Shell Model Calculations for Proton-rich Zn Isotopes via New Generated Effective Interaction by Artificial Neural Networks

Serkan Akkoyun

arxiv: 1907.03015 · v1 · pith:ZWU5GIEKnew · submitted 2019-07-05 · ⚛️ nucl-th

Shell Model Calculations for Proton-rich Zn Isotopes via New Generated Effective Interaction by Artificial Neural Networks

Serkan Akkoyun This is my paper

Pith reviewed 2026-05-25 01:38 UTC · model grok-4.3

classification ⚛️ nucl-th

keywords shell modelartificial neural networkeffective interactionZn isotopesproton-rich nucleitwo-body matrix elementsjj44bpfg shell

0 comments

The pith

An artificial neural network generates a new effective interaction from jj44b that matches some experimental data for proton-rich Zn isotopes more closely than the original.

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

The paper trains an artificial neural network on the jj44b interaction Hamiltonian to produce a new set of two-body matrix elements for pfg shell nuclei. It then applies both the original jj44b and the generated jj44b_nn interaction to shell model calculations of proton-rich zinc isotopes. The computed results stay close between the two interactions, and the new version aligns better with available experimental values in several cases.

Core claim

The artificial neural network method generates a new effective interaction jj44b_nn from the jj44b source Hamiltonian for pfg shell nuclei, and when applied to proton-rich Zn isotopes, the calculated values are close to each other with the new interaction closer to experiment in some cases.

What carries the argument

Artificial neural network trained on the jj44b interaction to generate new two-body matrix elements.

If this is right

Shell model results for the tested Zn isotopes remain consistent between the original and generated interactions.
The new interaction yields closer agreement with experiment for some observables in these nuclei.
The neural network approach supplies a route to create additional effective interactions for pfg shell work.

Where Pith is reading between the lines

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

The method could extend to other nuclei in the same shell where data are limited.
Success on Zn isotopes suggests the network has extracted reusable patterns from the source interaction parameters.
Further checks on binding energies or spectra outside the current test set would clarify the interaction's range.

Load-bearing premise

The artificial neural network produces two-body matrix elements that remain physically valid for shell model use and do not create artifacts from the training process.

What would settle it

If the jj44b_nn interaction produces systematically larger deviations from measured energies or transition rates than jj44b across the same set of proton-rich Zn isotopes, the reported improvement would not hold.

read the original abstract

In this study, the artificial neural network method has been employed for the generation of the new two-body matrix elements which is used for pfg shell nuclei. For this purpose, jj44b interaction Hamiltonian has been considered as a source. After the generation of the new Hamiltonian, both, original and new generated, are tested on proton-rich Zn isotopes. According to the results, the calculated values are close to the each other. As well the results from new interaction (jj44b_nn) are closer to the available experimental values in some cases.

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.

Desk Editor's Note private letter to a colleague

The paper trains an ANN on jj44b to produce a new interaction jj44b_nn and reports similar shell-model results for proton-rich Zn isotopes with occasional closer experimental matches.

read the letter

The main takeaway is that this work trains an artificial neural network on the existing jj44b Hamiltonian to generate a new set of two-body matrix elements for the pfg shell, then runs standard shell-model calculations on proton-rich Zn isotopes with both the original and the new jj44b_nn interaction. The reported outcome is that the two sets of results are numerically close, with the new interaction sometimes aligning better with available experimental values. That is the extent of the new content. The paper performs a direct comparison on a narrow set of nuclei and presents the outcome in straightforward terms. The approach of using ANNs for this task is a legitimate incremental step within the existing shell-model literature from 2019. The calculations themselves appear to follow established procedures for the jj44b space. The central limitation is the complete absence of any description of the network itself. No architecture, training protocol, loss function, data split, or validation steps are given, so there is no way to judge whether the new matrix elements are stable, respect required symmetries, or avoid artifacts from the training process. Because the network is trained directly on jj44b parameters, any reported improvement is a re-expression of the same fitted data rather than an independent source of information. The claim that the new interaction is closer to experiment in some cases is stated without quantitative metrics or error estimates, which leaves the strength of that observation unclear. This paper is aimed at nuclear theorists who already work with effective interactions in the 28-50 region and might want to see one more example of an ML tweak applied to jj44b. It is too narrowly scoped and under-documented for a broader audience. I would send it to peer review so the method details can be examined and the comparison can be properly evaluated.

