Resolving the 11B(p, ${\alpha_0}$) Cross Section Discrepancies between 0.5 and 3.5 MeV

Hans Otto Uldall Fynbo; Jacobus Andreas Swartz; Michael Munch; Oliver S{\o}lund Kirsebom

REVIEW 2 major objections 5 minor 20 references

Resolving the 11B(p, ${\alpha_0}$) Cross Section Discrepancies between 0.5 and 3.5 MeV

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A new measurement of the $^{11}$B(p,$\alpha_0$) cross section from 0.5 to 3.5 MeV resolves discrepancies of up to 70% among six earlier datasets and provides a reference normalization consistent with Becker (1987) and an energy scale…

desk verdict A useful new 11B(p,α0) measurement with a clean energy check; the 'resolved' conclusion is a bit stronger than the ratio analysis supports. read the letter →

arxiv 1908.04064 v1 pith:IYUENJJP submitted 2019-08-12 nucl-ex

Michael Munch , Oliver S{o}lund Kirsebom , Jacobus Andreas Swartz , Hans Otto Uldall Fynbo This is my paper · ORCID

classification nucl-ex

keywords 11B(palpha0)crosssectionborondepthprofilingnuclearreactionanalysisastrophysicsproton-inducedthin-targetmeasurementsegmentedsilicondetectors12Cresonancestructure

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 reports a new measurement of the cross section for the reaction $^{11}$B(p,$\alpha_0$), in which a proton removes one $\alpha$ particle from a boron-11 nucleus and leaves beryllium-8 in its ground state. The authors scanned proton energies from 0.5 to 3.5 MeV with a thin enriched $^{11}$B target and a close array of segmented silicon detectors, and they conclude that the result resolves long-standing disagreements among six earlier datasets on both the size of the cross section and its energy dependence. The reaction matters because it underpins boron depth profiling, light-element nucleosynthesis, and p–$^{11}$B fusion studies, all of which need a reliable reference cross section. In the new dataset, the normalization agrees with Becker (1987) and the energy scale agrees with Kokkoris (2010) to better than 5 keV, and the older datasets can be brought into agreement by constant scaling factors.

What carries the argument

The argument is carried by four pieces of apparatus, in the broad sense: a thin, isotopically enriched $^{11}$B target whose areal density ($12.6(12)\,\mu$g/cm$^2$) was deduced from the energy shift of a carbon peak using the calibration procedure of Ref. [14]; a close-geometry array of four double-sided silicon strip detectors (DSSDs) that recorded energy and position of the emitted $\alpha$ particles over a large solid angle; a Monte Carlo simulation (simX) that used SRIM stopping-power tables to compute the detector solid angle and to correct particle energies for losses in the target and dead layers; and a Legendre-polynomial decomposition of the angular distributions, $d\sigma/d\Omega(\theta)=\sigma/(4\pi)[1+\sum_{i=1}^4 a_i P_i(\cos\theta)]$, which yields both the angle-integrated cross section and its shape coefficients. The solid angle is normalized by simulation-to-data ratios, and the older datasets are reconciled by computing their median ratios to a linear interpolation of the new dataset.

What would settle it

Measure the areal density of the same $^{11}$B target by an independent method, such as Rutherford backscattering spectrometry or weighing a known area, and compare it with $12.6(12)\,\mu$g/cm$^2$; a discrepancy larger than the quoted 10% would scale the cross section proportionally and invalidate the normalization claim. Alternatively, repeat the 0.5–3.5 MeV scan on a second target with a different thickness and check that the deduced cross section is unchanged.

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Extended reading notes

Core claim

The central result is a self-consistent angle-integrated cross section for $^{11}$B(p,$\alpha_0$) between 0.5 and 3.5 MeV, extracted from fine energy steps (100 keV, with smaller steps near known resonances) and from Legendre-polynomial fits to the angular distributions recorded by four double-sided silicon strip detectors. When the present data are compared with the six earlier publications, the authors find that every old dataset can be reconciled by a constant multiplicative factor: the Becker (1987) normalization already agrees, Borchers (1983) agrees within $2\sigma$ where the ranges overlap, and Beckman (1953), Davidson (1979), Segel (1965), and Symons (1963) require scaling by 1.11, 0.77, 1.41, and 1.74, respectively. The energy scale agrees with the recent high-resolution dataset of Kokkoris et al. (2010) to better than 5 keV, while Segel's data appear to need a downward shift of about 38 keV. The paper concludes that the overall normalization is now known to better than 15%, while noting that the $\alpha_0$ channel alone cannot decide between competing interpretations of the resonance structure below 2 MeV; that question is left to a future $\alpha_1$ measurement.

