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Measurement of production branching ratio after muon nuclear capture reaction of Al and Si isotopes

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Pith's one-line read Absolute muon-capture branching ratios for aluminum and silicon reveal an even-odd proton-number effect.

desk verdict New absolute muon-capture branching ratios for Al and Si with a robust even-odd 0n0p effect; the neutron background needs a systematic and the 389.7-keV exclusion wants an explanation. read the letter →

arxiv 2507.19753 v2 pith:IZVH4JAP submitted 2025-07-26 nucl-ex

R. Mizuno , M. Niikura , T.Y. Saito , T. Matsuzaki , S. Abe , H. Fukuda , M. Hashimoto , A. Hillier
show 13 more authors
K. Ishida N. Kawamura S. Kawase T. Kawata K. Kitafuji F. Minato M. Oishi A. Sato K. Shimomura P. Strasser S. Takeshita D. Tomono Y. Watanabe
This is my paper
classification nucl-ex
keywords muonnuclearcaptureproductionbranchingratioin-beamactivationmethodaluminum-27siliconisotopesGamow-Tellerstrengthproton-neutronpairingeven-oddeffect
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 measures what happens after a negative muon is captured by an atomic nucleus in aluminum and silicon, counting the residual nuclei left after the excited system emits neutrons, protons, and alpha particles. It reports absolute production branching ratios—the probability of each emission channel—for 27Al and 28,29,30Si with the highest accuracy to date. The key result is that the no-particle-emission channel is 9.90(33)% for 27Al but 18.9(9)% for 28Si, a clear even-odd proton-number dependence. The authors trace this difference to low-energy Gamow-Teller strength below the neutron separation energy, enhanced by proton-neutron pairing in even-Z final nuclei. If the interpretation holds, these branching ratios provide a benchmark for muon-capture models and a way to probe isovector transitions in nuclei.

What carries the argument

The in-beam activation method is the central mechanism: a pulsed muon beam irradiates the target, a plastic scintillator counts the muons, germanium detectors record β-delayed γ-rays from the produced nuclei, and the absolute branching ratio is formed as $b=N_{\rm prod}/N_{\rm cap}$. Absolute normalisation comes from a low-intensity beam in which each pulse's muon number can be counted, and the calibrated high-intensity beam then gives high statistics for rare channels; enriched powder targets are normalised through a decomposition of the natural-silicon data. Around this core, the paper builds the interpretation from channel-by-channel threshold energies, shell-model Gamow-Teller strengths, and simulations of particle transport and evaporation.

What would settle it

A concrete check: measure the 0n0p branching ratios of 27Al and 28Si with the same beam but with target holders of very different surrounding mass, or insert an active neutron detector around the target. If the apparent 9.9% versus 18.9% difference moves by more than a few percent, the even-odd conclusion is contaminated by target-dependent neutron background.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that muon nuclear capture on 27Al and 28,29,30Si leaves a well-measured distribution of residual nuclei, and that distribution carries nuclear-structure information. The 0n0p channel—capture followed by no neutron or proton emission—is 9.90(33)% for 27Al versus 18.9(9)% for 28Si, and the paper argues this roughly two-fold gap cannot come from separation energies or average excitation energy alone. Instead, shell-model Gamow-Teller strengths summed below the one-neutron separation energy are 1.77 and 3.36 for the two transitions, nearly matching the same ratio as the branching ratios. The paper also establishes that neutron emission without charged particles dominates for all four isotopes, that the 0n1p and 2n2p channels fall with increasing neutron excess, and that production branching ratios can be inverted by a statistical evaporation model to estimate the excitation-energy distribution, yielding average excitation energies of about 16 MeV for 28Si and 15 MeV for 30Si.

Load-bearing premise

The load-bearing premise is that neutrons from muon captures in material around the target contribute negligibly to the measured 0n0p channels; the paper puts the maximum contamination at about 3%, comparable to its uncertainties, and does not correct for it.

