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arxiv: 2607.01309 · v1 · pith:UB4OYJWEnew · submitted 2026-07-01 · ⚛️ nucl-th · nucl-ex

Determining the dynamic deformation of ¹⁴⁰Ce by constraining coupled-channels parameters for fusion

Chandra Kumar , Rohan Biswas , J. Gehlot , Gonika , A. Parihari , N. Madhavan , A. Vinayak , Amritraj Mahato
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S. Nath
This is my paper

Pith reviewed 2026-07-03 17:56 UTC · model grok-4.3

classification ⚛️ nucl-th nucl-ex
keywords heavy-ion fusioncoupled-channels calculationsnuclear deformationbarrier distributioncerium-140two-neutron transferBayesian model averaging
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The pith

Fusion reactions with oxygen and sulfur projectiles fix the quadrupole and octupole deformations of cerium-140 at beta2 equals 0.09 and beta3 equals 0.18.

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

The paper measures fusion excitation functions for oxygen-16 on cerium-140 down to below the barrier and combines them with existing sulfur-36 data. It applies a Gaussian analytic barrier model together with coupled-channels calculations and Bayesian model averaging to extract consistent deformation parameters for the target. These parameters are then checked in a third system, silicon-28 plus cerium-140, where inclusion of two-neutron transfer reproduces both the excitation function and the barrier distribution. The work shows that the barrier distribution acts as a sensitive probe of the target's intrinsic shape when multiple projectile systems are analyzed together.

Core claim

Independent Bayesian Model Averaging applied to coupled-channels fits of the 16O+140Ce and 36S+140Ce fusion data yields beta2 = 0.09 plus or minus 0.03 and beta3 = 0.18 plus or minus 0.02 for 140Ce. The same values, when inserted into calculations for the 28Si+140Ce system that also include the positive-Q 2n-pickup channel, reproduce both the measured fusion excitation function and the experimental barrier distribution.

What carries the argument

Coupled-channels calculations inside a Gaussian analytic-barrier framework, with Bayesian model averaging used to constrain the target's quadrupole and octupole deformation parameters across multiple projectile systems.

If this is right

  • The extracted beta2 and beta3 values can be used to predict fusion behavior in additional systems involving 140Ce.
  • The Gaussian analytic recipe produces a barrier distribution that matches experimental structure and serves as a direct indicator of target deformation.
  • Projectile vibrational or rotational character does not alter the overall shape of the barrier distribution once target deformations are fixed.
  • Positive-Q-value two-neutron transfer enhances sub-barrier fusion and must be included for accurate reproduction of data in the silicon projectile case.

Where Pith is reading between the lines

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

  • If the same deformation parameters work across more projectile-target combinations, they could serve as a standard reference for modeling fusion near the barrier in the cerium region.
  • The consistency between Bayesian averaging and chi-square minimization suggests the deformation values are robust against modest changes in model assumptions.
  • Extending the method to other even-even nuclei near closed shells could test whether octupole softness is a general feature or specific to 140Ce.

Load-bearing premise

All important reaction channels and nuclear excitations are captured by the coupled-channels model and the assumed Gaussian barrier shape, with no large unaccounted effects.

What would settle it

A measurement of the barrier distribution for 28Si+140Ce that deviates significantly from the coupled-channels prediction when the extracted beta2 and beta3 values plus the 2n-transfer channel are included.

Figures

Figures reproduced from arXiv: 2607.01309 by Amritraj Mahato, A. Parihari, A. Vinayak, Chandra Kumar, Gonika, J. Gehlot, N. Madhavan, Rohan Biswas, S. Nath.

Figure 2
Figure 2. Figure 2: FIG. 2. Measured and calculated (a) fusion excitation func [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Measured and calculated (a) fusion excitation func [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Posterior probability distributions of the deforma [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Measured and calculated (a) fusion excitation func [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

We present a systematic study of the dynamic deformation of 140Ce using 16O and 36S projectiles in heavy-ion fusion reactions, combining experimental data, a Gaussian analytic-barrier framework and coupled-channels calculations. Fusion cross sections for 16O+140Ce are measured from ~17% above to ~12.4% below the Bass barrier. Fusion data for 36S+140Ce are obtained from the literature. Deformation parameters of 140Ce are extracted via chi-square minimization and Bayesian analysis, with independent Bayesian Model Averaging yielding beta_2 = 0.09 +/- 0.03 and beta_3 = 0.18 +/- 0.02, consistent across both systems. The extracted parameters are tested in the 28Si+140Ce system, where coupled-channels calculations including transfer of a pair of neutrons (2n) reproduce both the fusion excitation function and the barrier distribution. The positive Q-value 2n-pickup channel enhances fusion in this reaction, while the projectile's vibrational or rotational nature results in similar structure of the barrier distribution. This study demonstrates that the Gaussian analytic recipe is quite effective in deriving the fusion barrier distribution which proves to be a sensitive probe of intrinsic nuclear deformation. Further, coupled-channels analysis across multiple systems ensures robustness of the extracted deformation parameters.

