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arxiv: 2510.18199 · v2 · submitted 2025-10-21 · ⚛️ nucl-th

Nonlocality Effect in the Tunneling of Alpha Radioactivity with the Aid of Machine Learning

Jinyu Hu , Chen Wu This is my paper

Pith reviewed 2026-05-18 05:32 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords alpha decaynonlocality effecttwo-potential approachmachine learningsuperheavy nucleihalf-life predictiondecision tree regressionXGBRegressor
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The pith

Machine learning models that include alpha nonlocality cut prediction errors for superheavy nuclei by more than half.

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

The authors extend the nonlocality effect of alpha particles into the two-potential approach for tunneling calculations. They then train three regression models on reference half-life data and find that decision tree regression and XGBRegressor match the data far better than the basic approach. These models lower the standard deviation by 54.5 percent and 53.7 percent respectively. The trained models are applied to forecast half-lives of twenty even-even nuclei with Z equal to 118 and 120. The forecasts line up with results from the improved Deng-Zhang-Royer model and the New+D empirical formula that includes deformation.

Core claim

Integrating the coordinate-dependent effective mass arising from alpha-particle nonlocality into the two-potential approach, then optimizing the resulting predictions with decision tree regression and XGBRegressor, produces half-life values whose standard deviation is reduced by roughly 54 percent relative to the unmodified TPA; when these models are used to predict half-lives for even-even nuclei at Z=118 and Z=120, the outputs remain generally consistent with the eight-parameter Deng-Zhang-Royer formula and the New+D expression that accounts for nuclear deformation.

What carries the argument

The coordinate-dependent effective mass of the alpha particle inside the two-potential approach, further refined by decision tree regression and XGBRegressor models trained on reference decay data.

If this is right

  • The ML-refined models give closer agreement with measured half-lives for nuclei already studied.
  • Predictions for the twenty new superheavy nuclei remain consistent with two independent empirical formulas.
  • The decision tree model in particular tracks the New+D expression that includes deformation effects.
  • The approach supplies a practical route to estimate half-lives where direct measurement is still unavailable.

Where Pith is reading between the lines

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

  • If the models continue to perform well on future measurements, they could serve as a rapid screening tool before experiments on new superheavy elements are scheduled.
  • The same nonlocality-plus-ML pipeline might be tested on beta or cluster decay to see whether similar error reductions appear.
  • A modest expansion of the training set to include a few measured heavy nuclei could reduce the risk of extrapolation error for Z greater than 120.

Load-bearing premise

Machine learning models trained on lighter nuclei can be applied directly to predict half-lives of much heavier nuclei at Z=118 and Z=120 without large errors from limited training data or domain shift.

What would settle it

A new experimental measurement of the alpha-decay half-life for any even-even nucleus with Z=118 or Z=120 that deviates significantly from the numerical value predicted by the decision tree or XGBRegressor model.

Figures

Figures reproduced from arXiv: 2510.18199 by Chen Wu, Jinyu Hu.

Figure 1
Figure 1. Figure 1: FIG. 1. The difference in logarithmic form of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The difference in logarithmic form of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The contribution of the nonlocal effect on tunneling calculations. Selected example for [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The contribution of the nonlocal effect on tunneling calculations. Selected example for [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The contribution of the nonlocal effect on tunneling calculations. Selected example for [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The contribution of the nonlocal effect on tunneling calculations. Selected example for [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The predicted values of [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
read the original abstract

Recently, building upon the research findings of E. L. Medeiros, we have extended the alpha-particle non-locality effect to the two-potential approach (TPA). This extension demonstrates that the integration of the alpha-particle nonlocality effect into TPA yields relatively favorable results. In the present work, we employ machine learning methods to further optimize the aforementioned approach, specifically utilizing three classical machine learning models: decision tree regression, random forest regression, and XGBRegressor. Among these models, both the decision tree regression and XGBRegressor models exhibit the highest degree of agreement with the reference data, whereas the random forest regression model shows inferior performance. In terms of standard deviation, the results derived from the decision tree regression and XGBRegressor models represent improvements of 54.5% and 53.7%, respectively, compared to the TPA that does not account for the coordinate-dependent effective mass of alpha particles. Furthermore, we extend the decision tree regression and XGBRegressor models to predict the alpha-decay half-lives of 20 even-even nuclei with atomic numbers Z=118 and Z=120. Subsequently, the superheavy nucleus half-life predictions generated by our proposed models are compared with those from two established benchmarks: the improved eight-parameter Deng-Zhang-Royer (DZR) model and the new empirical expression (denoted as "New+D") proposed by V. Yu. Denisov, which explicitly incorporates nuclear deformation effects. Overall, the predictions from these models and formulas are generally consistent. Notably, the predictions of the decision tree regression model show a high level of consistency with those of the New+D expression, while the XGBRegressor model exhibits deviations from the other two comparative models.

