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Nonproportional Response of a GAGG Scintillator to Beta and Gamma Radiation over a Wide Energy Range in PIKACHU

T0 review · 3 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read The GAGG scintillator's light yield responds more nonlinearly to gamma rays than to beta rays over 50–2614 keV, and separating the two response curves makes the PIKACHU background model fit better.

desk verdict Useful new high-energy GAGG nonproportionality data, with a real but manageable multi-scatter contamination concern in the CCT beta points. read the letter →

arxiv 2608.05601 v1 pith:33C2EZON submitted 2026-08-06 physics.ins-det hep-ex

Takumi Omori , Takashi Iida , Yosuke Suga , Masao Yoshino , Ken-Ichi Fushimi , Azusa Gando , Nobuo Hinohara , Keishi Hosokawa
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Motonao Ishigami Kei Kamada Tadafumi Kishimoto Keita Mizukoshi Takuya Sako Yasuhiro Shoji Shota Sugi
This is my paper · ORCID
classification physics.ins-dethep-ex
keywords GAGGscintillatornonproportionalresponseComptoncoincidencetechniquebeta-raygamma-raybackgroundmodelPIKACHUcalibration
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, from the PIKACHU double-beta-decay program, measures how the light yield of a large GAGG scintillator crystal depends on whether energy is deposited by beta electrons or by gamma rays. The central result is that the two responses are not the same: gamma rays show a stronger nonproportional response than beta rays across 50–2614 keV, meaning a gamma-ray energy deposit produces less light at low energies than a beta electron depositing the same energy. The authors use a Compton coincidence technique with a germanium detector for beta rays and monoenergetic gamma sources for gamma rays, then feed the two measured curves into the PIKACHU background model as separate double-exponential functions. The corrected model reproduces the measured alpha and beta/gamma background spectra better than the previous model, which had assumed a proportional response below 80 keV. If the result is right, scintillator experiments that calibrate with gamma sources while detecting beta-like events need to correct for this particle-type dependence.

What carries the argument

The key object is the nonproportional-response ratio $\mathrm{nPR}=E_{\mathrm{GAGG}}/(E_\gamma-E_{\mathrm{Ge}})$, which is measured event-by-event using the Compton coincidence technique: a germanium detector tags the scattered gamma ray, and the Compton formula $E'_\gamma=E_\gamma/[1+(E_\gamma/m_e c^2)(1-\cos\theta)]$ fixes the energy that the GAGG crystal absorbed. For gamma rays, photopeak centroids from monoenergetic sources supply the same ratio without a coincidence requirement. The two response curves are then represented as double-exponential functions of deposited energy and used as separate correction factors in the background model, replacing the previous single assumption of 70% light yield below 80 keV.

What would settle it

Re-run the analysis with a sum-energy requirement that the GAGG and germanium energies add up to the incoming gamma energy; if the reported nonproportionality values shift by more than the quoted uncertainties, multiple Compton scattering contaminated the diagonal-band selection and the beta-ray curve is biased. A small-crystal version of the same setup, where a second scatter is kinematically suppressed, would provide a clean cross-check.

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Extended reading notes

Core claim

On its own terms, this paper establishes that the GAGG scintillator's light yield per deposited energy is not the same for gamma-ray and $\beta$-ray energy deposits. The $\beta$-ray response, measured with the Compton coincidence technique, is quantified as $\mathrm{nPR}=E_{\mathrm{GAGG}}/(E_\gamma-E_{\mathrm{Ge}})$ and falls to about 0.90 at 76 keV while remaining near 1.0 at higher energies; the gamma-ray response, from photopeak centroids, drops to about 0.88 at 100 keV after renormalizing to 661.7 keV. The fitted double-exponential curves asymptote to 1.07 for $\beta$ rays and 1.02 for gamma rays above 3000 keV. Inserting these two curves separately into the PIKACHU background model improves the fit to both $\alpha$ and $\beta$/gamma background spectra, with the 2.0 MeV discrepancy attributed to $^{234\mathrm{m}}$Pa largely removed.

