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REVIEW 4 major objections 5 minor 33 references

Effect of the near-proton-emission threshold resonance in $^{11}$B on the branching ratio of beta-delayed proton emission from $^{11}$Be

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The branching ratio of beta-delayed proton emission from 11Be is set by the energy of a narrow near-threshold resonance in 11B, with values ranging from about 1.3×10^-5 near 171 keV to about 3×10^-6 near 211 keV.

desk verdict Solid model study whose qualitative sensitivity claim holds up, but the central number is anchored to an unexplained 182 keV choice and the table of log(ft) values has arithmetic problems. read the letter →

arxiv 2411.10700 v2 pith:BSLG3BYQ submitted 2024-11-16 nucl-th nucl-ex

Nguyen Le Anh , Bui Minh Loc This is my paper · ORCID
classification nucl-thnucl-ex
keywords beta-delayedprotonemission11Behalonucleus11Bnear-thresholdresonancebranchingratioSkyrmeHartree-Fockpotentialmodelsingle-particleelasticscattering
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the long-debated branching ratio of $\beta$-delayed proton emission from the halo nucleus 11Be is essentially controlled by the energy of a narrow resonance in 11B just above the proton threshold. Using a Skyrme-Hartree-Fock potential model, the authors adjust two overall scaling factors so that the single-particle potentials reproduce the measured neutron separation energy and the resonance position. They find that moving the resonance by a few tens of keV changes the predicted branching ratio by a factor of several, from roughly 13×$10^{-6}$ at 171 keV to about 3×$10^{-6}$ at 211 keV. Because the experimental resonance energy is still uncertain, the accurate branching ratio cannot be fixed until that energy is pinned down; with the resonance placed at 182 keV and a spectroscopic factor of 0.51, all four Skyrme forces give about 9×$10^{-6}$.

What carries the argument

The central object is the overlap radial integral $I_{if}(E)=S_F^{1/2}\int_0^\infty \chi(E,r)\varphi(r)\,dr$, where $\varphi(r)$ is the bound halo-neutron wave function and $\chi(E,r)$ is the s-wave proton-core scattering wave function. Both wave functions come from solving a Schrödinger equation with a Skyrme-Hartree-Fock potential of the form $V_q(E,r)= \frac{m^*_q(r)}{m}\{V^{\rm HF}_q(r)+\frac12\frac{d^2}{dr^2}\left(\frac{\hbar^2}{2m^*_q(r)}\right)-\frac{m^*_q(r)}{2\hbar^2}\left[\frac{d}{dr}\left(\frac{\hbar^2}{2m^*_q(r)}\right)\right]^2\}+\left[1-\frac{m^*_q(r)}{m}\right]E$. The two potentials are each modified by one overall scaling factor, $N_i$ and $N_f$, which are adjusted so that the bound state sits at the experimental neutron separation energy and the resonance sits at the measured energy. This machinery lets the same single-particle potentials describe elastic scattering, the resonance width, and the $\beta$-decay final-state wave function, making the resonance location the key input that determines the branching ratio.

What would settle it

Measure the 11B resonance energy with uncertainty well below the current 20–40 keV, for example to ±5 keV, and simultaneously remeasure the 11Be $\beta$-delayed proton branching ratio. The model's predicted mapping—about 13×$10^{-6}$ at 171 keV, 9×$10^{-6}$ at 182 keV, and 2.9×$10^{-6}$ at 211 keV—would be falsified if a resonance at a well-determined energy yields a branching ratio outside the predicted value by more than the combined uncertainties, especially if the resonance is found below 200 keV but the branching ratio remains below $10^{-5}$.

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Extended reading notes

Core claim

The branching ratio of $\beta$-delayed proton emission from 11Be is governed by the location of a narrow s-wave single-particle resonance sitting just above the proton-emission threshold in 11B. The authors compute the decay within a potential model in which the initial halo-neutron bound state and the final proton-core scattering state are described by Skyrme-Hartree-Fock mean fields, calibrated by only two overall scaling parameters: one to reproduce the 501-keV neutron separation energy and one to place the 11B resonance at the measured energy. After this calibration, the predicted branching ratio changes rapidly with the resonance position—about 13×$10^{-6}$ at 171 keV, 9×$10^{-6}$ at 182 keV, and 2.9×$10^{-6}$ at 211 keV—and is nearly identical for four different Skyrme forces. The calculation therefore ties together low-energy 10Be+p elastic scattering and the weak $\beta$-decay branch, showing that the measured resonance energy, particularly whether it falls below 200 keV, determines whether the branching ratio is near $10^{-5}$ or near 3×$10^{-6}$.

