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arxiv: 2510.04456 · v2 · submitted 2025-10-06 · ⚛️ nucl-ex · nucl-th

β-Delayed Proton Pandemonium: A first look at the ³¹Cl(β p γ)³⁰P decay scheme

Tamas Budner (1 , 2) , Moshe Friedman (3 , 4) , Lijie Sun (2 , 5) , Christopher Wrede (1 , B. Alex Brown (1
show 74 more authors
David P\'erez-Loureiro (3) Jason Surbrook (1 Alexander Adams (1 Yassid Ayyad (3 6) Daniel W. Bardayan (7) Kyungyuk Chae (8) Alan A. Chen (9) Kelly A. Chipps (10 11) Marco Cortesi (2) Brent Glassman (1 3) Matthew R. Hall (7) Molly Janasik (1 Johnson Liang (9) Patrick O'Malley (7) Emanuel Pollacco (12) Athanasios Psaltis (13) Jordan Stomps (1 Tyler Wheeler (1 2) ((1) Department of Physics Astronomy Michigan State University East Lansing MI 48824 USA (2) Facility for Rare Isotope Beams (3) National Superconducting Cyclotron Laboratory (4) Racah Institute of Physics Hebrew University Jerusalem Israel 91904 (5) School of Physics Shanghai Jiao Tong University Shanghai 200240 China (6) IGFAE Universidade de Santiago de Compostela E-15782 Santiago de Compostela Spain (7) Department of Physics University of Notre Dame Notre Dame IN 46556 (8) Department of Physics Sungkyunkwan University Suwon 440-746 Republic of Korea (9) Department of Physics McMaster University Hamilton ON L8S 4L8 Canada (10) Physics Division Oak Ridge National Laboratory Oak Ridge TN 37830-37831 (11) Department of Physics University of Tennessee Knoxville TN 37996 (12) D\'epartement de Physique Nucl\'eaire IRFU CEA Universit\'e Paris-Saclay F-91191 Gif-sur-Yvette France (13) Department of Physics Saint Mary's University Halifax NS B3H 3C3 Canada)
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Pith reviewed 2026-05-18 09:55 UTC · model grok-4.3

classification ⚛️ nucl-ex nucl-th
keywords beta decaydelayed protonsgamma ray coincidencesGamow-Teller transitionsnuclear decay scheme31Clshell model
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The pith

Coincident proton and gamma detection uncovers up to 20 new transitions in the 31Cl beta decay scheme.

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

This work measures the positron decay of 31Cl by recording beta-delayed protons and gamma rays in coincidence using the GADGET and SeGA detectors. Up to 20 previously unobserved proton transitions are identified, most feeding excited states in 30P. The first detailed decay scheme constructed this way shows improved agreement with shell-model calculations of the Gamow-Teller strength distribution for 31S states in the 7.5 to 9.5 MeV range. The results demonstrate that coincidence measurements are required to avoid missing branches and to enable reliable comparisons with nuclear theory.

Core claim

Using a fast beam of 31Cl deposited in a gas detector for protons and a germanium array for gammas, the experiment detects beta-p-gamma sequences. This reveals up to 20 new proton lines that populate excited states of 30P. The resulting decay scheme provides a more complete picture of beta feeding and yields better agreement with theoretical Gamow-Teller strengths than previous non-coincidence studies.

What carries the argument

Detection of beta-delayed protons in coincidence with gamma rays to assign transitions and extract beta feeding to specific states in 31S.

Load-bearing premise

The efficiency corrections and background subtractions in the proton and gamma detectors fully capture all relevant decay branches without significant missing or misidentified transitions.

What would settle it

Finding proton-gamma coincidence events corresponding to transitions not included in the reported scheme or observing a clear mismatch in Gamow-Teller strength distribution when using the new scheme.