Load-bearing premise

The result assumes that each selected event is a single bounce of the gamma ray inside the GAGG crystal and that the germanium detector absorbs the outgoing gamma ray whole, so the energy deposited in the crystal is exactly the difference between the incoming and outgoing gamma-ray energies.

Editorial extensions

If this is right

  • The PIKACHU background model should use separate beta and gamma response functions; the paper reports that this correction lowers the chi-square of the fits to the measured alpha and beta/gamma background spectra.
  • The old assumption of a flat 70% light-yield factor below 80 keV is replaced by measured double-exponential curves, which shifts the modeled positions of sub-100 keV background peaks.
  • The dominant beta background, $^{234\mathrm{m}}$Pa with a 2.269 MeV Q-value, is modeled with the beta curve, which removes the model-data mismatch around 2.0 MeV.
  • The Compton coincidence setup can be applied directly to future GAGG crystals so their nonproportional response is known before deployment in the double-beta decay search.

Reading between the lines

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

  • Because the light yield depends on particle type, a scintillator calibrated with gamma sources will systematically misestimate energies of beta-like events unless the same two-curve correction is applied; this extends beyond the PIKACHU background to any GAGG-based detector.
  • The attributed mechanism, inner-shell photoelectric absorption followed by X-ray and Auger cascades, predicts that the gamma-beta gap should grow as the photoelectric fraction of the gamma interaction increases, which could be tested by comparing high-Z and low-Z scintillator compositions.
  • The double-exponential fit is unconstrained below 50 keV, so the curves could diverge differently at very low energies; a conversion-electron or x-ray source calibration below 50 keV would be a direct test of the extrapolation.
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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 / 4 minor

Summary. This manuscript reports measurements of the nonproportional response (nPR) of a large GAGG scintillator used in the PIKACHU double-beta-decay experiment. The beta-ray response is measured with the Compton coincidence technique using a germanium detector with 22Na and 208Tl sources, and the gamma-ray response is obtained from photopeak measurements with several radioactive sources. The authors find a stronger nonproportional response for gamma rays than for beta rays over 50-2614 keV, parameterize both responses with double-exponential functions, and incorporate them into a GEANT4-based background model. They report that the updated model reproduces measured alpha- and beta(gamma)-ray background spectra better than a model without the nPR correction.

Significance. If the reported beta-vs-gamma difference is correct, the paper provides the first nPR data for GAGG above 1 MeV and demonstrates a particle-type dependence of the light yield that is relevant for energy calibration and background modeling in scintillator-based rare-event searches. The manuscript is careful in describing the CCT setup, reports slice-width checks, and compares low-energy results with prior publications, which strengthens confidence in the lower-energy part of the beta curve and in the gamma curve. However, the high-energy beta points and the lack of a multi-scatter correction leave the central beta-vs-gamma comparison less secure than the text suggests.