Load-bearing premise

The calculation assumes the proton-emitting resonance in 11B is a single-particle s-wave state whose scattering wave function is fully described by a one-body Skyrme-Hartree-Fock potential; if the real resonance mixes multiple nuclear configurations, the computed beta-decay overlap and its dependence on the resonance energy could change significantly.

Editorial extensions

If this is right

  • The 11Be beta-delayed proton branching ratio is effectively determined by the 11B resonance energy, so measuring that energy to within a few tens of keV fixes whether the ratio is near 10^-5 or near 3×10^-6.
  • The experimental upper limit of 2.2×10^-6 from the ISOLDE decay study corresponds in this model to a resonance located at about 217 keV, above the 200 keV divide.
  • A resonance below 200 keV is required for the larger branching-ratio values: the model gives about 13×10^-6 at 171 keV and about 9×10^-6 at 182 keV.
  • After calibration to a common resonance energy, four different Skyrme forces give nearly identical branching ratios, indicating that the result does not depend on the choice of the effective interaction.
  • The same calibrated wave functions reproduce low-energy 10Be+p elastic scattering observables, directly linking a strong-interaction measurement to a weak-decay branching ratio.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the single-particle description holds, a single high-precision measurement of the 11B resonance energy, with uncertainty well below the current ±20 to ±40 keV, would effectively determine the 11Be branching ratio without requiring a new direct decay experiment.
  • The same bound-to-continuum overlap technique could be applied to other halo-nucleus beta-delayed emissions, such as 11Li, where near-threshold final-state resonances may similarly amplify rare decay branches.
  • The near-independence of the calibrated result across Skyrme forces suggests robustness to the mean-field parametrization, but configuration-mixing corrections outside the single-particle assumption remain untested by this calculation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The manuscript computes the beta-delayed proton emission branching ratio of 11Be using a Skyrme-Hartree-Fock potential model. The initial halo-neutron bound state and the final p+10Be scattering state are generated from the same mean-field framework with two overall scaling parameters, one tuned to the neutron separation energy and one to the location of the near-threshold resonance in 11B. The authors find that the computed branching ratio is highly sensitive to the resonance energy: calibrating to 171, 182, and 211 keV yields b_beta-p around 1.3e-5, 9e-6, and 2.9e-6, respectively. They conclude that experimental determination of whether the resonance lies below 200 keV is decisive for the branching-ratio puzzle.

Significance. The qualitative sensitivity identified here is physically plausible and worth publishing if placed on a firmer quantitative footing: a narrow s-wave resonance located inside the beta-decay window can indeed enhance the beta-delayed proton branch by orders of magnitude, and connecting low-energy elastic scattering data to a weak-decay observable is a useful bridge. The paper's demonstration that the tuned results are nearly independent of the four Skyrme forces is a strength. However, the central quantitative claim is not yet supported: the resonance energy used for the headline value is selected without justification, the reported log(ft) values disagree with the paper's own formula, and the single-particle assumption for the final state is not tested against measured widths. The paper reads better as a sensitivity study than as a determination of a central branching ratio.

