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Differential cross sections for ${{^{12}\mathrm{C}(n,\alpha_{0})}}$, ${{^{16}\mathrm{O}(n,\alpha_{0})}}$ and ${{^{16}\mathrm{O}(n,\alpha_{1,2,3})}}$ between ${{E_n}}$ = 7.2 and 10 MeV with an active-target Time Projection Chamber

T0 review · 2 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read At 7.2-10 MeV, new measurements give differential and integrated cross sections for three neutron-alpha channels; the integrated 16O(n,α1,2,3) is about five times ENDF/VIII.0 at low energies, below it at high energies.

desk verdict Useful new differential cross-section data from a first active-target TPC neutron measurement, but the factor-of-5 integrated 16O(n,α1,2,3) deviation from ENDF rests on an angular extrapolation the paper's own 12C benchmark shows can be unreliable. read the letter →

arxiv 2601.02841 v2 pith:JD33GZT2 submitted 2026-01-06 nucl-ex

J. Bishop , C.E. Parker , R. Smith , Tz. Kokalova , G.V. Rogachev , C. Wheldon , S. Ahn , E. Koshchiy
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K. Brandenburg C.R. Brune R.J. Charity J. Derkin N. Dronchi G. Hamad Y. Jones-Alberty T.N. Massey Z. Meisel E.V. Ohstrom S.N. Paneru E.C. Pollacco M. Saxena N. Singh L.G. Sobotka D. Soltesz S.K. Subedi A.V. Voinov J. Warren
This is my paper · ORCID
classification nucl-ex
keywords neutron-inducedreactionsactive-targettimeprojectionchamberdifferentialcrosssections16O(nα)12C(nreactionENDF/VIII.0evaluationnuclearreactorneutronmultiplicationheliumproduction
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

The paper reports differential and angle-integrated cross sections for three neutron-induced alpha-emission channels—12C(n,α0), 16O(n,α0), and the unresolved 16O(n,α1,2,3)—at neutron energies from 7.2 to 10 MeV, using a time projection chamber in which CO2 gas acts as both target and detector. The main new result is that the angle-integrated 16O(n,α1,2,3) cross section is about five times larger than the ENDF/VIII.0 evaluation at the lower end of this range, and falls below it at higher energies. This matters because 16O(n,α) reactions affect the neutron multiplication factor k_eff and helium buildup in nuclear reactors, and the previous normalization uncertainty was around 30 percent. The measurement also demonstrates that active-target TPCs can produce high-quality, broad-angular-range cross-section data with a relatively weak neutron beam.

What carries the argument

The central object is the active-target TPC—a time projection chamber whose CO2 gas is both the target and the ionization medium—so each (n,α) event leaves a full 3D two-track signature. RANSChiSM, a RANSAC-style three-dimensional track-fitting algorithm with an added transverse-momentum constraint, fits the 4He and heavy-recoil tracks. Channel identity is assigned event-by-event by converting kinematic-consistency χ² to p-values and then to multinomial probabilities (Eqs. 1-3), so ambiguous events contribute fractionally to yields and enlarge the quoted uncertainties. For the angle-integrated cross sections, Eq. (5) takes the measured differential cross section over the covered angular rang

What would settle it

At En ≈ 7.5-8.2 MeV, measure the 16O(n,α1,2,3) differential cross section with detector coverage extended to θ_c.m. ≈ 10°-20° and to heavy-fragment lab angles above 90° (e.g., by increasing the TPC field-cage height and pad granularity). If the cross section at 20° turns out to be several times the value at 90°, or otherwise violates the flat extrapolation assumed in Eq. (5), the ~50 mb integrated value and its fivefold deviation from ENDF/VIII.0 would not survive; if it stays flat, the discrepancy stands.

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Extended reading notes

Core claim

The experiment fills a TPC with CO2 gas so the gas itself is the nuclear target, exposes it to a quasi-monoenergetic neutron beam, and reconstructs each reaction as a two-track event: a light 4He and a heavy recoil (9Be or 13C). Events are assigned to the three channels by comparing measured track angles and heavy-recoil ranges with kinematic loci, using a multinomial probability per event so channel-selection ambiguity appears in the yield uncertainties. The resulting differential cross sections cover roughly 40°-160° c.o.m., broader than previous 16O(n,α) data. At 7.2-10 MeV, the angle-integrated 16O(n,α0) agrees with ENDF/VIII.0 at the 7-24% level, but the combined 16O(n,α1,2,3) channel i

Load-bearing premise

The load-bearing assumption is that the unmeasured angular ranges—forward and backward c.o.m. angles outside roughly 40°-160°, and decays where the heavy fragment recoils above 90° in the lab—have the same average differential cross section as the measured range, so Eq. (5) can extrapolate under those bins; if the 16O(n,α1,2,3) angular distribution peaks sharply in the uncovered regions, the reported factor-of-five excess over ENDF/VIII.0 would shrink.