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 / 0 minor

Summary. The manuscript reports a systematic extraction of the dynamic quadrupole (β₂) and octupole (β₃) deformation parameters of ¹⁴⁰Ce from heavy-ion fusion excitation functions and barrier distributions. New fusion data for ¹⁶O + ¹⁴⁰Ce are combined with literature data for ³⁶S + ¹⁴⁰Ce. Deformation parameters are determined via χ² minimization and Bayesian analysis within a coupled-channels framework using a Gaussian analytic-barrier model, yielding β₂ = 0.09 ± 0.03 and β₃ = 0.18 ± 0.02 via Bayesian model averaging. These parameters are validated by reproducing the ²⁸Si + ¹⁴⁰Ce fusion data when 2n transfer is included.

Significance. If the extracted deformations are robust, the work demonstrates a method to constrain nuclear structure parameters using fusion reactions across multiple projectile-target combinations, with cross-validation providing evidence against system-specific artifacts. The emphasis on barrier distributions as a sensitive probe and the inclusion of transfer channels adds to the understanding of near-barrier fusion dynamics. The Bayesian approach and consistency across systems are positive features.

major comments (1)
  1. [Validation with ²⁸Si+¹⁴⁰Ce] The reproduction of the fusion excitation function and barrier distribution using coupled-channels calculations that include only the 2n transfer channel does not demonstrate that other transfer channels (such as 1n, pn, or α transfer) are negligible. If these channels contribute at the 10-20% level near the barrier, they could alter the effective barrier distribution and require readjustment of the deformation parameters. This omission undermines the claim that the extracted β₂ and β₃ are uniquely confirmed by the ²⁸Si+¹⁴⁰Ce data.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive review and the opportunity to clarify aspects of our validation procedure. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Validation with ²⁸Si+¹⁴⁰Ce] The reproduction of the fusion excitation function and barrier distribution using coupled-channels calculations that include only the 2n transfer channel does not demonstrate that other transfer channels (such as 1n, pn, or α transfer) are negligible. If these channels contribute at the 10-20% level near the barrier, they could alter the effective barrier distribution and require readjustment of the deformation parameters. This omission undermines the claim that the extracted β₂ and β₃ are uniquely confirmed by the ²⁸Si+¹⁴⁰Ce data.

    Authors: We agree that a more complete demonstration would require explicit checks on additional transfer channels. In the ²⁸Si + ¹⁴⁰Ce system the 2n-pickup channel is the only transfer process with positive Q-value, while 1n, pn and α transfers have negative Q-values and are therefore strongly suppressed near the barrier. The coupled-channels calculation that includes only the 2n channel already reproduces both the measured excitation function and the barrier distribution to within experimental uncertainties, without any readjustment of the β₂ and β₃ values extracted from the ¹⁶O and ³⁶S systems. This internal consistency supports our interpretation that the 2n channel dominates the observed enhancement. Nevertheless, to strengthen the manuscript we will add a short paragraph (and the relevant Q-values) explaining why the other channels are expected to be negligible at the present level of precision. We therefore classify the revision as partial. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation uses independent test data

full rationale

The paper extracts β2 and β3 via χ² minimization and Bayesian Model Averaging from measured fusion data in the 16O+140Ce and 36S+140Ce systems, then applies those fixed parameters (plus an explicit 2n-transfer term) to reproduce excitation functions and barrier distributions in the separate 28Si+140Ce data set. This constitutes an out-of-sample test on distinct experimental measurements rather than a reduction of the claimed result to its own inputs by construction. No self-citation chains, uniqueness theorems, or ansatzes imported from prior author work are load-bearing in the derivation. The Gaussian analytic-barrier and coupled-channels framework are applied uniformly but the central claim rests on external data benchmarks, satisfying the self-contained criterion.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the coupled-channels model and the Gaussian barrier framework; the deformation parameters themselves are free parameters fitted to the fusion data.

free parameters (2)
  • beta_2 = 0.09
    Fitted parameter for quadrupole deformation of 140Ce
  • beta_3 = 0.18
    Fitted parameter for octupole deformation of 140Ce
axioms (2)
  • domain assumption Coupled-channels calculations accurately describe the fusion dynamics including deformations and 2n transfer
    Invoked to extract and validate the deformation parameters from cross sections
  • domain assumption Gaussian analytic-barrier framework correctly derives the fusion barrier distribution
    Used to interpret the data as a probe of intrinsic deformation

pith-pipeline@v0.9.1-grok · 5805 in / 1317 out tokens · 29598 ms · 2026-07-03T17:56:54.972355+00:00 · methodology

discussion (0)

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Reference graph

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