Figures

Figures reproduced from arXiv: 2510.04456 by (10) Physics Division, 11), (11) Department of Physics, (12) D\'epartement de Physique Nucl\'eaire, (13) Department of Physics, 2), 2) ((1) Department of Physics, (2) Facility for Rare Isotope Beams, 3), (3) National Superconducting Cyclotron Laboratory, 4), (4) Racah Institute of Physics, 5), (5) School of Physics, 6), (6) IGFAE, (7) Department of Physics, (8) Department of Physics, (9) Department of Physics, Alan A. Chen (9), Alexander Adams (1, Astronomy, Athanasios Psaltis (13), B. Alex Brown (1, Brent Glassman (1, Canada, Canada), CEA, China, Christopher Wrede (1, Daniel W. Bardayan (7), David P\'erez-Loureiro (3), E-15782 Santiago de Compostela, East Lansing, Emanuel Pollacco (12), F-91191, France, Gif-sur-Yvette, Halifax, Hamilton, Hebrew University, IN 46556, IRFU, Israel 91904, Jason Surbrook (1, Jerusalem, Johnson Liang (9), Jordan Stomps (1, Kelly A. Chipps (10, Knoxville, Kyungyuk Chae (8), Lijie Sun (2, Marco Cortesi (2), Matthew R. Hall (7), McMaster University, MI 48824, Michigan State University, Molly Janasik (1, Moshe Friedman (3, Notre Dame, NS B3H 3C3, Oak Ridge, Oak Ridge National Laboratory, ON L8S 4L8, Patrick O'Malley (7), Republic of Korea, Saint Mary's University, Shanghai 200240, Shanghai Jiao Tong University, Spain, Sungkyunkwan University, Suwon 440-746, Tamas Budner (1, TN 37830-37831, TN 37996, Tyler Wheeler (1, Universidade de Santiago de Compostela, Universit\'e Paris-Saclay, University of Notre Dame, University of Tennessee, USA, Yassid Ayyad (3.

Figure 1
Figure 1. Figure 1: FIG. 1. Particle identification spectrum for the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Drift times of sub-200-keV, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Reconstructed beam spot representing the trans [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Observed [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: , which plots only the γ-ray events detected in co￾incidence with proton decays for which 1.2 < Ep(c.m.) < 1.3 MeV. In this proton-gated γ spectrum, there are six photopeaks that clearly stand out from the background, whose energies correspond to all known γ rays emitted in the decay of the first four excited states of 30P [40–43]. Conversely, by placing coincidence gates on all 30P* γ rays, we are able to… view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (Top) All observed coincidences between [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: to within a factor of ≲ 2 when accounting for γ-ray detection efficiency [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Proton Detector efficiencies comparing [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. The [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. The cumulative GT strength distribution for [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
read the original abstract

Positron decays of proton-rich nuclides exhibit large $Q$ values, producing complex cascades which often involve various radiations, including protons and $\gamma$ rays. Often, only one of the two are measured in a single experiment, limiting the accuracy and completeness of the decay scheme. An example is $^{31}$Cl, for which protons and $\gamma$ rays have been measured in detail individually but never with substantial sensitivity to proton-$\gamma$ coincidences. The purpose of this work is to provide detailed measurements of $^{31}$Cl $\beta$-delayed proton decay including $\beta$-$p$-$\gamma$ sequences, extract spectroscopic information on $^{31}$S excited states as well as their $\beta$ feeding, and compare to shell-model calculations. A fast, fragmented beam of $^{31}$Cl provided was deposited in the Gaseous Detector with Germanium Tagging (GADGET) system. GADGET's gas-filled Proton Detector was used to detect $\beta$-delayed protons, and the Segmented Germanium Array (SeGA) was used to detect $\beta$-delayed $\gamma$ rays. Up to 20 previously unobserved $\beta$-delayed proton transitions have been discovered, most of which populate excited states of $^{30}$P. Here present the first detailed $^{31}$Cl($\beta p \gamma$)$^{30}$P decay scheme and find improved agreement with theoretical calculations of the Gamow-Teller strength distribution for $^{31}$S excitation energies $7.5 < E_x < 9.5$ MeV. The present work demonstrates that the capability to detect $\beta$-delayed protons and $\gamma$ rays in coincidence is essential to construct accurate positron decay schemes for comparison to theoretical nuclear structure calculations. In some respects, this phenomenon for $\beta$-delayed protons resembles the pandemonium effect originally introduced for $\beta$-delayed $\gamma$ rays.

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 manuscript reports the first measurement of β-delayed proton-γ coincidences for 31Cl decay using the GADGET gaseous proton detector and SeGA germanium array at a fragmentation facility. The authors identify up to 20 previously unobserved β-delayed proton transitions (most feeding excited states in 30P), construct the first detailed 31Cl(βpγ)30P decay scheme, extract β feeding and Gamow-Teller strengths to 31S states, and report improved agreement with shell-model calculations for 31S excitation energies between 7.5 and 9.5 MeV. The work emphasizes the pandemonium-like character of the decay and the necessity of coincidence data for complete schemes.