major comments (4)
  1. [Sec. I and Table I] The central value of 9e-6 is obtained by fixing the resonance at ER = 182 keV, but the manuscript gives no argument for this choice. The experimental values cited are 171 +/- 20 keV, 197 keV, and 211 +/- 40 keV; selecting 182 keV produces a branching ratio close to the 8.6e-6 reported in Ref. [9] and is then used to 'support' that same measurement. This is circular. Either the resonance energy should be determined from an independent observable, or the paper should present b_beta-p as a function of ER and explicitly refrain from quoting a central value.
  2. [Table III and Eq. (5)] The log(ft) column is inconsistent with Eq. (5) and the quoted BF and BGT values. For ER = 171 keV, using K = 6144 s, lambda = -1.268, BF = 1.364, and BGT = 4.092 gives ft = 6144 / (1.364 + 1.268^2 * 4.092) = 773.5 s, so log10(ft) = 2.89, not 2.621 as listed. Similar discrepancies occur for the other rows. Since the ft value and the transition strengths are used to interpret the branching-ratio scale, this normalization issue must be resolved before the absolute branching ratios can be trusted.
  3. [Eq. (10)] The overlap integral contains only the initial-state spectroscopic factor S_F^{1/2}; no final-state proton spectroscopic factor appears. If the near-threshold 11B resonance has multi-particle components, the beta-decay matrix element should be scaled by the square root of the proton single-particle content, and the energy dependence of the overlap could deviate from the single-particle prediction. The widths Gamma_p in Table III are single-particle widths; comparing them with the measured widths from Refs. [11,12] would provide a direct test of the single-particle assumption. Without such a test, the mapping between resonance energy and branching ratio is not robust.
  4. [Tables I and III; Fig. 3] No uncertainties are propagated anywhere in the paper. The branching ratio is quoted to two significant figures even though it changes by roughly a factor of 1.5 when the resonance is shifted from 171 to 182 keV and by another factor of 3 when shifted to 211 keV. The sensitivity curves in Fig. 3 are shown without uncertainty bands, and the central value 9e-6 carries no error from the spectroscopic factor, the scaling parameters, or the experimental resonance-energy uncertainties. For a quantitative claim that depends so strongly on a single input, this omission is load-bearing.
minor comments (5)
  1. [Throughout] Several exponents are missing their minus signs: '8.6 x 10^6' should be '8.6 x 10^-6' in Sec. I, and '2.2 x 10^6' should be '2.2 x 10^-6' in Sec. III and Sec. IV.
  2. [Table II] The table heading says the parameters reproduce the neutron separation energy Sn 'in 11B', but the initial-state separation energy is that of 11Be; the heading should be corrected. Also, the table lists 'SLy5' while the text and Table I use 'SLy4'.
  3. [Title] The abstract title and the main-text title differ ('Effect of the near-proton-emission threshold resonance...' versus 'Direct correlation between...'). The authors should choose one consistent title.
  4. [Reference [17]] The author list of Ref. [17] contains LaTeX corruption ('Soko/suppress lowska', 'Fija/suppress lkowska'), which must be repaired before publication.
  5. [Fig. 1 caption] The caption states the calculation is done 'without adjusting N', but the relevant parameter is N_f; the caption should specify N_f = 1 for clarity.

Circularity Check

1 steps flagged · score 6.0 of 10

Central 9e-6 branching ratio is evaluated at an unexplained ER=182 keV that is absent from the paper's own list of measured resonance energies, making the headline 'prediction' a function evaluation at a retro-fitted parameter rather than an independent result.

  1. fitted input called prediction [Sec. I (Introduction), paragraphs 4-6; Table I; Fig. 3]
    "In different experiments, its values are 171 keV [11], 197 keV [9], and 211 keV [12]. ... The estimated value 8.6 × 10−6 from Ref. [9] is consistent to the resonance location below 200 keV (197 keV [9]). The limit of 2.2 × 10−6 [8, 17] places the resonance at the energy above 200 keV (217 keV in our calculation). ... From our analysis, the branching ratio is 9 × 10−6. It is independent of the choice of the Skyrme forces. This value comes from the analysis with the resonance located at 182 keV, the spectroscopic factor of the neutron halo state being 0.51."

    By Eqs. (2)-(6) and (9)-(10), bβp is an integral over the overlap Iif(E), whose final-state wavefunction is generated by a potential scaled by Nf so the resonance sits at a chosen ER. Table I shows that after this calibration all Skyrme forces give nearly the same bβp at a fixed ER (8.91–9.05 × 10^-6 at 182 keV), so the result is controlled by the single number ER. The paper lists measured ER values 171, 197, and 211 keV; 182 keV is not among them. The quoted central value 9 × 10^-6 is therefore not derived from data but is a function evaluation at an unconstrained input.

