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arxiv: 2510.05726 · v1 · submitted 2025-10-07 · ⚛️ nucl-th · astro-ph.SR· hep-th· nucl-ex

Microscopic study of nuclei synthesis in pycnonuclear reaction ¹²C + ¹²C in neutron stars

S.P. Maydanyuk (1 , 2) , Ju-Jun Xie (1 , 3 , 4) , V.S. Vasilevsky (5) , K.A. Shaulskyi (2) ((1) Southern Center for Nuclear-Science Theory (SCNT) , Institute of Modern Physics
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Chinese Academy of Sciences Huizhou 516000 China (2) Institute for Nuclear Research National Academy of Sciences of Ukraine Kyiv 03680 Ukraine (3) Heavy Ion Science Technology Key Laboratory Lanzhou 730000 (4) School of Nuclear Sciences Technology University of Chinese Academy of Sciences Beijing 101408 (5) Bogolyubov Institute for Theoretical Physics Metrolohichna str. 14b 03143 Ukraine)
This is my paper

Pith reviewed 2026-05-18 09:20 UTC · model grok-4.3

classification ⚛️ nucl-th astro-ph.SRhep-thnucl-ex
keywords pycnonuclear reactionsneutron stars12C + 12C fusioncompound nucleus formationfolding potentialquasibound states24Mg synthesiscluster model
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The pith

Compound nucleus formation from carbon collisions is far more probable in quasibound states than zero-point vibrations inside neutron stars.

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

The authors study how two carbon-12 nuclei can fuse into magnesium-24 during pycnonuclear reactions in the extremely dense matter of neutron stars. They apply a microscopic folding model based on nucleon-nucleon forces and shell-model descriptions of the nuclei, then use the multiple internal reflections method to track the probability of compound nucleus formation. Their calculations reveal pronounced peaks in this probability at the lowest quasibound energies, which fall below the top of the interaction barrier. Because of the remaining barrier, the newly formed system cannot easily tunnel apart and remains as an excited 24Mg nucleus. This picture changes noticeably from earlier work that relied on a simple Woods-Saxon potential.

Core claim

The wave functions of resonance states of 24Mg are set by the interaction between two 12C nuclei. Clear maxima appear in the probability of compound-nucleus formation at the first quasibound energies. These energies lie below the barrier maximum, so the compound system is held by a barrier that blocks decay by tunneling. This produces a new excited nucleus 24Mg inside the neutron star. The folding potential built from a semi-realistic nucleon-nucleon interaction and shell-model wave functions for p-shell nuclei gives results that differ essentially from those obtained with a Woods-Saxon potential.

What carries the argument

Folding potential derived from semi-realistic nucleon-nucleon interaction and shell-model wave functions for p-shell nuclei, together with the multiple internal reflections method for calculating formation probabilities.

Load-bearing premise

The folding potential built from semi-realistic nucleon-nucleon interaction and shell-model wave functions for p-shell nuclei correctly describes the effective force between two carbon nuclei in dense stellar matter, while the multiple internal reflections method gives the true formation probability without extra medium corrections.

What would settle it

Finding that the lowest quasibound energy for the 12C + 12C system exceeds the barrier maximum, or that formation probability is larger in zero-point vibration states than in quasibound states, would show the proposed mechanism for stable 24Mg synthesis does not hold.

Figures

Figures reproduced from arXiv: 2510.05726 by 03143, 03680, 14b, 2), (2) Institute for Nuclear Research, 3, (3) Heavy Ion Science, 4), (4) School of Nuclear Sciences, (5) Bogolyubov Institute for Theoretical Physics, Beijing 101408, China, Chinese Academy of Sciences, Huizhou 516000, Institute of Modern Physics, Ju-Jun Xie (1, K.A. Shaulskyi (2) ((1) Southern Center for Nuclear-Science Theory (SCNT), Kyiv, Lanzhou 730000, Metrolohichna str., National Academy of Sciences of Ukraine, S.P. Maydanyuk (1, Technology, Technology Key Laboratory, Ukraine, Ukraine), University of Chinese Academy of Sciences, V.S. Vasilevsky (5).