Significance. If the coincidence analysis and efficiency corrections hold, the result is significant for nuclear structure studies of proton-rich sd-shell nuclei. It provides new spectroscopic information on 31S and 30P levels, demonstrates how p-γ coincidences mitigate the pandemonium effect in β-delayed proton decays, and supplies a more complete experimental GT strength distribution for direct comparison to theory. The methodological demonstration that single-radiation measurements are insufficient for accurate decay schemes is broadly useful for future experiments on exotic nuclei.

major comments (2)
  1. [Data Analysis and Results sections] The central claims of ~20 new transitions and improved GT agreement rest on the proton-γ coincidence identification after background subtraction and efficiency corrections. However, the manuscript provides insufficient quantitative detail on the analysis cuts, random-coincidence estimation, sideband modeling, and energy-dependent efficiency corrections (particularly in the 7.5–9.5 MeV region). This makes it difficult to assess whether a few reported lines could be artifacts or whether branching ratios are misassigned, directly affecting the 'first detailed' scheme and the quantitative improvement claim.
  2. [Discussion and Comparison to Theory] The extracted Gamow-Teller strengths and the statement of 'improved agreement' with shell-model calculations for 7.5 < Ex < 9.5 MeV lack a clear presentation of the full error budget, including systematic uncertainties from undetected weak branches and efficiency modeling. Without this, the improvement cannot be evaluated as statistically significant or robust against the pandemonium risk noted in the abstract.
minor comments (2)
  1. [Figure 3 and associated text] Figure captions and text should explicitly state the coincidence time window and energy gates used for the p-γ matrices to allow reproducibility.
  2. [Results] A table summarizing all observed proton transitions (new and previously known), their energies, branching ratios, and assigned 30P final states would improve clarity and facilitate comparison with prior work.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of the significance of this first coincidence measurement and for the constructive comments on analysis details and the Gamow-Teller comparison. We have revised the manuscript to incorporate additional quantitative information addressing both major points while preserving the original scientific claims.

read point-by-point responses

  1. Referee: [Data Analysis and Results sections] The central claims of ~20 new transitions and improved GT agreement rest on the proton-γ coincidence identification after background subtraction and efficiency corrections. However, the manuscript provides insufficient quantitative detail on the analysis cuts, random-coincidence estimation, sideband modeling, and energy-dependent efficiency corrections (particularly in the 7.5–9.5 MeV region). This makes it difficult to assess whether a few reported lines could be artifacts or whether branching ratios are misassigned, directly affecting the 'first detailed' scheme and the quantitative improvement claim.

    Authors: We agree that more explicit quantitative documentation will strengthen the presentation. In the revised manuscript we have expanded the Data Analysis section with a dedicated paragraph (and new supplementary figures) that specifies the proton and γ-ray energy and timing gates used for coincidence selection, the off-time window method for random-coincidence subtraction with the measured subtraction fraction, the sideband regions and polynomial modeling employed for continuum background, and the full energy-dependent efficiency curve obtained from GEANT4 simulations cross-checked with calibration sources. These additions allow direct evaluation that the reported lines are not artifacts and that the branching ratios are correctly assigned from the coincidence intensities. revision: yes

  2. Referee: [Discussion and Comparison to Theory] The extracted Gamow-Teller strengths and the statement of 'improved agreement' with shell-model calculations for 7.5 < Ex < 9.5 MeV lack a clear presentation of the full error budget, including systematic uncertainties from undetected weak branches and efficiency modeling. Without this, the improvement cannot be evaluated as statistically significant or robust against the pandemonium risk noted in the abstract.

    Authors: We have added a new subsection to the Discussion that tabulates the complete error budget: statistical uncertainties from the coincidence yields, systematic uncertainties from the efficiency model (quantified at the 10–15 % level across the 7.5–9.5 MeV interval), and an explicit assessment of possible undetected weak branches by comparing the summed experimental strength to the shell-model prediction and to the Ikeda sum rule. A revised figure now displays the experimental GT distribution with total uncertainties overlaid on the theoretical curve, and we report a χ² comparison that quantifies the improved agreement in the stated energy window. These additions demonstrate that the reported improvement is robust against the pandemonium effects mitigated by the coincidence technique. revision: yes

Circularity Check

0 steps flagged

No significant circularity: direct experimental measurement of decay scheme

full rationale

The paper reports an experimental measurement of β-delayed proton-γ coincidences in 31Cl decay using the GADGET and SeGA detectors. The central claims—discovery of up to 20 new proton transitions and improved agreement with external shell-model Gamow-Teller calculations for 7.5 < Ex < 9.5 MeV—rest on observed event data after standard efficiency corrections and background subtraction. No derivation chain reduces a prediction or first-principles result to its own inputs by construction; there are no fitted parameters renamed as predictions, no self-definitional relations, and no load-bearing self-citations or ansatzes invoked to justify the scheme. The comparison to theory is an external benchmark, not an internal closure. This is a self-contained experimental result with no circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The measurement relies on standard nuclear decay assumptions and detector response models typical for beta-delayed particle spectroscopy; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Standard assumptions about beta decay selection rules and detector efficiencies allow unambiguous assignment of observed coincidences to specific transitions.
    Invoked to interpret the new proton transitions and construct the decay scheme.

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