Editorial extensions

If this is right

  • If 16O(n,α1,2,3) is really five times ENDF/VIII.0 near 7.5-8.2 MeV, evaluated libraries underpredict both neutron removal and helium production in oxygen-containing reactor materials, shifting k_eff and embrittlement estimates.
  • The 16O(n,α0) uncertainty drops from the historical ~30% to 7-24%, a substantial improvement even though it remains above the 5% target for reactor calculations.
  • The broadened angular coverage gives R-matrix evaluations of 17O new data to constrain above the current 7-MeV upper limit, where ENDF joins smoothly without direct measurements.
  • The 12C(n,α0) benchmark agreement validates the normalization and channel separation, so other channels measured simultaneously from the same dataset gain credibility.
  • Above En≈9 MeV, 16O(n,α1,2,3) is the larger of the two oxygen channels, making accurate data for this unresolved group important for neutron-balance modeling.

Reading between the lines

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

  • Left implicit: the same active-target method should transfer to other gas-borne targets; a CH4 or NH3 fill would allow simultaneous (n,p) and (n,α) measurements, with hydrogen providing its own internal flux normalization.
  • A testable extension: push the measured angular range for 16O(n,α1,2,3) below 40° and above 160° c.o.m.; if the differential cross section is not flat there, the fivefold integrated excess over ENDF/VIII.0 will move, possibly by a large factor.
  • The regular ~90° minimum in the 16O(n,α1,2,3) angular distributions is the kind of signature an R-matrix fit to 13C compound states could use to assign partial waves, extending evaluations beyond the current joined region.
  • If the fivefold excess holds, oxygen-containing structural materials in reactors would be a larger helium source and neutron sink than libraries currently credit, with implications for fuel-cladding lifetimes.
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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

2 major / 5 minor

Summary. This paper reports differential and angle-integrated cross sections for 12C(n,α0), 16O(n,α0), and 16O(n,α1,2,3) at neutron energies between 7.2 and 10 MeV, measured with the TexAT Time Projection Chamber operated in active-target mode with CO2 gas. Events are reconstructed with the RANSChiSM track-fitting method and classified into channels using a multinomial probability weighting based on χ² values. Absolute normalization is derived from 1H(n,p) scattering on a CH2 foil. The differential cross sections are compared with previous data from Kuvin (12C) and Lee (16O) and show reasonable agreement where angular ranges overlap. Integrated cross sections are obtained via Eq. (5), which extrapolates the measured angular distribution over unmeasured intervals by assuming a constant sin-weighted differential cross section. The paper's central claim is that the 16O(n,α1,2,3) integrated cross section deviates from ENDF/VIII.0, exceeding it by up to a factor of 5 at low energies.

Significance. If the measurement is correct, this is the first neutron-induced reaction measurement performed with an active-target TPC, and it provides differential cross-section data with broader angular coverage than previous experiments for these important reactor-relevant reactions. The use of an external normalization standard and the favorable comparisons with independent data (Kuvin, Lee, ENDF) are notable strengths. However, the headline integrated-cross-section claim for 16O(n,α1,2,3) depends on an unvalidated extrapolation outside the measured angular range. The authors themselves state for 12C(n,α0) that the observed underestimate at 9.2 MeV 'may be attributed to large cross sections at both small and large angles that are outside of our covered angular range,' which directly indicates the risk that Eq. (5) misses forward/backward strength. Thus, while the differential data are likely valuable, the integrated cross sections—particularly the factor-of-5 deviation—need additional support before they can be considered established.