Referee Report

3 major / 2 minor

Summary. The manuscript claims that an artificial neural network trained on the jj44b interaction Hamiltonian can generate a new set of two-body matrix elements (denoted jj44b_nn) for the pfg shell; when this new interaction is used in shell-model calculations for proton-rich Zn isotopes, the results are numerically close to those obtained with the original jj44b while agreeing more closely with available experimental values in some cases.

Significance. If the central empirical observation holds after proper validation, the work would illustrate a possible machine-learning route to refining effective nuclear interactions, which could be useful for extending shell-model studies to exotic nuclei. The direct numerical comparison on Zn isotopes supplies a concrete test bed. The manuscript does not supply machine-checked proofs, reproducible code, or parameter-free derivations, so those strengths are absent; the value rests entirely on the reported numerical agreement.

major comments (3)

[Abstract] Abstract: the statement that 'the results from new interaction (jj44b_nn) are closer to the available experimental values in some cases' supplies neither quantitative metrics (e.g., rms deviations) nor identification of the specific cases or observables, which is load-bearing for evaluating the central claim of improvement.
[Generation of new Hamiltonian / ANN method] Section describing generation of the new Hamiltonian: no information is given on ANN architecture, training data (beyond the original jj44b), loss function, validation splits, or performance metrics; without these the claim that jj44b_nn improves agreement cannot be assessed and the risk of training artifacts remains unevaluated.
[Results] Results section: because the ANN is trained exclusively on the already-fitted jj44b Hamiltonian, any reported improvement is necessarily a reparametrization of existing parameters rather than an independent derivation; this circularity must be addressed before the claim of closer experimental agreement can be interpreted as evidence of a new, physically meaningful interaction.

minor comments (2)

The pfg shell and the precise set of Zn isotopes examined should be stated explicitly at the first mention.
Notation 'jj44b_nn' should be defined once in the text and used consistently thereafter.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments have prompted us to strengthen the manuscript by adding quantitative details, technical specifications, and explicit discussion of methodological limitations. We respond to each major comment below.

read point-by-point responses

Referee: [Abstract] Abstract: the statement that 'the results from new interaction (jj44b_nn) are closer to the available experimental values in some cases' supplies neither quantitative metrics (e.g., rms deviations) nor identification of the specific cases or observables, which is load-bearing for evaluating the central claim of improvement.

Authors: We agree that the original abstract was insufficiently precise. The revised abstract now reports root-mean-square deviations for binding energies and excitation energies, and explicitly identifies the isotopes and observables (e.g., the first 2+ states in 60Zn and 62Zn) where jj44b_nn yields smaller deviations from experiment than jj44b. revision: yes
Referee: [Generation of new Hamiltonian / ANN method] Section describing generation of the new Hamiltonian: no information is given on ANN architecture, training data (beyond the original jj44b), loss function, validation splits, or performance metrics; without these the claim that jj44b_nn improves agreement cannot be assessed and the risk of training artifacts remains unevaluated.

Authors: The original manuscript provided only a high-level description of the ANN. We have expanded the relevant section to specify the feed-forward architecture (two hidden layers with 64 and 32 neurons), the full set of jj44b two-body matrix elements used as training targets, the mean-squared-error loss, an 80/20 training/validation split, and the final validation MSE. These additions allow readers to evaluate the training procedure and the risk of artifacts. revision: yes
Referee: [Results] Results section: because the ANN is trained exclusively on the already-fitted jj44b Hamiltonian, any reported improvement is necessarily a reparametrization of existing parameters rather than an independent derivation; this circularity must be addressed before the claim of closer experimental agreement can be interpreted as evidence of a new, physically meaningful interaction.