Figure 1
Figure 1. Figure 1: FIG. 1: (Color online) Potential of interaction between two [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Folding potentials for the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (Color online) The potential of Woods-Saxon type [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The part of inter-cluster potential which is related [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: (Color online) Position of the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: (Color online) Phase shifts of the elastic scatterin [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: (Color online) Wave functions of the 0 [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: (Color online) The average distance netween cluster [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: (Color online) Spectrum of the eigenenergies of the [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: (Color online) Average distance [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: (Color online) Coefficients of penetrability [PITH_FULL_IMAGE:figures/full_fig_p015_15.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: (Color online) The folding potential with F-form in [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: (Color online) Resonant scattering [PITH_FULL_IMAGE:figures/full_fig_p016_17.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: (Color online) Probabilities of formation of com [PITH_FULL_IMAGE:figures/full_fig_p016_16.png] view at source ↗
read the original abstract

Purpose To investigate synthesis of nuclei in pycnonuclear reactions in dense medium of neutron stars on the basis of understanding, how the compound nucleus is formed during collision of two nuclei. To implement microscopic formulation of nuclear interactions and fusion in pycnonuclear reactions in dense medium. Methods (1) Nuclei synthesis in pycnonuclear reaction in dense medium of neutron star is investigated in the folding approximation of the cluster model. (2) Formation of compound nucleus in dense medium is studied with the method of Multiple Internal Reflections. Results (1) Wave functions of resonance states of $^{24}$Mg are determined by interaction of two $^{12}$C nuclei. (2) Clear maxima of probability of formation of compound nucleus in dense stellar medium are established at first time. (3) Difference between quasibound energies for potential of Woods-Saxon type and folding potentials with the shell-model approximation for wave functions is essential. (4) Formation of the compound nucleus is much more probable in the quasibound states than in states of zero-point vibrations. (5) Only the first quasibound energies for $^{12}$C + $^{12}$Care smaller than the barrier maximums. At these energies compound nuclear system has barrier which prevents its decay going through tunneling phenomenon. This is the new excited nucleus $^{24}$Mg synthesised in the neutron star. \item[Conclusions] Cluster approach with folding potential provides significant modification of picture of formation of compound nucleus, previously obtained concerning the potential of Woods-Saxon type. The highest precision is provided by the folding potential, created by semi-realistic nucleon-nucleon potential and shell-model description of the internal structure of interacting $p$-shell nuclei.

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 investigates nuclei synthesis in the pycnonuclear reaction 12C + 12C within the dense medium of neutron stars. It employs a microscopic folding potential constructed from a semi-realistic nucleon-nucleon interaction and shell-model wave functions for p-shell nuclei, combined with the multiple internal reflections (MIR) method, to compute resonance wave functions of 24Mg, identify probability maxima for compound-nucleus formation, and compare quasibound energies against the barrier maximum. The central conclusion is that compound-nucleus formation is far more probable in quasibound states than in zero-point vibrations, with only the lowest quasibound energies lying below the barrier, thereby stabilizing a new excited 24Mg state via tunneling suppression.

Significance. If the numerical results hold, the work supplies a parameter-sensitive but microscopically grounded alternative to phenomenological Woods-Saxon treatments of fusion in stellar interiors, potentially refining models of neutron-star crust nucleosynthesis. The explicit contrast between folding and Woods-Saxon potentials and the use of shell-model inputs constitute a clear methodological advance, though the absence of tabulated energies, probabilities, and convergence diagnostics limits immediate usability.

major comments (3)
  1. [Abstract / Results] Abstract and Results section: the claims that 'clear maxima of probability of formation of compound nucleus in dense stellar medium are established at first time' and that 'formation of the compound nucleus is much more probable in the quasibound states' rest on unshown numerical solutions of the MIR equations; no tables of quasibound energies, barrier heights, formation probabilities, or error estimates are supplied, preventing verification of the ordering relative to the barrier maximum.
  2. [Methods / Results] Methods and Results: the folding potential is built from fitted semi-realistic NN parameters and shell-model wave functions, yet the manuscript does not quantify how variations in these inputs (or the addition of electron-screening or lattice-polarization corrections appropriate to neutron-star densities) shift the quasibound energies relative to the barrier; this sensitivity directly affects the claim that only the first quasibound energies lie below the barrier maximum.
  3. [Results] Results: the statement that 'only the first quasibound energies for 12C + 12C are smaller than the barrier maximums' is presented without the corresponding numerical values, without a direct comparison table to the Woods-Saxon case, and without convergence checks on the MIR truncation, rendering the stabilization argument for the excited 24Mg untestable from the given text.
minor comments (2)
  1. [Abstract] Abstract: 'at first time' should read 'for the first time'; '12C + 12Care' is missing a space.
  2. [Methods] The manuscript would benefit from explicit statements of the MIR basis size, integration limits, and numerical precision used to locate the probability maxima.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and constructive feedback on our manuscript. We address each major comment point by point below, indicating revisions where the manuscript will be updated to improve verifiability and completeness while maintaining the focus of the original microscopic approach.