Load-bearing premise

The cross-section normalization is directly proportional to the target thickness of $12.6(12)\,\mu$g/cm$^2$, deduced from the carbon-peak energy shift using SRIM stopping-power tables; if that thickness or the stopping-power conversion is wrong, every cross-section value and every scaling factor used to reconcile older datasets shifts by the same proportion.

Editorial extensions

If this is right

The new table can serve as the reference cross section for $^{11}$B(p,$\alpha_0$) from 0.5 to 3.5 MeV, with per-point uncertainties around 10–12% and a dataset-level normalization stated as better than 15%.
The six earlier measurements, once rescaled by the reported factors, no longer disagree in shape; this removes the need to choose or average conflicting absolute normalizations when using the reaction for depth profiling or yield estimates.
Because the energy scale matches Kokkoris et al. to better than 5 keV, applications that rely on resonance positions near 16.1–19.2 MeV excitation in $^{12}$C can trust the present energy calibration, and the claimed discrepancy between Kokkoris and Symons is not reproduced.
The unresolved sub-2 MeV resonance interpretation is explicitly outside what this dataset settles; settling it requires measuring the $\alpha_1$ channel and its three-alpha Dalitz distribution, feeding a new R-matrix analysis.

Reading between the lines

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

If the thickness-normalization assumption holds, the 12% uncertainty on the target thickness is the dominant systematic in the final cross section; any future use of this dataset at the stated precision inherits that uncertainty, so an independent, non-destructive thickness measurement would be the most direct upgrade.
The constant scaling factors (e.g., 1.41 for Segel and 1.74 for Symons) suggest that those experiments carried systematic normalization errors of tens of percent, most plausibly in beam-current integration or target stoichiometry; re-examining their original run conditions could identify the cause.
The same detector-plus-simulation approach could be applied to the $\alpha_1$ channel, and the paper's own conclusion implies that a Dalitz-plot analysis of that channel would discriminate between the ghost-resonance and broad-$1^-$ interpretations of the region below 2 MeV.
Because the reconciliation is achieved with constant scaling factors over the overlapping energy ranges, the data imply that the energy dependence was already approximately correct in the old measurements and that only absolute normalizations and energy offsets were wrong; if true, renormalized old angular distributions can be combined with the new dataset for improved Legendre coefficients.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper is a solid experimental contribution. It reports a new 11B(p,α0) cross section dataset from 0.5 to 3.5 MeV using modern DSSD detectors, a thin enriched target, and careful Monte Carlo solid-angle correction. The energy calibration is independently checked against Kokkoris to better than 5 keV, which is a real strength. The ratio analysis in Fig. 7 shows that several older datasets can be brought into normalization agreement by constant scaling factors within limited energy windows — that is a genuine step toward understanding the 70% spread in the literature, and the authors deserve credit for putting it together clearly.

The tabulated cross sections and Legendre coefficients are useful, and the authors are appropriately cautious when they say they cannot resolve the low-energy resonance interpretation. The agreement with Becker and the visual consistency after scaling are convincing enough to make this a reference-level dataset for NRA and fusion applications.

The soft spots are real but not fatal. The conclusion states that disagreements on "both the magnitude and energy dependence" are resolved, but the body of the paper says the scaling works only below about 1.3 MeV for Beckman and in the 1.5–2.75 MeV range for Segel and Symons, with larger deviations outside those ranges. Segel also needs a 38 keV energy shift and shows a systematic a4 shift. So the energy dependence of the historical datasets is not fully reconciled across the whole 0.5–3.5 MeV range. The new data can still serve as a reference, but the "resolved" claim is broader than the evidence.

There is one more normalization caveat: the absolute scale depends entirely on the target thickness of 12.6±1.2 µg/cm², deduced from a carbon-peak shift using SRIM stopping powers. Any systematic error there propagates linearly into the cross sections and into all the scaling factors. The authors acknowledge the ~10% uncertainty, which is honest, but it is a single point of failure.

No raw data or analysis code is provided, which is a minor annoyance in 2019, though the table is complete enough for most users.

Overall, this is a well-executed measurement, clearly written, with citation practice that looks fair. The central dataset deserves to be in EXFOR and cited. My main advice to the editor is to let it through peer review with a request to soften the conclusion and explicitly state the energy windows where the scaling holds.

Referee Report

2 major / 5 minor

Summary. The paper reports a new measurement of the 11B(p,α0) cross section for proton energies between 0.5 and 3.5 MeV using four double-sided silicon strip detectors on a thin isotopically enriched 11B target. Angular distributions, Legendre coefficients, and angle-integrated cross sections are extracted, and the energy scale is checked against the high-resolution dataset of Kokkoris et al. to better than 5 keV (Fig. 6). The authors compare their data with six older datasets using constant scaling factors (Fig. 7) and conclude that the previous discrepancies in both magnitude and energy dependence have been resolved, with an overall normalization better than 15%.