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 extends the two-potential approach (TPA) for alpha decay by incorporating nonlocality effects via a coordinate-dependent effective mass. It then trains three machine-learning regressors (decision tree regression, random forest regression, XGBRegressor) on reference half-life data and reports that the decision-tree and XGB models reduce the standard deviation by 54.5% and 53.7% relative to the baseline TPA without nonlocality. The same models are applied to predict alpha-decay half-lives for 20 even-even nuclei at Z=118 and Z=120; the resulting predictions are compared with the eight-parameter Deng-Zhang-Royer (DZR) model and the New+D empirical formula that includes deformation, showing general consistency.

Significance. If the reported improvements are robust and the extrapolations reliable, the work would supply a practical data-driven route to refine alpha-decay predictions in the superheavy region where direct measurements remain sparse. The explicit comparison with two established benchmarks and the focus on even-even nuclei provide a clear testbed, but the absence of documented validation procedures substantially reduces the immediate significance.

major comments (2)
  1. The manuscript states that decision-tree regression and XGBRegressor yield 54.5% and 53.7% reductions in standard deviation relative to the TPA without coordinate-dependent effective mass, yet supplies no information on training-set size, cross-validation procedure, feature-selection criteria, or uncertainty quantification. This omission is load-bearing for the central claim of improvement, because without these details it is impossible to distinguish genuine generalization from overfitting to the reference data used for training.
  2. The predictions for the 20 even-even nuclei at Z=118 and Z=120 are obtained by direct extrapolation of models trained on lighter systems. No held-out validation on nuclei with Z values lying between the training distribution and Z=118 is presented, nor is any feature-importance or domain-shift analysis provided. This gap directly affects the reliability of the superheavy-nucleus results that constitute the paper’s principal application.
minor comments (2)
  1. The abstract and introduction refer to “the coordinate-dependent effective mass of alpha particles” without a concise equation or diagram showing how this mass enters the TPA potential; a short explicit definition would improve readability.
  2. Table or figure captions that list the 20 predicted nuclei should also indicate the range of Z and A values used in the original training set so that readers can immediately gauge the extrapolation distance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which have helped us clarify the methodological details and strengthen the presentation of our results. We address each major comment below and indicate the revisions made to the manuscript.

read point-by-point responses

  1. Referee: The manuscript states that decision-tree regression and XGBRegressor yield 54.5% and 53.7% reductions in standard deviation relative to the TPA without coordinate-dependent effective mass, yet supplies no information on training-set size, cross-validation procedure, feature-selection criteria, or uncertainty quantification. This omission is load-bearing for the central claim of improvement, because without these details it is impossible to distinguish genuine generalization from overfitting to the reference data used for training.

    Authors: We agree that the original manuscript did not provide sufficient documentation of the machine-learning procedures, which limits the ability to fully assess generalization. In the revised version we have added a new subsection that specifies the composition of the training set (experimentally known alpha-decay half-lives for even-even nuclei), the cross-validation protocol used, the physical criteria applied for feature selection, and the uncertainty estimates obtained from the ensemble methods. These additions directly address the concern and allow readers to evaluate the robustness of the reported standard-deviation improvements. revision: yes

  2. Referee: The predictions for the 20 even-even nuclei at Z=118 and Z=120 are obtained by direct extrapolation of models trained on lighter systems. No held-out validation on nuclei with Z values lying between the training distribution and Z=118 is presented, nor is any feature-importance or domain-shift analysis provided. This gap directly affects the reliability of the superheavy-nucleus results that constitute the paper’s principal application.

    Authors: We acknowledge that the application to Z=118 and Z=120 constitutes an extrapolation beyond the range of the training data and that intermediate validation would be desirable. In the revision we have included a feature-importance analysis for both the decision-tree and XGBRegressor models, together with an explicit discussion of the training domain and the consistency checks performed against the DZR and New+D benchmarks. While a dedicated held-out test on nuclei with intermediate Z was not originally reported, we have added a supplementary sensitivity test and a clear statement of the extrapolation limits in the discussion section. revision: partial

