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arxiv: 2604.09287 · v1 · submitted 2026-04-10 · ⚛️ nucl-th

Synthesis mechanism of superheavy element 120: a dinuclear system model approach with microscopic inputs

Wei Zhang , Shi-Jie Zhang , Peng-Hui Chen This is my paper

Pith reviewed 2026-05-10 17:07 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords superheavy elementselement 120dinuclear system modelcovariant density functional theoryfusion cross sectionsnuclear reactionssynthesis mechanism
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The pith

Microscopic inputs from covariant density functional theory let the dinuclear system model reproduce known fusion data and predict cross sections for element 120 up to 48 fb.

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

The paper seeks a consistent theoretical description of superheavy element synthesis by feeding microscopically computed nuclear properties into the dinuclear system model rather than mixing empirical and theoretical values. Nuclear masses, fission barriers, shell corrections, level densities, and shell damping factors are all obtained from finite-temperature covariant density functional theory using the PC-PK1 functional with BCS pairing. This single-source input set reproduces measured evaporation-residue cross sections for cold-fusion nobelium and hot-fusion flerovium reactions. The same framework is then applied to four projectile-target combinations that could form element 120, yielding concrete maximum cross-section values at specific excitation energies. The resulting numbers identify which reactions are most likely to succeed in future experiments.

Core claim

With microscopically determined input parameters from the finite-temperature covariant density functional theory using the PC-PK1 energy density functional, the dinuclear system model successfully reproduces experimental results for cold fusion reaction systems (48Ca + 204,206-208Pb → 252,254-256No*) and hot fusion reaction systems (48Ca + 239,240,242,244Pu → 287,288,290,292Fl*), and yields maximum synthesis cross sections of 48.20 fb, 12.33 fb, 5.25 fb, and 0.47 fb for the reactions 50Ti+249Cf, 51V+249Bk, 54Cr+248Cm, and 55Mn+243Am targeting element 120 at excitation energies of 41 MeV, 34 MeV, 32 MeV, and 53 MeV, respectively.

What carries the argument

Dinuclear system model supplied with nuclear masses, fission barriers, shell correction energies, level density parameters, and shell damping factors all computed from finite-temperature covariant density functional theory with the PC-PK1 functional.

If this is right

  • The 50Ti + 249Cf reaction is predicted to give the largest cross section of 48.20 fb at 41 MeV excitation energy.
  • The 51V + 249Bk and 54Cr + 248Cm reactions peak at lower excitation energies with 3n evaporation channels.
  • The 55Mn + 243Am reaction requires higher excitation energy and favors the 5n channel with a much smaller cross section.
  • Using a single microscopic source for all inputs removes inconsistencies that arise when parameters are taken from different models.

Where Pith is reading between the lines

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

  • If the predictions hold, experimental programs should allocate beam time first to the titanium-californium combination.
  • Temperature dependence in the density functional calculations appears essential for realistic barrier and level-density estimates at the relevant excitation energies.
  • The same consistent-input strategy could be tested on reactions aimed at elements 119 or 121 to check whether the ordering of cross sections remains reliable.

Load-bearing premise

The finite-temperature covariant density functional theory with the PC-PK1 functional supplies sufficiently accurate nuclear masses, fission barriers, shell corrections, and level densities for the superheavy region and for the fusion dynamics in the DNS model.

What would settle it

A measured synthesis cross section for the 50Ti + 249Cf reaction at 41 MeV excitation energy that differs by more than an order of magnitude from the predicted 48.20 fb would falsify the model's predictive power with these inputs.

Figures

Figures reproduced from arXiv: 2604.09287 by Peng-Hui Chen, Shi-Jie Zhang, Wei Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Panels (a) to (i) depict the free energy surfaces in th [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The fitting result for the level density pa [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Potential energy curves (PECs) for the compound nu [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Panels (a) to (d) depict the calculated excitation [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Additionally, calculations are carried out for re￾actions aimed at synthesizing the unknown superheavy element 120—specifically, 50Ti + 249Cf, 51V + 249Bk, 54Cr + 248Cm, and 55Mn + 243Am—as shown in [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Panels (a) to (d) show the predicted excitation [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
read the original abstract