major comments (3)
  1. [§3.2 (Eq. 2), Fig. 4] The diagonal-band event selection in Fig. 4 does not exclude multiple Compton scattering inside the large GAGG crystal (65 mm diameter, 100 mm length). For events where the scattered photon undergoes a second Compton scatter in the GAGG and is then fully absorbed in the Ge detector, the relation E_GAGG + E_Ge = E_gamma still holds, so these events remain on the diagonal. In a fixed Ge-energy slice, such events contribute at the same nominal deposited energy E_gamma - E_Ge, but the GAGG energy is deposited by two lower-energy electrons rather than one. Since nPR depends on the electron track structure, the fitted E_GAGG peak is biased. The 2614 keV datasets, and especially the 2313 keV point, are most exposed because the multi-scatter probability grows with incident energy. No sum-energy cut, multi-scatter fraction estimate, or simulation-based correction is provided, so the beta nPR curve in Fig. 6 is not robustly established.
  2. [§4, Fig. 6, Fig. 5(c)] The two highest-energy beta points (E_gamma - E_gamma' = 2016 and 2313 keV, from 208Tl) are based on only 0.7 h and 28.1 h of data at approximately 0.1 Hz coincidence rate, yielding sparse GAGG spectra in each Ge slice. The spectrum in Fig. 5(c) is fit with a double Gaussian whose background component is an empirical Gaussian attributed to accidental coincidences; the text states that nPR was 'confirmed to be insensitive' to this component, but no quantitative systematic uncertainty is provided. No systematic error budget is given for the background model choice, the Ge slice midpoint approximation, or the energy calibration. These two points drive the asymptotic nPR value of 1.07 for beta rays and the claimed difference from gamma nPR; without a systematic error estimate the central comparison is underdetermined.
  3. [§4, Fig. 7] The claim that the background model incorporating the measured nPR 'successfully reproduced' the alpha- and beta(gamma)-ray data is supported only by showing chi-square values in Fig. 7. Because the updated model adds the double-exponential nPR parameters, a reduction in chi-square is expected even without a genuine improvement, and the reader cannot evaluate whether the improvement is statistically significant. A quantitative comparison, such as delta chi-square with the number of added parameters or a likelihood-ratio test, is needed to support the abstract and conclusion.
minor comments (4)
  1. [Sec. 3.2 / Table 1] The phrase 'which was calculated using Eq. (1)' in the Table 1 caption is awkwardly placed; consider moving this information to the text.
  2. [Sec. 4] There is a typo in the sentence 'the model with correction of the nonproprotional response': 'nonproprotional' should be 'nonproportional'.
  3. [Sec. 2.2] The quoted Ge detector energy resolution (0.26% sigma at 662 keV) and nonlinearity (<0.17 keV) would be easier to assess if the set of calibration gamma lines used to determine them were specified.
  4. [Fig. 6 caption] The figure caption does not explain the filled/open marker convention for the 22Na and 208Tl beta data; the explanation appears only in the body text and should be repeated in the caption.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the measured nPR curves are direct CCT and photopeak inputs, and their use in the background model is a downstream application rather than a construction of the result.

full rationale

The paper's derivation chain is self-contained. The beta nPR values are obtained from Compton-coincidence measurements: for each Ge-energy slice, E_GAGG is the fitted peak in the GAGG spectrum and E_gamma - E_Ge is the kinematic Compton energy, so Eq. (2) is a direct measured ratio, not a fitted parameter later renamed as a prediction. The gamma nPR values are photopeak ratios normalized to the 1274 keV calibration; this normalization is an explicit convention and does not by construction force the observed energy dependence. The double-exponential curves are fits to those measured nPR values and are then inserted as fixed response functions into the GEANT4 background model. The subsequent comparison of background fits with and without this correction validates an independently measured input against a different dataset; it does not reduce the output to the input. The paper cites its own prior work for the purified crystal [4] and for the uncorrected background model [7], but these citations supply the test detector and the baseline model rather than the beta/gamma nPR result, so they are not load-bearing for the central claim. No equation defines the claimed result in terms of itself, and no fitted quantity is relabeled as a prediction. Concerns about multiple Compton scattering inside the large GAGG crystal or about the diagonal-band selection would be systematic-error considerations, not circularity, and therefore do not affect the circularity score.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central measurement rests on standard Compton kinematics, the assumed linearity of the Ge reference detector, the single-scatter interpretation of the coincidence data, and the empirical double-exponential model used to interpolate the response. No new physical entities are introduced.