Circularity Check

0 steps flagged

No significant circularity in ML-based extension and extrapolation of TPA nonlocality model

full rationale

The paper extends prior nonlocality results from Medeiros into the two-potential approach (TPA) and then applies standard supervised regressors (decision tree, random forest, XGBRegressor) trained on reference alpha-decay half-lives for lighter nuclei. Reported improvements in standard deviation (54.5 % and 53.7 %) are explicit performance metrics of the trained models against the baseline TPA on the same reference set; these are not labeled or used as predictions. The subsequent half-life values for the 20 unmeasured Z=118 and Z=120 nuclei are extrapolations that are directly compared to two independent external benchmarks (improved DZR model and New+D expression). No load-bearing step reduces by construction to a self-definition, a fitted parameter renamed as a prediction, or a self-citation chain; the derivation remains self-contained against external benchmarks and does not invoke uniqueness theorems or ansatzes from the authors' own prior work.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The approach rests on standard nuclear tunneling assumptions plus fitted machine-learning parameters; no new physical entities are postulated.

free parameters (2)
  • coordinate-dependent effective mass function
    Introduced to capture non-locality inside the nucleus and adjusted within the two-potential framework.
  • machine-learning hyperparameters
    Tuned for decision tree, random forest, and XGBRegressor to minimize deviation from reference half-lives.
axioms (1)
  • domain assumption Alpha decay occurs by quantum tunneling through the Coulomb barrier
    Invoked as the physical mechanism underlying the two-potential approach.

pith-pipeline@v0.9.0 · 5843 in / 1577 out tokens · 79304 ms · 2026-05-18T05:32:07.254017+00:00 · methodology

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Reference graph

Works this paper leans on

46 extracted references · 46 canonical work pages · 1 internal anchor

  1. [1]

    Xingzhi College, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China Recently, building upon the research findings of E. L. Medeiros [1], we have extended theα-particle non- locality effect to the two-potential approach (TPA) [2]. This extension demonstrates that the integration of the α-particle nonlocality effect into TPA yields relatively favor...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  2. [2]

    E. L. Medeiros, N. Teruya, S. B. Duarte, and O. Tavares, Nonlo- cality effect inαdecay of heavy and superheavy nuclei, Physi- cal Review C106, 024608 (2022)

    work page 2022

  3. [3]

    Hu and C

    J. Hu and C. Wu, Nonlocality effect inαdecay half-lives for even-even nuclei within a two potential approach, The Euro- pean Physical Journal A61, 129 (2025)

    work page 2025

  4. [4]

    Deng, H.-F

    J.-G. Deng, H.-F. Zhang, and G. Royer, Improved empirical for- mula forα-decay half-lives, Physical Review C101, 034307 (2020)

    work page 2020

  5. [5]

    V . Y . Denisov, Empirical relations forα-decay half-lives: The effect of deformation of daughter nuclei, Physical Review C 110, 014604 (2024)

    work page 2024

  6. [6]

    R. W. Gurney and E. U. Condon, Wave mechanics and radioac- tive disintegration, Nature122, 439 (1928)

    work page 1928

  7. [7]

    Gamow, Zur quantentheorie des atomkernes, Zeitschrift für Physik51, 204 (1928)

    G. Gamow, Zur quantentheorie des atomkernes, Zeitschrift für Physik51, 204 (1928)

    work page 1928

  8. [8]

    Matsuse, M

    T. Matsuse, M. Kamimura, and Y . Fukushima, Study of the alpha-clustering structure of 20ne based on the resonating group method for 16o+α: Analysis of alpha-decay widths and the exchange kernel, Progress of Theoretical Physics53, 706 (1975)

    work page 1975

  9. [9]

    Wauters, N

    J. Wauters, N. Bijnens, P. Dendooven, M. Huyse, H. Y . Hwang, G. Reusen, J. von Schwarzenberg, P. Van Duppen, R. Kirchner, and E. Roeckl, Fine structure in the alpha decay of even-even nuclei as an experimental proof for the stability of the z= 82 magic shell at the very neutron-deficient side, Physical review letters72, 1329 (1994)

    work page 1994

  10. [10]

    Kucuk, A

    Y . Kucuk, A. Soylu, and L. Chamon, Role of the dynamical polarization potential in explaining theα+ 12c system at low energies, Nuclear Physics A994, 121665 (2020)

    work page 2020

  11. [11]

    Y . Wang, J. Cui, Y . Zhang, S. Zhang, and J. Gu, Competition betweenαdecay and proton radioactivity of neutron-deficient nuclei, Physical Review C95, 014302 (2017)

    work page 2017

  12. [12]

    Y . Xiao, S. Zhang, J. Cui, and Y . Wang,α-decay with extremely long half-lives, Indian Journal of Physics94, 527 (2020)

    work page 2020

  13. [13]

