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arxiv: 2604.24174 · v1 · submitted 2026-04-27 · ⚛️ nucl-th

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Survival of Pairing Correlations and Shell Effects at Scission in Finite-Temperature Nuclear Fission: Implications for Odd-Even Staggering

K. Pomorski , A. Augustyn , T. Cap , Y. J. Chen , M. Kowal , M. Warda , Z. G. Xiao
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Pith reviewed 2026-05-07 17:52 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords pairingshellfinite-temperaturescissioneffectsfissionattenuationcorrelations
0
0 comments X

The pith

Pairing correlations persist near scission in hot fission and explain odd-even staggering in charge yields, while shell corrections are suppressed with rising temperature.

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

When a heavy nucleus fissions, it passes through highly deformed shapes before splitting. At finite temperature the microscopic energy corrections from nucleon pairing and from shell structure both weaken, but they do so differently. The authors apply a temperature-dependent BCS treatment for pairing together with the Strutinsky shell-correction method at selected points along a typical fission trajectory. They find that the pairing free-energy contribution remains strongly sensitive to the nuclear shape even close to scission, and that this contribution changes noticeably depending on whether a constant or surface-dependent pairing strength is used. Shell corrections, by contrast, are already sizable at low temperature near scission but are steadily washed out as excitation energy increases. Because the two effects attenuate at different rates and retain different deformation dependences, the work argues they must be treated with separate temperature- and shape-dependent factors in any dynamical fission calculation. The surviving pairing is offered as the microscopic origin of the observed odd-even staggering in the charge distribution of fission fragments.

Core claim

These results support the interpretation of odd-even staggering in fragment charge yields as a manifestation of pairing correlations surviving into the strongly deformed pre-scission configuration.

Load-bearing premise

The finite-temperature BCS treatment combined with the Strutinsky method, together with the chosen constant versus surface-dependent pairing-strength prescriptions, faithfully represents the microscopic free-energy corrections near scission.

Figures

Figures reproduced from arXiv: 2604.24174 by A. Augustyn, K. Pomorski, M. Kowal, M. Warda, T. Cap, Y. J. Chen, Z. G. Xiao.

Figure 1
Figure 1. Figure 1: FIG. 1. Zero-temperature deformation-energy landscape of view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Temperature dependence of the proton (red solid lines) and neutron (blue dashed lines) pairing gap view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Scaling representation of the temperature dependence view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Temperature dependence of the proton (red solid lines) and neutron (blue dashed lines) pairing free-energy corrections view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Average temperature dependence of the normalized view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Temperature evolution of the shell free-energy correction around scission for view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Average temperature dependence of the normalized view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Illustration of the charge-polarization mechanism view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Calculated fragment charge yield for thermal view at source ↗
read the original abstract

We investigate the finite-temperature evolution of microscopic free-energy corrections in nuclear fission, focusing on pairing and shell effects near scission. The analysis is based on a finite-temperature BCS treatment combined with the Strutinsky method and is performed for representative deformation points along the fission path. Both pairing and shell contributions exhibit regular thermal attenuation, but their deformation dependencies differ substantially. In particular, pairing remains strongly deformation-dependent in the scission region, and its free-energy contribution differs markedly between the constant and surface-dependent pairing-strength prescriptions. The shell correction near scission is also significant at low temperature and is progressively suppressed with increasing excitation energy. These results support the interpretation of odd-even staggering in fragment charge yields as a manifestation of pairing correlations surviving into the strongly deformed pre-scission configuration. They also show that pairing and shell effects should be treated separately in finite-temperature dynamical calculations, with distinct deformation- and temperature-dependent attenuation laws.

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

3 major / 2 minor

Summary. The manuscript examines the finite-temperature evolution of microscopic free-energy corrections due to pairing and shell effects near scission in nuclear fission. Using a finite-temperature BCS treatment combined with the Strutinsky method applied to representative deformation points along the fission path, it finds that both contributions exhibit regular thermal attenuation, but pairing remains strongly deformation-dependent at scission with marked differences between constant and surface-dependent pairing-strength prescriptions. The shell correction is significant at low temperature and suppressed with increasing excitation energy. These results are interpreted as supporting the view that odd-even staggering in fragment charge yields manifests pairing correlations surviving into the strongly deformed pre-scission configuration, and they advocate treating pairing and shell effects separately in dynamical calculations with distinct deformation- and temperature-dependent attenuation laws.