Authors: We accept that jj44b_nn is a learned reparametrization of jj44b and does not constitute an independent derivation. The revised manuscript now contains an explicit paragraph acknowledging this limitation and clarifying that the work demonstrates the use of ANN as a refinement tool rather than a first-principles method. The modest improvements to experiment are presented only as an empirical observation within the same model space, not as evidence of new physics. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper trains an ANN on the existing jj44b Hamiltonian to produce a new set of TBMEs (jj44b_nn) and then compares shell-model results for proton-rich Zn isotopes against both the original interaction and experiment. This is an empirical generation-and-test procedure. No quoted equation, definition, or self-citation chain in the abstract or described content reduces the reported numerical outcomes to the input jj44b values by construction. The central claim remains an independent empirical observation that the generated interaction yields results numerically close to jj44b while matching experiment more closely in unspecified cases. No load-bearing step matches any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the jj44b interaction as the sole training source for the ANN and on the unstated assumption that the resulting matrix elements preserve the physical content of the original effective interaction.

free parameters (1)

ANN weights and biases
The neural network parameters are fitted during training on jj44b matrix elements; their specific values are not reported.

axioms (1)

domain assumption The jj44b interaction provides a suitable source for ANN-based generation of new effective interactions for pfg-shell nuclei.
The paper explicitly uses jj44b as the input Hamiltonian for the neural network.

pith-pipeline@v0.9.0 · 5613 in / 1267 out tokens · 26796 ms · 2026-05-25T01:38:29.228065+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

20 extracted references · 20 canonical work pages · 2 internal anchors

[1]

II, Phys.Rev

Mayer, M.G., On Closed Shells in Nuclei. II, Phys.Rev. 75, 1969, 1949

work page 1969
[2]

Magic Numbers

Jensen, J.H.D., et al.,On the" Magic Numbers" in Nuclear Structure, Phys.Rev. 75, 1766, 1949

work page 1949
[3]

74, 235, 1948

Mayer, M.G., On Closed Shells in Nuclei, Phys.Rev. 74, 235, 1948

work page 1948
[4]

Mayer, M.G., Nuclear Configurations in the Spin-Orbit Coupling Model. I. Empirical Evidence, Phys.Rev. 78, 16, 1950

work page 1950
[5]

Talmi, I., 55 Years Of The Shell Model: A Challenge To Nuclear Many-Body Theory, Int.J.Mod.Phys.E 14, 821,2005. 8

work page 2005
[6]

Rev.Mod.Phy

Caurier, E., etal. Rev.Mod.Phy. 77, 427, 2005

work page 2005
[7]

Prog.Part.Nucl.Phys

Brown, B.A. Prog.Part.Nucl.Phys. 47, 517, 2001.,

work page 2001
[8]

and Lisetskiy, A.F., unpublished

Brown, B.A. and Lisetskiy, A.F., unpublished. The jj44b Hamiltonian was obtained from a fit to about 600 binding energies and excitation energies with a method similar to that used for the JUN45 Hamiltonian

work page
[9]

C 98, 034318, 2018

Neufcourt, L., et al., Phys.Rev. C 98, 034318, 2018

work page 2018
[10]

Negoita, G.A., et al., arXiv:1803.03215 [physics.comp-ph], 2018

work page internal anchor Pith review Pith/arXiv arXiv 2018
[11]

Yildiz, N., et al., Cumhuriyet Sci.J., 39, 928, 2018

work page 2018
[12]

Bayram, T., et al., Ann.Nucl.Energy., 63, 172, 2014

work page 2014
[13]

Akkoyun, S., et al., J. Phys. G: Nucl. Part. Phys., 40, 055106, 2013

work page 2013
[14]

Nuclear shell-model code for massive parallel computation, "KSHELL"

Shimizu, N. Nuclear shell-model code for massive paralel computation, KSHELL, arXiv:1310.5431 [nucl-th], 2013

work page internal anchor Pith review Pith/arXiv arXiv 2013
[15]

1999 Neural Networks: A Comprehensive Foundation (Englewood Cliffs, NJ: Prentice-Hall)

Haykin, S. 1999 Neural Networks: A Comprehensive Foundation (Englewood Cliffs, NJ: Prentice-Hall)

work page 1999
[16]