    B. Buck, A. Merchant, and S. Perez,αdecay calculations with a realistic potential, Physical Review C45, 2247 (1992)

    work page 1992

  14. [14]

    Duarte, O

    S. Duarte, O. Rodriguez, O. P. Tavares, M. Gonçalves, F. Gar- cía, and F. Guzmán, Cold fission description with constant and varying mass asymmetries, Physical Review C57, 2516 (1998)

    work page 1998

  15. [15]

    Goncalves and S

    M. Goncalves and S. Duarte, Effective liquid drop description for the exotic decay of nuclei, Physical Review C48, 2409 (1993). 7

    work page 1993

  16. [16]

    Basu, Role of effective interaction in nuclear disintegration processes, Physics Letters B566, 90 (2003)

    D. Basu, Role of effective interaction in nuclear disintegration processes, Physics Letters B566, 90 (2003)

    work page 2003

  17. [17]

    P. R. Chowdhury, C. Samanta, and D. Basu,αdecay half- lives of new superheavy elements, Physical Review C—Nuclear Physics73, 014612 (2006)

    work page 2006

  18. [18]

    L. Ma, Z. Zhang, Z. Gan, X. Zhou, H. Yang, M. Huang, C. Yang, M. Zhang, Y . Tian, Y . Wang,et al., Short-livedα- emitting isotope np 222 and the stability of the n= 126 magic shell, Physical Review Letters125, 032502 (2020)

    work page 2020

  19. [19]

    Y . T. Oganessian, F. S. Abdullin, P. Bailey, D. Benker, M. Ben- nett, S. Dmitriev, J. G. Ezold, J. Hamilton, R. Henderson, M. Itkis,et al., Eleven new heaviest isotopes of elements z= 105 to z= 117 identified among the products of bk 249+ ca 48 reac- tions, Physical Review C—Nuclear Physics83, 054315 (2011)

    work page 2011

  20. [20]

    Y . T. Oganessian, V . Utyonkoy, Y . V . Lobanov, F. S. Abdullin, A. Polyakov, I. Shirokovsky, Y . S. Tsyganov, G. Gulbekian, S. Bogomolov, A. Mezentsev,et al., Experiments on the synthe- sis of element 115 in the reaction am 243 (ca 48, xn) 115 291- x, Physical Review C—Nuclear Physics69, 021601 (2004)

    work page 2004

  21. [21]

    Zhang, H

    Z. Zhang, H. Yang, M. Huang, Z. Gan, C. Yuan, C. Qi, A. An- dreyev, M. Liu, L. Ma, M. Zhang,et al., Newα-emitting iso- tope u 214 and abnormal enhancement ofα-particle cluster- ing in lightest uranium isotopes, Physical Review Letters126, 152502 (2021)

    work page 2021

  22. [22]

    Y . T. Oganessian, V . Utyonkov, Y . V . Lobanov, F. S. Abdullin, A. Polyakov, I. Shirokovsky, Y . S. Tsyganov, G. Gulbekian, S. Bogomolov, B. Gikal,et al., Observation of the decay of 292 116, Physical Review C63, 011301 (2000)

    work page 2000

  23. [23]

    Y . T. Oganessian, Synthesis of the heaviest elements in 48ca- induced reactions, Radiochimica Acta99, 429 (2011)

    work page 2011

  24. [24]

    Gurvitz and G

    S. Gurvitz and G. Kalbermann, Decay width and the shift of a quasistationary state, Physical review letters59, 262 (1987)

    work page 1987

  25. [25]

    B. Buck, A. Merchant, and S. Perez, Half-lives of favored alpha decays from nuclear ground states, Atomic Data and Nuclear Data Tables54, 53 (1993)

    work page 1993

  26. [26]

    Samanta, P

    C. Samanta, P. R. Chowdhury, and D. Basu, Predictions of al- pha decay half lives of heavy and superheavy elements, Nuclear Physics A789, 142 (2007)

    work page 2007

  27. [27]

    S. M. S. Ahmed, Alpha-cluster preformation factor within cluster-formation model for odd-a and odd–odd heavy nuclei, Nuclear Physics A962, 103 (2017)

    work page 2017

  28. [28]

    Zhang, W

    H. Zhang, W. Zuo, J. Li, and G. Royer,αdecay half-lives of new superheavy nuclei within a generalized liquid drop model, Physical Review C—Nuclear Physics74, 017304 (2006)

    work page 2006

  29. [29]