Editorial extensions

If this is right

  • The 0n0p channel becomes a systematic observable: for even-Z final nuclei, enhanced proton-neutron pairing should suppress neutron emission and raise the no-emission branching ratio, and the current data place the first precise anchor points at 27Al and 28,29,30Si.
  • Prompt γ-ray measurements of the 0n0p channel cover at least 88% of the absolute branching ratio for 28Si and essentially all of it for 27Al, so direct ground-state populations after muon capture are small.
  • Current transport-code simulations overestimate neutron multiplicities, particularly for 27Al and 30Si, because they underestimate direct and pre-equilibrium emission; reproducing the new absolute branching ratios requires fixing that component.
  • Microscopic evaporation models can reproduce the overall ordering of channels but underestimate charged-particle emission, so their treatment of the high-energy excitation tail needs revision.
  • Production branching ratios alone can constrain the low-energy part of the muon-capture excitation function, below roughly 40 MeV, where statistical evaporation dominates.

Reading between the lines

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

  • A direct test of the pairing interpretation would be a coincidence measurement of emitted neutron energy and charged particles for 27Al and 28Si, checking whether the extra low-energy Gamow-Teller strength in 28Si actually removes neutrons from the evaporation cascade.
  • The same absolute-normalisation technique could be extended to other s-d shell nuclei; if the even-odd 0n0p pattern tracks cumulative B(GT) below the neutron separation energy, the branching ratio would become a cheap isovector probe for nuclei where charge-exchange data are scarce.
  • The uncorrected neutron background is the main threat: if it varies with target size and holder material, the 9.9% versus 18.9% comparison could shift by up to a few percent, so a dedicated background run with a low-mass target holder would sharpen the physics claim.
  • The observed 4n4p and 6n4p channels in silicon isotopes, interpreted as multi-alpha emission, suggest that production branching ratios could also constrain cluster structures in highly excited states beyond the Gamow-Teller picture.
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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

3 major / 5 minor

Summary. This paper reports absolute production branching ratios (BRs) for muon nuclear capture on 27Al and 28,29,30Si, measured with the in-beam activation method at two pulsed muon facilities (RIKEN-RAL and J-PARC). The authors count stopped muons with a plastic scintillator and detect beta-delayed gamma rays with germanium detectors, with a low-intensity countable beam at RAL providing absolute normalization and a high-intensity beam at J-PARC providing high statistics after calibration. The main results are the BRs of residual nuclei after particle emission, presented in Tables II–VI, including the 0n0p channels: 9.90(33)% for 27Al and 18.92(10)(91)% for 28Si. The paper interprets these results as evidence for an even-odd proton-number dependence of the 0n0p channel, a decreasing 0n1p and 2n2p probability with increasing neutron excess, and a general predominance of neutron emission. The measured BRs are compared with previous activation and prompt-gamma measurements, with PHITS and microscopic evaporation model (MEM) calculations, and with shell-model Gamow-Teller strengths. A method for estimating the excitation energy distribution from the measured BRs is also proposed.

Significance. If the results hold, they provide the most accurate absolute muon-capture production BRs in the aluminum-silicon mass region to date, and the cross-facility consistency between RAL and J-PARC is a notable strength. The even-odd Z dependence of the 0n0p channel, supported by the large 27Al vs 28Si difference, is a valuable constraint on the low-energy isovector response and on proton-neutron pairing effects. The paper also gives a careful uncertainty decomposition that separates relative and absolute components, propagates ENSDF decay-data uncertainties, and treats enriched-target impurities and stopping rates in some detail. The comparisons with PHITS and MEM, and the proposal to extract excitation functions from BRs, are useful contributions even though the model comparisons remain partly qualitative. The manuscript does not include a data-release or code repository, but the methodology is documented in sufficient detail to be reproducible in principle.