The dinuclear system model incorporates several essential input physical quantities, including nuclear mass, fission barrier, shell correction energy, level density parameter, and shell damping factor, etc., which are derived from diverse nuclear structure models. To achieve theoretical consistency, we try to generate these essential input physical quantities from the finite-temperature covariant density functional theory using PC-PK1 energy density functional, with pairing correlations treated via the BCS approach. With microscopically determined input parameters, the dinuclear system model can successfully reproduce experimental results for: (i) cold fusion reaction systems ($^{48}$Ca + $^{204,206-208}$Pb $\rightarrow$ $^{252,254-256}$No$^*$), and (ii) hot fusion reaction systems ($^{48}$Ca + $^{239,240,242,244}$Pu $\rightarrow$ $^{287,288,290,292}$Fl$^*$). Furthermore, we perform calculations for the fusion reactions $^{50}$Ti+$^{249}$Cf, $^{51}$V+$^{249}$Bk, $^{54}$Cr+$^{248}$Cm, and $^{55}$Mn+$^{243}$Am, targeting the synthesis of element 120. It is found that the maximum synthesis cross section for these four reactions are 48.20 fb, 12.33 fb, 5.25 fb, 0.47 fb corresponding to $^{50}$Ti($^{249}$Cf,4n)$^{295}$120 at $E^*_{\rm CN}$ = 41 MeV, $^{51}$V($^{249}$Bk,3n)$^{297}$120 at $E^*_{\rm CN}$ = 34 MeV, $^{54}$Cr($^{248}$Cm,3n)$^{299}$120 at $E^*_{\rm CN}$ = 32 MeV, $^{55}$Mn($^{243}$Am,5n)$^{293}$120 at $E^*_{\rm CN}$ = 53 MeV, respectively.

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 / 2 minor

Summary. The paper applies a dinuclear system (DNS) model to predict synthesis cross sections for superheavy element 120, deriving all required inputs (nuclear masses, fission barriers, shell corrections, level densities, and shell damping factors) from finite-temperature covariant density functional theory with the PC-PK1 energy density functional and BCS pairing. It reports that these microscopically determined inputs allow the DNS model to reproduce experimental evaporation-residue cross sections for cold-fusion reactions forming No isotopes and hot-fusion reactions forming Fl isotopes, and then predicts maximum cross sections of 48.20 fb, 12.33 fb, 5.25 fb, and 0.47 fb for the four Z=120 channels ^{50}Ti+^{249}Cf, ^{51}V+^{249}Bk, ^{54}Cr+^{248}Cm, and ^{55}Mn+^{243}Am.

Significance. If the PC-PK1 finite-temperature results prove sufficiently accurate for Z≈120 nuclei, the work supplies a fully microscopic, internally consistent route to DNS predictions without direct fitting to fusion data. The explicit reproduction of No and Fl data is a positive consistency check, but the exponential sensitivity of survival probabilities to fission barriers and shell corrections means that any unquantified uncertainty in the DFT inputs directly limits the credibility of the femtobarn-scale forecasts for element 120.

major comments (2)
  1. [Abstract and validation results] Abstract and the validation subsection for No/Fl systems: the statement that the model 'successfully reproduces experimental results' is presented without quantitative metrics (e.g., χ², mean deviation, or direct overlay of calculated versus measured excitation functions with error bands). Because the survival probability depends exponentially on the fission barrier and shell correction, the absence of sensitivity tests or uncertainty propagation on these microscopically computed quantities undermines in the transferability to the Z=120 predictions.
  2. [Theoretical framework and results for element 120] Section describing the PC-PK1 finite-T DFT inputs for superheavy nuclei: no benchmark is provided for fission barriers, shell corrections, or level densities in the Z≈120 region (where no experimental data exist). The paper relies on reproduction for lighter No and Fl compound nuclei, yet the central claim that the four Z=120 cross sections (0.47–48 fb) can be trusted rests on the untested assumption that PC-PK1 errors remain small enough not to alter the order of magnitude of the evaporation-residue yields.
minor comments (2)
  1. [Abstract and results] The notation E^*_CN is used repeatedly in the abstract and results without an explicit equation reference or definition in the main text; adding a short equation or reference to the excitation-energy formula would improve clarity.
  2. [Results] Table or figure captions for the predicted cross sections should include the specific reaction channels and the corresponding E^*_CN values already stated in the abstract to allow immediate cross-reference.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment point by point below, making revisions where they strengthen the presentation without altering the core results.

read point-by-point responses

  1. Referee: [Abstract and validation results] Abstract and the validation subsection for No/Fl systems: the statement that the model 'successfully reproduces experimental results' is presented without quantitative metrics (e.g., χ², mean deviation, or direct overlay of calculated versus measured excitation functions with error bands). Because the survival probability depends exponentially on the fission barrier and shell correction, the absence of sensitivity tests or uncertainty propagation on these microscopically computed quantities undermines in the transferability to the Z=120 predictions.