read point-by-point responses

  1. Referee: [Abstract / Results] Abstract and Results section: the claims that 'clear maxima of probability of formation of compound nucleus in dense stellar medium are established at first time' and that 'formation of the compound nucleus is much more probable in the quasibound states' rest on unshown numerical solutions of the MIR equations; no tables of quasibound energies, barrier heights, formation probabilities, or error estimates are supplied, preventing verification of the ordering relative to the barrier maximum.

    Authors: We agree that explicit numerical tabulation would strengthen verifiability of the claims. The probability maxima are derived from solutions of the MIR equations and are visualized in the figures, but we will add a dedicated table in the revised Results section listing the quasibound energies, barrier maxima, and formation probabilities for the key states. This will allow direct confirmation that formation is more probable in quasibound states than zero-point vibrations. No formal error estimates were part of the original analysis, but we will note the numerical stability of the MIR implementation. revision: yes

  2. Referee: [Methods / Results] Methods and Results: the folding potential is built from fitted semi-realistic NN parameters and shell-model wave functions, yet the manuscript does not quantify how variations in these inputs (or the addition of electron-screening or lattice-polarization corrections appropriate to neutron-star densities) shift the quasibound energies relative to the barrier; this sensitivity directly affects the claim that only the first quasibound energies lie below the barrier maximum.

    Authors: The parameters for the semi-realistic NN interaction and shell-model wave functions are taken from established literature values for p-shell nuclei, as described in the Methods. A full quantitative sensitivity study to input variations or inclusion of electron-screening and lattice-polarization effects at neutron-star densities would require extensive new computations outside the present scope. We will add a paragraph discussing the expected robustness, noting that such corrections are typically smaller than the differences between folding and phenomenological potentials already highlighted, and reference prior work on screening in dense media. revision: partial

  3. Referee: [Results] Results: the statement that 'only the first quasibound energies for 12C + 12C are smaller than the barrier maximums' is presented without the corresponding numerical values, without a direct comparison table to the Woods-Saxon case, and without convergence checks on the MIR truncation, rendering the stabilization argument for the excited 24Mg untestable from the given text.

    Authors: We accept that the absence of tabulated values and a direct comparison limits immediate testability. In the revision we will insert a table in the Results section with the quasibound energies for the folding potential, the corresponding Woods-Saxon values, and the barrier maxima, explicitly showing that only the lowest quasibound states lie below the barrier. We will also add a statement confirming that the MIR truncation parameter was chosen to achieve convergence of resonance positions to better than the precision needed for the stabilization conclusion. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results are computed outputs from independent microscopic model

full rationale

The paper applies a folding potential built from a semi-realistic NN interaction plus shell-model wave functions for p-shell nuclei, together with the multiple internal reflections method, to compute quasibound energies, barrier comparisons, and formation probabilities for the 12C+12C system. The reported findings—that formation is more probable in quasibound states, that only the lowest quasibound energies lie below barrier maxima, and that these differ substantially from Woods-Saxon results—are direct numerical outputs of this framework rather than redefinitions or statistical forcings of the inputs. No equations reduce the target claims to prior fits by construction, and the model choices remain externally falsifiable against nuclear structure data and alternative potentials without self-referential loops.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central results rest on the cluster-model folding approximation and the shell-model description of the internal structure of the colliding nuclei; both are taken from prior nuclear-structure literature rather than derived inside the paper.

free parameters (2)
  • parameters of the semi-realistic nucleon-nucleon potential
    Used to construct the folding potential; values are chosen to reproduce known nuclear properties.
  • parameters of the Woods-Saxon potential
    Used for comparison; standard phenomenological parameters fitted to scattering data.
axioms (2)
  • domain assumption Shell-model wave functions adequately describe the internal structure of p-shell nuclei such as 12C
    Invoked to generate the folding potential in the cluster model.
  • domain assumption The folding approximation remains valid inside the dense medium of a neutron star
    Basis for applying the microscopic interaction to pycnonuclear conditions.

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