major comments (3)
  1. [Sect. V] The paragraph beginning 'The maximum potential contamination...' states that neutron-induced background from muon stops in surrounding material could contaminate the 0n0p channels by up to approximately 3%, that this is comparable to the measurement uncertainty, and that it was not corrected. Since the even-odd 0n0p comparison (9.90(33)% for 27Al, Table II, vs 18.92(10)(91)% for 28Si, Table IV) is the paper's main physics conclusion, this systematic must be included in the quoted uncertainties. The underlying assumption that the number of muons stopping in the surroundings equals the number stopping in the target is questionable for the enriched powder targets, whose measured stopping rates are only 0.298–0.652 (Table I). Please quantify the contamination separately for plate and powder targets, including the target self-induced neutron contribution, and state explicitly how the quoted BRs change if the estimated contamination is applied as a correction or as a one-sided systematic.
  2. [Sect. V, Tables III, V, VI] For 25Na in the J-PARC silicon data, the BR extracted from the 389.7-keV line is significantly lower than those from the 585.0- and 974.7-keV lines, and the 389.7-keV point is excluded from the weighted average without identifying the cause. This unexplained discrepancy raises the possibility of an unaccounted efficiency, self-absorption, or background effect at low energy that could also affect other lines in the same data set. Please either identify the cause or provide a quantitative demonstration that including the 389.7-keV point does not change the compiled 25Na BRs beyond the quoted uncertainties.
  3. [Tables I and V; Sect. VI B] The stopping rate for the enriched 29Si target has a relative uncertainty of 24–26% at both facilities (0.652(169) at RAL and 0.260(63) at J-PARC), which propagates into roughly 25% scale uncertainties in the 29Si BRs (e.g., 29Al 15.01(48)(373) and 28Al 48.68(18)(1188)). The neutron-excess trend discussion in Section VI B uses these 29Si values, so the trend statements should either be restricted to the well-determined 28Si and 30Si points or explicitly quantify how the 29Si uncertainties affect the conclusions.
minor comments (5)
  1. [Abstract and headings] There are several typographical errors that should be corrected: 'irradiating the target. using a plastic scintillator' in the abstract, 'exitat states' in the Introduction, 'T rend' as a section heading, 'SUMMAR Y' in Section VII, 'Comparson' in the conclusions, 'reprocude' in Section VI C, 'Monte-Calro' in Section V, and 'whreas' in Section VI A.
  2. [Sect. IV A, Eq. (5)] The definition of Pdecay is confusing as written: the text says the numerator is computed 'assuming all the irradiated muon produced the given nucleus (Pcapϵstopb = 1)'. Please clarify that this is a normalization convention used to account for the time structure of the beam, and not a physical assumption that every muon produces every residue.
  3. [Sect. VI D] The excitation-function extraction uses H = 20 Gaussian functions with fixed centers and widths, and the hyperparameters were selected to minimize chi-square. Please state explicitly that the resulting excitation functions are model-dependent and not unique, and avoid presenting the quoted average excitation energies (16.4(3) and 15.4(3) MeV) without also stating that the uncertainties do not include the model-choice and evaluation-input uncertainties.
  4. [Fig. 12] The figure legend contains the typo 'Average Mutiplicity'; also, the use of open triangles for direct and pre-equilibrium emission and open squares for evaporation is described in the text but the symbols in the figure are not labeled directly, which makes the figure difficult to read.
  5. [Sect. VI A] The sentence 'This measurement represents the first reliable absolute data...' is stronger than the analysis supports, given the uncorrected neutron background and the unresolved 389.7-keV discrepancy. Please soften the claim to something like 'the first absolute BR measurement with percent-level precision in this mass region' or add the caveats needed to justify 'reliable'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the absolute calibration chain is anchored to an independent low-intensity RAL measurement, and the excitation-function estimate is explicitly a fit, not a prediction.