full rationale

The model does contain genuine, non-circular content: the mapping bβp(ER) shown in Fig. 3 and Table I, and the values computed at the measured resonance energies (e.g., ~1.3 × 10^-5 at 171 keV and ~2.9 × 10^-6 at 211 keV), are testable outputs of Eqs. (2)-(11) that would differ among alternative final-state models. The qualitative claim that a near-threshold s-wave resonance below Q = 281 keV enhances the branching ratio does not reduce to a fit. The circularity is concentrated in the headline number 9 × 10^-6, which is evaluated at an ER = 182 keV that has no experimental source in the paper's own list of 171, 197, and 211 keV and that numerically reproduces the previously measured 8.6 × 10^-6 of Ref. [9]. Since Table I makes clear bβp is essentially a function of the chosen ER, this central value is the model's response to a retro-fitted parameter rather than an independent prediction. The single-particle assumption and the omission of a final-state proton spectroscopic factor are correctness concerns rather than circularity, and the self-citation [13] is not the step that forces the numerical result. Score 6 reflects partial circularity in the central value while the ER-dependence mapping retains independent content.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim depends on two fitted potential-scaling parameters, a chosen resonance energy, and a selected spectroscopic factor. The model therefore maps an input resonance position onto a branching ratio rather than predicting the branching ratio independently.

free parameters (4)
  • Nf (final-state potential scaling) = 0.978-1.028 (Table II)
    Scales the proton-core potential to reproduce the chosen resonance location ER; fitted to experimental resonance energy.
  • Ni (initial-state potential scaling) = 1.086-1.149 (Table II)
    Scales the neutron-core potential to reproduce the halo neutron separation energy Sn=501 keV; fitted to experimental separation energy.
  • Resonance energy ER = 182 keV for central result; scanned over 171-211 keV
    The central value 182 keV is not directly an experimental measurement (experiments report 171±20, 197, 211±40 keV) and its choice is not explained; it strongly determines the branching ratio.
  • Spectroscopic factor SF = 0.51
    Taken from Ref. [32] rather than the alternative 0.71 from Ref. [6]; the branching ratio scales linearly with SF.
assumptions (5)
  • domain assumption Standard beta-decay rate formulas of Eqs. (2)-(9), including the Fermi function approximation, apply to this halo decay.
    These formulas are taken from prior work (Baye and Tursunov) and are not re-derived or tested here.
  • domain assumption Skyrme Hartree-Fock provides a reliable single-particle potential for the p+10Be and n+10Be systems, with only the overall depth adjusted.
    The potential shape is fixed by HF, and only the scaling parameters Ni and Nf are adjusted; no alternative potential shapes are tested.
  • ad hoc to paper Gamow-Teller strength is taken as exactly three times the Fermi strength (Eq. 9).
    This simplification assumes the final wave function is independent of jf, which may not hold in general.
  • domain assumption The final state is a single-particle s-wave scattering state; the near-threshold resonance is single-particle.
    This is the core modeling assumption; multi-particle configuration mixing is neglected.
  • domain assumption The decay proceeds directly from the halo neutron bound state to the proton-core continuum; no core-excitation or three-body channels.
    The model ignores possible core excitations or more complex decay paths.

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Cite this review

Pith. "Pith review of Effect of the near-proton-emission threshold resonance in $^{11}$B on the branching ratio of beta-delayed proton emission from $^{11}$Be." pith.science (2026). https://pith.science/paper/BSLG3BYQ

@misc{pith2026241110700,
  author       = {Pith},
  title        = {Pith review of: Effect of the near-proton-emission threshold resonance in $^11$B on the branching ratio of beta-delayed proton emission from $^11$Be},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BSLG3BYQ}},
  note         = {Machine review of arXiv:2411.10700}
}
abstract

Beta-delayed proton emission from neutron halo nuclei $^{11}\mathrm{Be}$ represents a rare decay process. The existence of the narrow resonance near the proton-emission threshold in $^{11}\mathrm{B}$ explains its unexpectedly high probability. However, the accurate value of the branching ratio remains challenging to determine. We aim to quantify the influence of the narrow resonance near the proton emission threshold on the result of the branching ratio. We employ the Skyrme Hartree-Fock calculation within the potential model to obtain the branching ratio. We derive the single-particle potentials for the halo neutron and the emitting proton with minimal adjustment. Slight variations in the resonance position significantly impact the branching ratio, with the upper limit reaching the order of $10^{-5}$. Experimental determination of the resonance energy, particularly whether it lies below $200$ keV, is crucial for determining the value of the branching ratio.

Figures

Figures reproduced from arXiv: 2411.10700 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Excitation functions in the center-of-mass fram [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) The excitation functions in the center-of-mass [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

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