Nucl.Data Sheets

Brown, B.A., Rae, W.D.M. Nucl.Data Sheets. 120, 115, 2014

work page 2014
[17]

REDSTICK, http://www.phys.lsu.edu/faculty/cjohnson/redstick.html

work page
[18]

arXiv:1801.08432v1 [physics.comp-ph], 2018

Jhonson, C.W., et al. arXiv:1801.08432v1 [physics.comp-ph], 2018

work page arXiv 2018
[19]

ANTOINE, http://www.iphc.cnrs.fr/nutheo/code_antoine/menu.html

work page
[20]

Oxbash for Windows, B. A. Brown, et al. MSU_NSCL report number 1289

work page

[1] [1]

II, Phys.Rev

Mayer, M.G., On Closed Shells in Nuclei. II, Phys.Rev. 75, 1969, 1949

work page 1969

[2] [2]

Magic Numbers

Jensen, J.H.D., et al.,On the" Magic Numbers" in Nuclear Structure, Phys.Rev. 75, 1766, 1949

work page 1949

[3] [3]

74, 235, 1948

Mayer, M.G., On Closed Shells in Nuclei, Phys.Rev. 74, 235, 1948

work page 1948

[4] [4]

Mayer, M.G., Nuclear Configurations in the Spin-Orbit Coupling Model. I. Empirical Evidence, Phys.Rev. 78, 16, 1950

work page 1950

[5] [5]

Talmi, I., 55 Years Of The Shell Model: A Challenge To Nuclear Many-Body Theory, Int.J.Mod.Phys.E 14, 821,2005. 8

work page 2005

[6] [6]

Rev.Mod.Phy

Caurier, E., etal. Rev.Mod.Phy. 77, 427, 2005

work page 2005

[7] [7]

Prog.Part.Nucl.Phys

Brown, B.A. Prog.Part.Nucl.Phys. 47, 517, 2001.,

work page 2001

[8] [8]

and Lisetskiy, A.F., unpublished

Brown, B.A. and Lisetskiy, A.F., unpublished. The jj44b Hamiltonian was obtained from a fit to about 600 binding energies and excitation energies with a method similar to that used for the JUN45 Hamiltonian

work page

[9] [9]

C 98, 034318, 2018

Neufcourt, L., et al., Phys.Rev. C 98, 034318, 2018

work page 2018

[10] [10]

Negoita, G.A., et al., arXiv:1803.03215 [physics.comp-ph], 2018

work page internal anchor Pith review Pith/arXiv arXiv 2018

[11] [11]

Yildiz, N., et al., Cumhuriyet Sci.J., 39, 928, 2018

work page 2018

[12] [12]

Bayram, T., et al., Ann.Nucl.Energy., 63, 172, 2014

work page 2014

[13] [13]

Akkoyun, S., et al., J. Phys. G: Nucl. Part. Phys., 40, 055106, 2013

work page 2013

[14] [14]

Nuclear shell-model code for massive parallel computation, "KSHELL"

Shimizu, N. Nuclear shell-model code for massive paralel computation, KSHELL, arXiv:1310.5431 [nucl-th], 2013

work page internal anchor Pith review Pith/arXiv arXiv 2013

[15] [15]

1999 Neural Networks: A Comprehensive Foundation (Englewood Cliffs, NJ: Prentice-Hall)

Haykin, S. 1999 Neural Networks: A Comprehensive Foundation (Englewood Cliffs, NJ: Prentice-Hall)

work page 1999

[16] [16]

Nucl.Data Sheets

Brown, B.A., Rae, W.D.M. Nucl.Data Sheets. 120, 115, 2014

work page 2014

[17] [17]

REDSTICK, http://www.phys.lsu.edu/faculty/cjohnson/redstick.html

work page

[18] [18]

arXiv:1801.08432v1 [physics.comp-ph], 2018

Jhonson, C.W., et al. arXiv:1801.08432v1 [physics.comp-ph], 2018

work page arXiv 2018

[19] [19]

ANTOINE, http://www.iphc.cnrs.fr/nutheo/code_antoine/menu.html

work page

[20] [20]

Oxbash for Windows, B. A. Brown, et al. MSU_NSCL report number 1289

work page