from explicit statements on numerical convergence (e.g., basis size or oscillator shells used in the RMF calculations) to allow readers to assess the reliability of the reported β_2 and PEC features.
  3. [Results on separation energies] Notation for differential variation dS_{2n} should be defined more clearly when first introduced, including the finite-difference formula employed.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comment below and will revise the text accordingly to improve clarity and balance.

read point-by-point responses

  1. Referee: The central claim of stability at N=92 and shape transitions around it rests on PECs computed under the axial symmetry constraint (see abstract and the section investigating variation of PECs with quadrupole deformation). In the A≈150 region, triaxial softness is known to lower energies, shift or smooth prolate-oblate transitions, and alter barrier heights; the manuscript performs no triaxial relaxation or estimate of its effect. This assumption is load-bearing for the reported minima, barriers, and inferred transition point, and could qualitatively change the location or character of the features used to support the N=92 stability conclusion.

    Authors: We agree that triaxial degrees of freedom are relevant in the A≈150 region and can modify barrier heights and the sharpness of shape transitions. Our calculations are performed in the axially symmetric RMF framework with the PK1 and NL-SH parametrizations, which is a standard and computationally tractable approach for systematic studies of long isotopic chains. The axial PECs still exhibit clear minima and evolution patterns that indicate enhanced stability at N=92, consistent with the trends seen in binding energies, S_{2n}, and β_2. We will revise the manuscript to explicitly discuss the axial approximation as a limitation, note that triaxial effects may smooth some features, and reference existing triaxial calculations in the rare-earth region for context. This addition will qualify our conclusions without changing the reported axial results or the overall interpretation. revision: yes

Circularity Check

0 steps flagged

No circularity: standard RMF computations compared to external data

full rationale

The paper applies the established axially deformed RMF framework with literature parametrizations (PK1, NL-SH) to compute B.E./A, S_{2n}, dS_{2n}, β_2, r_ch, r_np, SPE levels and PECs for ^{126-188}Nd. These outputs are directly compared to experimental values and FRDM results; the reported stability at N=92 and shape transitions are interpretations of the computed curves and quantities, not quantities defined into the inputs or obtained by fitting a subset and relabeling the remainder. No self-citation is invoked as a uniqueness theorem or load-bearing premise, and the model equations are independent of the target observables. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the mean-field approximation and the transferability of the PK1 and NL-SH forces to the Nd region. No new entities are postulated.

free parameters (1)
  • PK1 and NL-SH force parameters
    Standard RMF parametrizations fitted to nuclear matter and finite nuclei properties in prior literature; their specific values are not re-derived here.
axioms (2)
  • domain assumption Axial symmetry is sufficient to describe the ground-state shapes of even-even Nd isotopes.
    Invoked by the choice of axially deformed RMF solver.
  • domain assumption The mean-field approximation adequately captures binding energies, deformations, and separation energies near N=92.
    Underlying assumption of the RMF framework used throughout.

pith-pipeline@v0.9.0 · 5490 in / 1478 out tokens · 33212 ms · 2026-05-08T16:28:57.829257+00:00 · methodology

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