Significance. If the dataset is accepted, it provides a valuable reference cross section for applications in nuclear reaction analysis, pB fusion studies, and R-matrix analyses of 12C. The experiment has several clear strengths: the energy calibration is independently tested against an external dataset, the angular distributions are fitted with Legendre polynomials in a standard parameterization, the data are tabulated and made available through EXFOR, and the comparison with earlier measurements is quantitative rather than qualitative. The main caveat is that the absolute normalization rests on a single target-thickness determination, 12.6 ± 1.2 µg/cm², which propagates linearly into all reported cross sections.

major comments (2)

[Sec. 4 and Sec. 5, Fig. 7] The concluding claim that disagreements with previous measurements on both magnitude and energy dependence "have been resolved" overstates the evidence. As the text states, simple constant scaling of the older data works only for Beckman below about 1.3 MeV and for Segel and Symons in the range 1.5–2.75 MeV, with larger deviations outside these ranges; the comparison with Segel additionally requires a 38 keV energy shift, and a systematic offset in the a4 Legendre coefficient remains at all energies. The conclusion should be qualified to say that the present dataset provides a consistent reference scale and reconciles the older datasets only within the stated energy windows, rather than claiming a full resolution of the energy dependence across 0.5–3.5 MeV.
[Sec. 2 and Sec. 3, Table 1] The absolute normalization is directly proportional to the target thickness of 12.6(12) µg/cm², whose 9.5% relative uncertainty nearly saturates the quoted 10–12% total uncertainties. The paper does not give a detailed uncertainty budget showing how the target-thickness systematic, the dead-layer corrections, the integrated-charge measurement, and the simulation-derived solid angles are propagated into the final cross sections. This budget, or an independent normalization check, is needed to justify the statement that the overall normalization is better than 15%.

minor comments (5)

[Sec. 4, Fig. 6] The comparison with Kokkoris et al. is made after normalizing both datasets to their maxima, so it validates the relative energy scale but not the absolute normalization; this distinction should be stated explicitly in the text.
[Sec. 5] The sentence beginning "Considering the good agreement..." defines the 15% normalization claim only by agreement with two datasets; please specify whether this figure includes the target-thickness systematic and the simulation efficiency uncertainty.
[Table 1] The table contains two entries at Ep = 950 keV and two at Ep = 1900 keV with slightly different cross sections; please label these as repeat runs or duplicate points to avoid confusion.
[Fig. 4 caption] The caption contains the typo "evulotion"; it should read "evolution".
[Title page] The placeholder PACS line "PACS-key discribing text of that key" should be removed or replaced with actual PACS codes.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper reports a new measured cross section and compares it with earlier independent datasets; no fitted input is relabeled as a prediction.

full rationale

This is an experimental nuclear-physics paper, not a derivation from first principles, so the circularity patterns are largely inapplicable. The central result, the angle-integrated 11B(p, alpha0) cross section, is obtained directly from measured particle yields, deadtime-corrected integrated current, Monte Carlo solid-angle simulation, and a target thickness inferred from a carbon-peak energy shift. The target-thickness procedure is taken from the same group's earlier publication (Ref. [14]), but it is an experimental calibration method, not a theoretical claim that presupposes the present cross-section values; a self-citation describing a measurement technique is not load-bearing in the sense of circular reasoning. The comparison with older datasets (Becker, Borchers, Davidson, Segel, Symons, Beckman) is done by forming ratios to the present dataset and then applying constant scaling factors to bring the older data into visual agreement. This is a legitimate use of a new independent measurement as a reference; the scaling factors are descriptive fits to the comparison, not predictions derived from the data in a way that would make the agreement tautological. The paper does not fit parameters to a subset and then claim to predict that same subset, nor does it invoke a uniqueness theorem or an ansatz from prior work to force its normalization. The only caveat is that the conclusion that disagreements are 'resolved' over the full 0.5-3.5 MeV range is stronger than the scaling evidence, since the simple scaling relations are stated to hold only in limited energy windows (Beckman below ~1.3 MeV; Segel and Symons in 1.5-2.75 MeV). That is an evidentiary/correctness concern about the breadth of the claim, not a circularity. Accordingly, no circular steps are identified and the score is 0.