Significance. If the results hold under a designated pairing prescription, the work provides a useful microscopic basis for understanding the persistence of odd-even effects in fission yields by demonstrating survival of pairing correlations at large deformations. The application of standard finite-temperature BCS plus Strutinsky methods to fission is a strength, yielding concrete insights into differing deformation dependencies that can inform future dynamical models. The emphasis on separate attenuation laws for pairing and shell effects is a constructive contribution, though the conditional character of the central interpretation limits broader immediate impact.

major comments (3)
  1. [Results and discussion of pairing prescriptions] The calculations show that the pairing free-energy correction near scission differs markedly between the constant and surface-dependent pairing-strength prescriptions, yet the manuscript does not designate a preferred prescription for the scission region. This renders the support for the odd-even staggering interpretation conditional on an unresolved model choice (see abstract and results on deformation dependence).
  2. [Implications for odd-even staggering] The paper infers implications for odd-even staggering in fragment charge yields from the surviving pairing free-energy corrections but does not quantify how the free-energy differences between prescriptions would propagate into the charge-yield distribution. Without this step, the link between the computed corrections and observed yields remains qualitative.
  3. [Method and deformation-point selection] The analysis is based on static sampling of representative deformation points. It remains open whether the free-energy landscape evaluated at these discrete points controls the final fragment yields, since dynamical evolution during the descent to scission is not modeled.
minor comments (2)
  1. [Abstract] The abstract could usefully specify the nuclei or fission systems studied to allow immediate assessment of applicability.
  2. [Figures] Figures displaying free-energy corrections versus deformation should explicitly mark the scission region and distinguish the two pairing prescriptions in legends and captions for clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We appreciate the referee's positive evaluation of our work and the insightful comments provided. Below we respond to each major comment in detail, outlining the revisions we intend to implement in the manuscript.

read point-by-point responses

  1. Referee: [Results and discussion of pairing prescriptions] The calculations show that the pairing free-energy correction near scission differs markedly between the constant and surface-dependent pairing-strength prescriptions, yet the manuscript does not designate a preferred prescription for the scission region. This renders the support for the odd-even staggering interpretation conditional on an unresolved model choice (see abstract and results on deformation dependence).

    Authors: We thank the referee for highlighting this aspect. The manuscript presents both prescriptions to demonstrate that the survival of pairing correlations at scission is a robust feature, independent of the specific pairing strength prescription. The quantitative differences are discussed to inform model choices in future work. To address the concern, we will revise the abstract and the relevant sections to explicitly state that the interpretation of odd-even staggering holds qualitatively for both prescriptions, while noting the differences in magnitude. revision: partial

  2. Referee: [Implications for odd-even staggering] The paper infers implications for odd-even staggering in fragment charge yields from the surviving pairing free-energy corrections but does not quantify how the free-energy differences between prescriptions would propagate into the charge-yield distribution. Without this step, the link between the computed corrections and observed yields remains qualitative.

    Authors: We agree that our inference remains qualitative. Performing a quantitative mapping to charge yields would require a complete dynamical fission calculation incorporating these free energies, which is not within the scope of this study. Our focus is on providing the microscopic temperature and deformation dependence of the corrections. We will update the discussion to more clearly indicate the qualitative character of the link and to suggest how these results can be used in dynamical models. revision: yes

  3. Referee: [Method and deformation-point selection] The analysis is based on static sampling of representative deformation points. It remains open whether the free-energy landscape evaluated at these discrete points controls the final fragment yields, since dynamical evolution during the descent to scission is not modeled.

    Authors: This comment correctly identifies a limitation of our static approach. The representative points are chosen to evaluate the corrections specifically in the scission region, providing essential information on how pairing and shell effects attenuate with temperature and deformation. We do not model the full dynamical path, as our goal is to supply these corrections for use in dynamical simulations. We will add text in the conclusions to clarify this scope and the intended application of our findings. revision: yes

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the finite-temperature BCS pairing treatment and the Strutinsky shell-correction procedure applied at selected points along the fission path; the choice between constant and surface-dependent pairing strength acts as a model parameter that visibly alters the reported free-energy contribution.

free parameters (1)
  • pairing-strength prescription
    Constant versus surface-dependent pairing strength is shown to produce markedly different free-energy contributions near scission; the choice is therefore a free modeling parameter.
axioms (2)
  • domain assumption Finite-temperature BCS treatment remains valid for strongly deformed nuclei near scission.
    Invoked as the basis for all pairing calculations.
  • domain assumption Strutinsky shell corrections can be evaluated at finite temperature without additional temperature-dependent renormalization.
    Used to obtain the shell free-energy contribution.

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