full rationale

The derivation chain is self-contained against external measurements. The RAL absolute BRs rest on directly counting muons with a low-intensity beam: the plastic-scintillator charge-integral peaks are fitted to muon numbers, so the RAL 27Al 27Mg BR is an independent absolute measurement, not an output of the same calibration it is later used for. The J-PARC calibration in Sect. IV B uses that RAL value explicitly as a normalization pivot, and the paper does not list a separate J-PARC value for the 27Mg calibration channel, so no result is being verified with the same number used to set it. The enriched-silicon stopping rates are solved from the overdetermined natSi decomposition, Eq. (6), with ϵstop as a nuisance parameter extracted from measured relative yields, not an input that forces the final BRs. The excitation-function estimate in Sect. VI D is presented as an unfolding: Eq. (10) minimizes χ2 against the measured BRs, and the outcome is labeled an 'estimated excitation function', not an independent prediction. The KSHELL B(GT) calculation is a separate theoretical input. Self-citations to Ref. [1] (in-beam activation method), Ref. [7] (muonic-atom capture probabilities), and Ref. [11] (detector performance) are external techniques or measurements that are not fitted to the target BRs; they therefore do not make the central claim circular. The uncorrected ~3% neutron-induced background on the 0n0p channels (Sect. V) is a genuine systematic limitation and should be propagated as an uncertainty, but it is a correction/error-budget issue, not a case of a result being defined by its own input.

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

No new particles, forces, or conserved quantities are introduced. The pn-pair enhancement discussed in Sect. VI B is an existing nuclear structure phenomenon, and the excitation function is an inferred distribution, not a new entity. The main free parameters are the stopping rates for powder targets, the J-PARC muon-count calibration constant, and the Gaussian coefficients used in the excitation-function unfolding.

free parameters (4)
  • Stopping rate ϵ_stop for enriched silicon powder targets = 28Si: 0.407(14) (RAL), 0.298(9) (J-PARC); 29Si: 0.652(169) (RAL), 0.260(63) (J-PARC); 30Si: 0.349(26) (RAL), 0.261(19)…
    Determined by least-squares decomposition of natural silicon data using Eq. (6). These are fitted to the same BR data and carry large uncertainties for 29Si and 30Si, directly affecting the absolute BRs of the enriched targets.
  • J-PARC plastic scintillator calibration parameter A = anchored to b(27Mg from 27Al)=9.90(33)% from RAL
    Converts charge integral Q to muon number n_beam = A×Q. It is fitted to the single RAL 27Mg BR and assumes linearity across beam intensities; any nonlinearity affects all J-PARC absolute BRs.
  • Excitation function Gaussian coefficients c_j (H=20) = not tabulated; Bayesian-optimized to minimize χ²
    In Eq. (9), ω(E*) is a sum of 20 Gaussians fit to the measured BRs using CCONE. The resulting average excitation energies (16.4(3), 15.4(3) MeV) are derived from this fit and are not independent of the input BRs.
  • Hyperparameters for excitation function fit = H=20, Ej=2.5 MeV×j, σj=5.0 MeV; RBF kernel length 3, variance 2; range constraint ω>0
    Chosen to minimize χ²; these are additional free choices in the unfolding.
assumptions (4)
  • domain assumption ENSDF evaluated decay data (half-lives, γ-ray intensities) are correct.
    Used in Eq. (4) to convert γ-ray yields to production numbers; uncertainties are propagated from ENSDF. If ENSDF has undisclosed systematic errors, all BRs shift.
  • domain assumption Muon capture probabilities Pcap from Ref. [7] are accurate.
    Pcap enters Eq. (3) and is taken from the authors' accepted paper. The quoted uncertainties are small (<0.4%), but a bias in this input would scale all absolute BRs.
  • ad hoc to paper The excitation function ω(E*) can be represented as a sum of Gaussians with H=20, fixed centers and widths (Eq. 9).
    This ansatz is introduced in Sect. VI D for the unfolding; it is not derived from theory and imposes a specific smooth shape.
  • domain assumption PHITS and MEM model parameters describe muon capture and subsequent de-excitation.
    Used for comparison in Sect. VI C; SCM parameters h0 and D are from Ref. [82], and the models have known deficiencies noted by the authors.