    Viola Jr and G

    V . Viola Jr and G. Seaborg, Nuclear systematics of the heavy elements—ii lifetimes for alpha, beta and spontaneous fission decay, Journal of Inorganic and Nuclear Chemistry28, 741 (1966)

    work page 1966

  30. [30]

    C. Qi, F. Xu, R. J. Liotta, and R. Wyss, Universal decay law in charged-particle emission and exotic cluster radioactivity, Phys- ical review letters103, 072501 (2009)

    work page 2009

  31. [31]

    Royer, Alpha emission andspontaneous fission through quasi-molecularshapes, Journal of Physics G: Nuclear and Par- ticle Physics26, 1149 (2000)

    G. Royer, Alpha emission andspontaneous fission through quasi-molecularshapes, Journal of Physics G: Nuclear and Par- ticle Physics26, 1149 (2000)

    work page 2000

  32. [32]

    Hofmann and G

    S. Hofmann and G. Münzenberg, The discovery of the heaviest elements, Reviews of Modern Physics72, 733 (2000)

    work page 2000

  33. [33]

    Hamilton, S

    J. Hamilton, S. Hofmann, and Y . T. Oganessian, Search for su- perheavy nuclei, Annual Review of Nuclear and Particle Sci- ence63, 383 (2013)

    work page 2013

  34. [34]

    Nazarewicz, The limits of nuclear mass and charge, Nature physics14, 537 (2018)

    W. Nazarewicz, The limits of nuclear mass and charge, Nature physics14, 537 (2018)

    work page 2018

  35. [35]

    S. A. Giuliani, Z. Matheson, W. Nazarewicz, E. Olsen, P.- G. Reinhard, J. Sadhukhan, B. Schuetrumpf, N. Schunck, and P. Schwerdtfeger, Colloquium: Superheavy elements: Oganes- son and beyond, Reviews of Modern Physics91, 011001 (2019)

    work page 2019

  36. [36]

    Jalili, F

    A. Jalili, F. Pan, J. P. Draayer, A.-X. Chen, and Z. Ren, -decay half-life predictions with support vector machine, Scientific Re- ports14, 30776 (2024)

    work page 2024

  37. [37]

    S. M. S. Ahmed, R. Yahaya, S. Radiman, and M. S. Yasir, Alpha-cluster preformation factors in alpha decay for even– even heavy nuclei using the cluster-formation model, Journal of Physics G: Nuclear and Particle Physics40, 065105 (2013)

    work page 2013

  38. [38]

    S. M. S. Ahmed, R. Yahaya, and S. Radiman, Clusteriza- tion probability in alpha-decay 212po nucleus within cluster- formation model; a new approach, Romanian Reports in Physics65, 1281 (2013)

    work page 2013

  39. [39]

    X.-D. Sun, P. Guo, and X.-H. Li, Systematic study ofαdecay half-lives for even-even nuclei within a two-potential approach, Physical Review C93, 034316 (2016)

    work page 2016

  40. [40]

    J. J. Morehead, Asymptotics of radial wave equations, Journal of Mathematical Physics36, 5431 (1995)

    work page 1995

  41. [41]

    X.-D. Sun, C. Duan, J.-G. Deng, P. Guo, and X.-H. Li, System- atic study ofαdecay for odd-a nuclei within a two-potential approach, Physical Review C95, 014319 (2017)

    work page 2017

  42. [42]

    Jaghoub, M

    M. Jaghoub, M. Hassan, and G. Rawitscher, Novel source of nonlocality in the optical model, Physical Review C—Nuclear Physics84, 034618 (2011)

    work page 2011

  43. [43]

    Zureikat and M

    R. Zureikat and M. Jaghoub, Surface and volume term nonlo- calities in the proton–nucleus elastic scattering process, Nuclear Physics A916, 183 (2013)

    work page 2013

  44. [44]

    Alameer, M

    S. Alameer, M. Jaghoub, and I. Ghabar, Nucleon-nucleus velocity-dependent optical model: Revisited, Journal of Physics G: Nuclear and Particle Physics49, 015106 (2021)

    work page 2021

  45. [45]

    Breiman, Random forests, Machine learning45, 5 (2001)

    L. Breiman, Random forests, Machine learning45, 5 (2001)

    work page 2001

  46. [46]

    Chen and C

    T. Chen and C. Guestrin, Xgboost: A scalable tree boosting system, inProceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining(2016) pp. 785–794. 8 FIG. 3. The contribution of the nonlocal effect on tunneling calculations. Selected example forα-decay from 108 54 Xe : (a) effective reduced massµconsidering nonlocali...

    work page 2016