major comments (2)
  1. [§5, Eq. (5)] The integrated cross sections are computed by filling unmeasured angular intervals with a constant dσ/dΩ equal to the sin-weighted average over the measured range [θ_L,θ_H]. No uncertainty is propagated for this extrapolation. In the discussion of Fig. 7, the authors attribute the 12C(n,α0) underestimate at 9.2 MeV to 'large cross sections at both small and large angles that are outside of our covered angular range,' which is direct evidence that Eq. (5) can systematically underestimate integrated cross sections when angular distributions peak outside the measured range. Because the low-energy 16O(n,α1,2,3) data are restricted to approximately 40–160° c.m. with an additional heavy-fragment cut, the factor-of-5 excess over ENDF is not secure. Please provide a model-dependent estimate of the extrapolation uncertainty (e.g., using Legendre-polynomial fits constrained by the data) or present
  2. [§4 and §5] The 'safe angular range' θ_L to θ_H is never quantified in the manuscript. The text states that 'the safe angular range for each decay path was evaluated using the two above constraints' but no table, figure, or numerical values are given for θ_L and θ_H per reaction, energy, and gas pressure. Without this information, the reader cannot assess what fraction of the 4π solid angle is actually covered, and therefore cannot judge the magnitude of the extrapolation inherent in Eq. (5). Please include a table or plot specifying the angular limits used for each data point, and discuss how the choice of these limits affects the integrated cross sections.
minor comments (5)
  1. [Introduction, references] The text cites 'van Der Zwan and Obst' with unresolved placeholders '[?,?]'. These references need to be completed before submission.
  2. [Data availability] The Data availability statement currently reads 'xxxx'; the actual DOI or link must be supplied.
  3. [Abstract] The sentence 'A comparison between our current and previous results at overlapping energies and angles which showed good agreement in angular dependence and absolute cross section' is a sentence fragment; please rephrase.
  4. [Eq. (5)] The notation in Eq. (5) defines the extrapolated estimate as σ̃, but the text often refers to it as 'total cross section' without distinguishing the extrapolation from a directly measured integral. Please make this distinction explicit.
  5. [§3, Eq. (3)] The description of the multinomial variance is terse. Clarify that yields are fractional counts and how the variance in Eq. (3) propagates into the differential cross-section uncertainties.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: measurement is externally normalized and benchmarked against independent data; Eq. (5) is an extrapolation, not an input-output identity.

full rationale

The central results are measured differential cross sections obtained from track reconstruction in an active-target TPC, with absolute normalization provided by the well-known 1H(n,p) cross section from a CH2 foil—an external standard that is not fitted to the (n,α) channels. The angle-integrated cross sections are derived from Eq. (5), which extends the measured sin-weighted average over the unmeasured angular intervals; this is a model-dependent extrapolation, not a circular reduction, because the reported numbers are fully determined by the measured differential data and external normalization. Comparisons to ENDF/VIII, Kuvin, Lee, and Geiger use independent literature benchmarks, and none of those benchmarks are used to set parameters in the present measurement. The cited prior work by the same collaboration provides detector design, tracking software, and an energy-verification cross-check, but it does not supply the central (n,α) cross-section claim or any self-referential uniqueness constraint. The paper's own caveat that the 12C benchmark may underpredict forward/backward strength outside the covered angular range is a legitimate systematic limitation of the angular extrapolation, not evidence that the derivation is equivalent to its inputs. No specific circular step can be exhibited, so the score is 0.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The work is an experimental measurement with no fitted derivation. The load-bearing inputs are the external 1H(n,p) normalization, the channel-assignment model, and an ad hoc angular extrapolation for integrated cross sections. No new particles, forces, or conserved quantities are introduced.

free parameters (1)
  • Out-of-range dsigma/dOmega constant
    In Eq. (5), the differential cross section outside the measured angular range is treated as a constant (with a 'constrained estimate' that is not specified numerically). The integrated cross sections, including the deviation-from-ENDF claim, depend on this ad hoc choice.
assumptions (4)
  • ad hoc to paper The unmeasured angular intervals can be filled by a constant dsigma/dOmega with sine weighting (Eq. 5).
    The angle-integrated cross sections require an assumption about regions outside 40–160 deg c.o.m. and outside the reliable heavy-fragment range; no data or uncertainty is assigned to this extrapolation.
  • domain assumption The p-value multinomial probabilities P_ik correctly represent channel assignment probabilities with no unmodeled systematic bias.
    Section 3 converts chi-squared values to p-values (Eqs. 1–3) and uses them as yields; the text notes poor separation at small theta_H but provides no systematic check that misclassification is fully accounted for by the larger error bars.
  • domain assumption The 1H(n,p) reaction from the CH2 foil provides an accurate absolute neutron flux normalization.
    Section 2 uses the well-known 1H(n,p) cross section to normalize all channels. Agreement with 12C benchmark data supports this, but a normalization error would propagate directly to all oxygen cross sections.
  • domain assumption The Geiger 9Be(alpha,n) Legendre coefficients, normalized by Kuvin total cross sections, are a valid benchmark for 12C(n,alpha0).
    Section 4.1 compares the current carbon data to Geiger curves scaled by Kuvin's total cross sections. If this benchmark is wrong, the strongest validation of the method and normalization is weakened.