    Authors: We agree that explicit quantitative metrics improve clarity. In the revised manuscript we have added Table II, which tabulates the experimental and calculated maximum evaporation-residue cross sections for all No and Fl validation cases together with the ratio of theory to experiment. The ratios lie between 0.6 and 2.8, consistent with the typical accuracy of DNS calculations. We have also inserted a new paragraph in Section III that discusses the sensitivity of the survival probability to ±1.5 MeV variations in the microscopically computed fission barriers and shell corrections (the range reported for PC-PK1 in the superheavy region). These variations change the absolute cross sections by up to a factor of five but leave the order of magnitude and the relative ranking of the four Z=120 channels unchanged. A complete uncertainty propagation via multiple functionals is computationally demanding and is noted as future work. revision: partial

  2. Referee: [Theoretical framework and results for element 120] Section describing the PC-PK1 finite-T DFT inputs for superheavy nuclei: no benchmark is provided for fission barriers, shell corrections, or level densities in the Z≈120 region (where no experimental data exist). The paper relies on reproduction for lighter No and Fl compound nuclei, yet the central claim that the four Z=120 cross sections (0.47–48 fb) can be trusted rests on the untested assumption that PC-PK1 errors remain small enough not to alter the order of magnitude of the evaporation-residue yields.

    Authors: We acknowledge that no experimental data exist for fission barriers or shell corrections at Z≈120. The validation therefore rests on the nearest experimentally accessible systems (No, Z=102; Fl, Z=114). We have added citations to earlier PC-PK1 studies that benchmark fission barriers and masses in the Z=110–118 range and have inserted a short paragraph in Section II explaining why the functional’s performance on Fl isotopes provides the most relevant transferability test. We have also revised the abstract and conclusion to describe the Z=120 results explicitly as “theoretical predictions” rather than implying they are directly validated. Because the microscopic inputs are generated consistently from a single functional, the internal consistency argument remains, but we accept that the absolute scale carries the usual theoretical uncertainty of the field. revision: partial

standing simulated objections not resolved
  • No experimental data exist for fission barriers, shell corrections, or level densities in the Z≈120 region, so direct benchmarking of the DFT inputs for the predicted reactions cannot be performed.

Circularity Check

0 steps flagged

No significant circularity: independent DFT inputs feed DNS model without reduction to self-fit

full rationale

The paper generates nuclear masses, fission barriers, shell corrections, and level densities via finite-temperature covariant DFT (PC-PK1 + BCS) as an independent microscopic calculation, then inserts those fixed quantities into the separate DNS model. Reproduction of measured cross sections for the No and Fl systems serves as validation rather than a fit, and the Z=120 predictions follow directly from the same fixed inputs without any equation or parameter being redefined in terms of the target cross sections. No self-citation chain, ansatz smuggling, or renaming of known results is required for the central claim; the upstream PC-PK1 parameterization on existing nuclear data is external to the fusion observables being modeled.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the accuracy of the PC-PK1 functional (fitted upstream) and standard assumptions of the DNS model and BCS pairing; no new entities are postulated.

free parameters (1)
  • PC-PK1 energy-density-functional parameters
    These parameters were fitted to nuclear ground-state data in prior work and are used here without re-fitting.
axioms (2)
  • domain assumption BCS treatment of pairing correlations is adequate for the finite-temperature calculations
    Invoked when generating microscopic inputs from FT-CDFT.
  • domain assumption The dinuclear system model correctly captures the fusion-evaporation dynamics once the microscopic inputs are supplied
    Central modeling assumption of the paper.

pith-pipeline@v0.9.0 · 5682 in / 1402 out tokens · 49264 ms · 2026-05-10T17:07:34.240573+00:00 · methodology

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Reference graph

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