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Pith. "Pith review of Measurement of production branching ratio after muon nuclear capture reaction of Al and Si isotopes." pith.science (2026). https://pith.science/paper/IZVH4JAP

@misc{pith2026250719753,
  author       = {Pith},
  title        = {Pith review of: Measurement of production branching ratio after muon nuclear capture reaction of Al and Si isotopes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IZVH4JAP}},
  note         = {Machine review of arXiv:2507.19753}
}
read the original abstract

Background: Muon nuclear capture is a reaction between a muon and a proton inside a nucleus through weak interactions. This reaction results in the formation of an excited nucleus, which subsequently de-excites by emitting several particles. Examination of the excited state allows for an investigation of the properties of nuclear excitation and particle emission in highly excited nuclei. Purpose: This study investigates muon nuclear capture of 27Al and 28,29,30Si, focusing on determining the absolute production branching ratio (BR) following muon nuclear capture and subsequent particle emissions. By measuring the absolute production BR, we can collect valuable information on the excitation energy distribution of muon nuclear capture. Methods: Measurements were conducted using the in-beam activation method at two pulsed muon facilities: RIKEN-RAL beamline and MLF at J-PARC. Absolute BRs were determined by measuring the number of muons irradiating the target using a plastic scintillator and the beta-delayed gamma-rays emitted from the produced nuclei using germanium detectors. Results: The absolute production branching ratios of muon nuclear capture on 27Al and 28,29,30Si were obtained with the highest accuracy to date. Predominant neutron emissions, even-odd atomic number dependence of particle emission probabilities, and influence of the neutron excess were observed. These results were compared with previous measurements and theoretical models and discussed regarding the excitation energy distribution, particle emission mechanism, and nuclear properties, such as resonance in the isovector transition. Conclusion: This study emphasizes the importance of considering nuclear structure effects, even-odd effects of proton and neutron numbers, neutron excess, nucleon pairing effect, and particle emission mechanisms, in the context of the muon nuclear capture reaction.

Figures

Figures reproduced from arXiv: 2507.19753 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic of the experimental setup at (a) ISIS, [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Photographs of isotopically enriched silicon targets. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Raw signal of the plastic scintillator from PMT in [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (10 more)
Figure 3
Figure 3. Figure 3: FIG. 3. Part of the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Spectra of the charge integral obtained by utiliz [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Excitation function of the muon nuclear capture re [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Threshold energy of each particle emission for [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Summary of the BR of the 0n0p channel obtained [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Gamow-Teller strength of the transition from [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Comparison of the BR of neutron emission channels [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]
Figure 10
Figure 10. Figure 10: The PHITS calculation reproduced the overall trend of the BR: predominantly emitting neutrons and emit￾ting smaller charged particles, and especially accurately reproduced the BR of charged particle emissions. When focusing on the BR of the 0n0p channel, we observed t…
Figure 12
Figure 12. Figure 12: FIG. 12. Average multiplicity of neutron emission, calculated [PITH_FULL_IMAGE:figures/full_fig_p022_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Estimated excitation function from the experimen [PITH_FULL_IMAGE:figures/full_fig_p023_13.png]

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    Even-odd isotope dependence of no particle emission channel Comparing the neutron emission probabilities of 27Al and 28,29,30Si in Table VIII, the 0n0p channel ofµ−+27Al, 9.9(3)%, is obviously smaller than that of silicon isotopes. Although the 1n0p channel of 27Al and 28Si were not measured in the current measurement owing to their sta- ble residuals, th...

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    charged particle emission The BRs of one-proton and two-proton emission chan- nels are listed in Tables IX and X. When comparing the BRs of charged particle emission from isotopically en- riched silicon targets, the BRs of the 0n1p and 2n2p 19 2 4 6 8 10 00.2 0.4 0.6 0.8 1 Al 27 Si 28 Excitation Energy (MeV) B(GT) FIG. 9. Gamow-Teller strength of the tran...

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