free parameters (2)
  • Double-exponential fit parameters for beta nPR = not reported (4 parameters)
    A double-exponential function is fitted to the beta-ray nPR data points in Fig. 6 and then used in the background model. Values are not given in the text.
  • Double-exponential fit parameters for gamma nPR = not reported (4 parameters)
    A double-exponential function is fitted to the gamma-ray nPR data points in Fig. 6 and used in the background model. Values are not given in the text.
assumptions (5)
  • standard math Compton scattering formula (Eq. 1) relates scattering angle to scattered photon energy.
    Used to set scattering angles and to compute deposited energy E_gamma - E_Ge in the CCT analysis.
  • domain assumption The Ge detector response is linear with residual nonlinearity less than 0.17 keV over 276-2614 keV.
    Quoted from calibration in Section 2.2; systematic deviations would propagate into nPR.
  • domain assumption The diagonal bands in the 2D energy spectra represent single Compton scattering events with full energy deposition of the scattered gamma in the Ge detector.
    This is the basis for assigning deposited energy and extracting E_GAGG in Section 3.2. The paper does not explicitly cut on the energy sum or quantify multi-scatter contamination.
  • ad hoc to paper A double-exponential function adequately describes nPR as a function of deposited energy over 50-3000+ keV for both beta and gamma rays.
    Chosen as an empirical fit in Section 4; no physical model is given and behavior outside measured points is extrapolated.
  • domain assumption The background model components and normalizations in Ref. [7] are correct aside from the nPR correction.
    The model improvement claim in Section 4 assumes the only significant deficiency is the nPR response; if the baseline model is deficient elsewhere, the chi-square improvement could be coincidental.

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Cite this review

Pith. "Pith review of Nonproportional Response of a GAGG Scintillator to Beta and Gamma Radiation over a Wide Energy Range in PIKACHU." pith.science (2026). https://pith.science/paper/33C2EZON

@misc{pith2026260805601,
  author       = {Pith},
  title        = {Pith review of: Nonproportional Response of a GAGG Scintillator to Beta and Gamma Radiation over a Wide Energy Range in PIKACHU},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/33C2EZON}},
  note         = {Machine review of arXiv:2608.05601}
}
abstract

Nonproportional response of scintillation light yield for sub-MeV radiations is a well-known characteristic of inorganic scintillators. In the PIKACHU experiment, a precise understanding of the nonproportional response of the GAGG ($\mathrm{Ce:Gd_3Al_2Ga_3O_{12}}$) scintillator is essential for background modeling. In this study, the nonproportional response of the GAGG scintillator was evaluated for both $\beta$ and $\gamma$ rays. The response for $\beta$ rays was measured using the Compton coincidence technique with a germanium detector, while that for $\gamma$ rays was evaluated using several monoenergetic $\gamma$-ray sources. The measurement results showed different responses for $\beta$ and $\gamma$ rays, with a stronger nonproportional response for $\gamma$ rays than for $\beta$ rays over the energy range of 50--2614~keV. The background model incorporating the measured nonproportional responses reproduced the measured background spectra more accurately compared with the model without the nonproportional response correction. These results demonstrate the importance of precise evaluation of the nonproportional response of the GAGG scintillator which is essential not only for background modeling in the PIKACHU experiment but also for accurate energy calibration in scintillator-based experiments.

Figures

Figures reproduced from arXiv: 2608.05601 by the authors.

Figure 1
Figure 1. Experimental setup used in this study. CCT measurements. The 208Tl source used in this study originated from a radioactive iso￾tope contained in a 2% thoriated tungsten electrode used for tungsten inert gas welding. The expected energies of the Compton electrons, Eγ − E′ γ which was calculated using Eq. (1), are also listed in the table. The coincidence events were acquired at approximate rates of 1–2 Hz for the 22N… view at source ↗
Figure 2
Figure 2. GAGG scintillator used in the PIKACHU experiment. The crystal has a diameter of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. An example of the waveforms from the GAGG scintillator (red) and Ge detector [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Two-dimensional energy spectra for events selected using the ∆ [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Representative GAGG energy spectra for selected Ge-energy slices. The green dashed [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: The nonproportional response of the GAGG scintillator. The nPR values for [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Background-model fits to the measured α- and β(γ)-ray spectra. The black points represent the background spectrum of the GAGG scintillator measured at the Kamioka underground laboratory. The blue and red curves correspond to the models without and with the nonproportio…

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