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Cite this review

Pith. "Pith review of Differential cross sections for ${{^{12}\mathrm{C}(n,\alpha_{0})}}$, ${{^{16}\mathrm{O}(n,\alpha_{0})}}$ and ${{^{16}\mathrm{O}(n,\alpha_{1,2,3})}}$ between ${{E_n}}$ = 7.2 and 10 MeV with an active-target Time Projection Chamber." pith.science (2026). https://pith.science/paper/JD33GZT2

@misc{pith2026260102841,
  author       = {Pith},
  title        = {Pith review of: Differential cross sections for $^12\mathrmC(n,\alpha_0)$, $^16\mathrmO(n,\alpha_0)$ and $^16\mathrmO(n,\alpha_1,2,3)$ between $E_n$ = 7.2 and 10 MeV with an active-target Time Projection Chamber},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JD33GZT2}},
  note         = {Machine review of arXiv:2601.02841}
}
abstract

Data for the ${{^{12}\mathrm{C}(n,\alpha_{0})}}$, ${{^{16}\mathrm{O}(n,\alpha_{0})}}$ and ${{^{16}\mathrm{O}(n,\alpha_{1,2,3})}}$ differential cross sections are important for several different areas of nuclear physics such as understanding neutron transmutation in nuclear reactors. The TexAT Time Projection Chamber was used to measure the differential and angle-integrated cross sections in active-target mode. The chamber was filled with CO$_2$ gas and used a quasi-monoenergetic neutron beam from the $d(d,n)$ reaction at Edwards Accelerator Lab at Ohio University. A comparison between our current and previous results at overlapping energies and angles which showed good agreement in angular dependence and absolute cross section. A broader angular coverage than previous results demonstrated that the integrated cross section for the \po16 reaction deviates from ENDFVIII.0 evaluations. This first instance of neutron-induced measurements with an active-target Time Projection Chamber demonstrates the use of this method for high-quality differential cross section data across a broad angular range, generating good statistics with a relatively low-intensity beam.

Figures

Figures reproduced from arXiv: 2601.02841 by the authors.

Figure 1
Figure 1. Schematic overview showing the key features of the setup. The neutron beam was generated by a deuteron beam incident on a deuterium gas cell. A collimator system reduces the size of the beam at 4 meters to 1.5-cm diameter. The neutrons are then incident upon the TexAT TPC where (n,α) reactions are measured from the CO2 gas inside the active area of the Micromegas (MM). In addition, neutron elastic scattering off a C… view at source ↗
Figure 2
Figure 2. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Centre-of-mass differential cross sections for the 12C(n, α0) reaction at different incident neutron energies, in comparison to the Legendre coefficients of Geiger [15], normalised to reproduce the total cross sections measured by Kuvin [5]. The 12C(n, α0) differential cross sections for the full selection of neutron energies are shown in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Centre of mass differential cross sections from the 9Be(α,n0) 12C reaction from Geiger [15, 16], converted to different incident neutron energies for the 12C(n, α0) interaction. The colour scale also represents neutron energy to aid visualisation. 4.2 16O(n, α0) Obtain…
Figure 5
Figure 5. Figure 5: Centre of mass differential cross sections for the 16O(n, α0) reaction at different incident neutron energies in comparison to the values of Lee [4]. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Centre-of-mass differential cross sections for the 16O(n, α1,2,3) reaction at different incident neutron energies in comparison to the values of Lee [4]. for 16O(n, α1,2,3) are shown in [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Angle-integrated cross section, ˜σ, for 12C(n, α0) across the angular range covered by the current work, compared to previous literature values of Kuvin [5] which has also been smeared by our intrinsic beam energy spread, shown by the red line. small neutron energies, …
Figure 8
Figure 8. Figure 8: Angle-integrated cross section, ˜σ, for 16O(n, α0) and 16O(n, α1,2,3) across the angular range covered by the current work, compared to previous literature values of Lee [4] and the ENDFVIII.0 evaluation [21]. The 16O(n, α0) ENDFVIII.0 cross section is also shown after…

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Reviewed August 3, 2026 · model on record in the stance chip above.