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

The cross section extraction relies on standard nuclear-physics assumptions about kinematics, detector response, and stopping powers. No ad hoc free parameters or invented entities are introduced. The main fitted quantities (Legendre coefficients) are measured outputs, not inputs.

assumptions (4)

domain assumption SRIM stopping-power tables accurately model energy loss and straggling of alpha particles in the boron target and detector dead layers.
Used in the event-by-event energy corrections and in the SimX Monte-Carlo simulation (Section 3, Fig. 3). A systematic error in SRIM would shift the energy scale and normalization.
domain assumption The target thickness of 12.6(12) µg/cm² deduced from the carbon-peak energy shift following Ref. [14] is accurate.
The absolute normalization of the cross section is inversely proportional to target thickness (Section 2).
domain assumption The α0 reaction products are cleanly separated by a cut on the CM energy spectrum.
The α0 peak is the highest-energy group in Fig. 3, well separated from α1 and elastic scattering, so the cut does not introduce significant contamination.
standard math The Legendre-polynomial expansion (Equation 1) truncated at 4th order is adequate for the angular distributions.
The fits reproduce the measured angular distributions and agree with prior Legendre coefficients (Fig. 5).

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Cite this review

Pith. "Pith review of Resolving the 11B(p, ${\alpha_0}$) Cross Section Discrepancies between 0.5 and 3.5 MeV." pith.science (2026). https://pith.science/paper/IYUENJJP

@misc{pith2026190804064,
  author       = {Pith},
  title        = {Pith review of: Resolving the 11B(p, $\alpha_0$) Cross Section Discrepancies between 0.5 and 3.5 MeV},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IYUENJJP}},
  note         = {Machine review of arXiv:1908.04064}
}

abstract

The reaction 11B(p, 3${\alpha}$) is relevant for fields as diverse as material science, nuclear structure, nuclear astrophysics, and fusion science. However, for the channel proceeding via the ground state of 8Be, the available cross-section data shows large discrepancies of both normalization and energy scale. The present paper reports on a measurement of the 11B(p, ${\alpha_0}$) cross section using an array of modern large area segmented silicon detectors and low beam current on an enriched thin target with the aim of resolving the discrepancies amongst previous measurements.

Figures

Figures reproduced from arXiv: 1908.04064 by the authors.

**Figure 1.** Angle-integrated α0 cross section as reported by Refs. [9, 6, 7, 10,11, 12] (tabulated data available via EXFOR [13]). Deviations both in the absolute normalization and energy calibration are evident. arXiv:1908.04064v1 [nucl-ex] 12 Aug 2019 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗

**Figure 3.** Center-of-mass energy distribution for a proton energy of 800 keV. At high energy, one sees a sharp peak corresponding to α0. Below this peak is a broad distribution corresponding to reactions proceeding via the α1 channel. Around 1 MeV there are various peaks corresponding to elastic proton scattering. The energy of the elastic protons might be larger than the beam energy since they have been corrected for α partic… view at source ↗

**Figure 4.** Selection of angular distribution from 900 to 3500 keV. A slow evulotion from slightly forward focussed below 2 MeV to approximately symmetric around 2.4 MeV to strongly backward focussed above 3 MeV [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: Angle-integrated cross section and Legendre coefficients shown as a function of beam energy together with the coefficients obtained by Refs. [6,7, 12]. The dashed vertical lines indicate the position of natural parity states in 12C as listed in Ref. [18]. low energies…

**Figure 6.** Figure 6: Comparison of the present data and the recent highresolution dataset by Kokkoris et al. (KO) for θ = 150◦ [1]. Each dataset has been normalized so the maximum value is 1. The energy scale of the two dataset agrees better than 5 keV. 0.75 0.90 Borchers (1983) 0.86+0.01…

**Figure 7.** Figure 7: Ratio of datasets [9, 6, 7, 10, 11, 12] to a linear interpolation of the present dataset. The dashed line indicates the median, while the two dotted lines indicate the 25 and 75 quartiles. See the text for details. data and Symons et al. (SY) while the agreement with…

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Reference graph

Works this paper leans on

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Kokkoris, A

M. Kokkoris, A. Kafkarkou, V. Paneta, R. Vlastou, P. Mis- aelides, A. Lagoyannis, Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms268, 3539 (2010)

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[2] [2]

Boesgaard, C.P

A.M. Boesgaard, C.P. Deliyannis, A. Steinhauer, The As- trophysical Journal 621, 991 (2005)

work page 2005

[3] [3]

Lamia, C

L. Lamia, C. Spitaleri, V. Burjan, N. Carlin, S. Cheru- bini, V. Crucillà, M.G. Munhoz, M.G.D. Santo, M. Gulino, Z. Hons et al., Journal of Physics G: Nuclear and Particle Physics 39, 015106 (2012)

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D. Moreau, Nuclear Fusion17, 13 (1977)

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M.H. Sikora, H.R. Weller, Journal of Fusion Energy35, 538 (2016)

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Symons, P

G. Symons, P. Treacy, Nuclear Physics46, 93 (1963)

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Segel, S.S

R.E. Segel, S.S. Hanna, R.G. Allas, Physical Review139, B818 (1965)

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Barker, Nuclear Physics A707, 277 (2002)

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