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Nuclear level density of ${}^{128}$Te from $(\mathrm{p},\mathrm{p}'\gamma)$ scattering and complementary photonuclear data

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A particle-gamma coincidence measurement yields the nuclear level density of 128Te up to 5.8 MeV with the scale and slope set by photonuclear data and known levels, avoiding constant-temperature or Fermi-gas normalization.

desk verdict A careful Oslo-method NLD measurement for 128Te that is independent of CT/FG parameterizations but not model-free—the photonuclear normalization rests on an untested spin-independence assumption, so the abstract's 'no model dependencies' claim is too strong. read the letter →

arxiv 2501.09360 v2 pith:KT3HBUKI submitted 2025-01-16 nucl-ex

P.-A. Söderström , A. Kuşoğlu , S. Aogaki , D. L. Balabanski , S.-R. Ban , R. Borcea , M. Brezeanu , S. Calinescu
show 28 more authors
C. Costache R. Corbu M. Cuciuc A. Dhal I. Dinescu N. M. Florea T. Furuno A. Gavrilescu A. Gupta Y. Honda J. Isaak N. C. Jerca T. Kawabata V. Lelasseux R. Lica C. Marin C. Mihai S. Niculae H. Pai I. P. Pârlea T. Petruse A. Spataru D. A. Testov D. Tofan T. Tozar A. Turturică G. V. Turturică S. Ujeniuc
This is my paper · ORCID
classification nucl-ex
keywords nuclearleveldensity128Teparticle-gammacoincidencephotonuclearnormalizationgamma-raystrengthfunctionBrink-AxelhypothesisconstanttemperaturemodelFermigas
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 a measurement of the nuclear level density of 128Te across excitation energies from roughly 0 to 5.8 MeV, extracted from proton inelastic-scattering data in coincidence with gamma rays. The analysis uses the standard particle-gamma coincidence method, which determines the functional form of the level density and the gamma-ray transmission coefficient up to an exponential scale-and-slope ambiguity. That ambiguity is resolved here by normalizing the gamma-ray strength function to photonuclear absorption data and the level density to known discrete levels, without invoking the constant-temperature or Fermi-gas models. The resulting level density falls between the constant-temperature and Fermi-gas predictions and clearly diverges from a microscopic Skyrme-force calculation. The result provides a model-independent anchor for statistical-model reaction rates in this mass region.

What carries the argument

The mechanism carrying the argument is the first-generation decay probability identity $P(E_x, E_\gamma) = \rho(E_x - E_\gamma) T(E_\gamma) / \sum_{E_\gamma} \rho(E_x - E_\gamma) T(E_\gamma)$ and the associated continuous ambiguity given by the exponential transformation of $\rho$ and $T$ (the scale–slope transformation). The paper fixes this ambiguity by using the photonuclear absorption cross-section as an external constraint on $T(E_\gamma)$ (fixing $B$ and $\alpha$) and complete discrete-level spectroscopy as a constraint on $\rho$ (fixing $A$). This yields an absolute level density without constant-temperature or Fermi-gas normalization.

What would settle it

Measure the gamma-ray strength function of 128Te using a probe that selects a narrow, high-spin window (for instance, by tagging specific final states in a particle-γ coincidence experiment or using a future high-resolution photon beam to isolate J^π = 1 states) and compare it with the photoabsorption-derived strength function. A significant mismatch would invalidate the spin-independence assumption and change the extracted level density. Alternatively, if new discrete levels are found below 3.345 MeV, the completeness assumption used to set the absolute normalization A would need revision, altering the level density scale.

Watch

Extended reading notes

Core claim

The central claim is that the nuclear level density of 128Te from about 0 to 5.8 MeV can be obtained directly from experimental data, with the absolute normalization fixed by photonuclear data and complete low-lying spectroscopy rather than by constant-temperature or Fermi-gas extrapolations. The coincidence measurement yields a decay probability matrix from which, through the standard particle-gamma coincidence analysis, one obtains a family of equally good solutions for the level density $\rho(E_x)$ and transmission coefficient $T(E_\gamma)$, related by the transformation $\tilde{\rho} = A \rho \exp[\alpha(E_x - E_\gamma)]$ and $\tilde{T} = B T \exp(\alpha E_\gamma)$. The slope parameter $\alpha$ and absolute scale $B$ are set by matching the transmission coefficient to the photoabsorption cross-section, and the scale $A$ of the level density is set by matching to the evaluated discrete level scheme in the 2–3 MeV region. The extracted level density, listed in Table 1, lies between the constant-temperature and Fermi-gas parametrizations, but clearly diverges from the microscopic Skyrme-force prediction. The authors emphasize that this removes the intrinsic model dependence of the normalization, leaving only the spin-independence (Brink-Axel) assumption about the strength function.

Load-bearing premise

The gamma-ray strength function determined from photoabsorption states, which are almost entirely spin ~1, is the same as the strength function that governs the decay of the much broader spin distribution populated in the (p,p'γ) reaction; if that equality fails, the normalization of the strength function is systematically off, and with it the level density's absolute scale and slope.

Editorial extensions

If this is right

  • The tabulated level density can be used directly as input to statistical-model reaction-rate calculations for 128Te without the usual two-parameter model extrapolation.
  • The measurement provides a benchmark against which constant-temperature and Fermi-gas parametrizations can be tested in this mass region.
  • The observed divergence from the Skyrme-force calculation indicates that this microscopic model does not reproduce the empirical level density for 128Te.
  • The same normalization strategy can be extended to other nuclei without neutron-resonance data, potentially removing model dependencies from many existing particle-gamma coincidence level densities.
  • The gamma-ray strength function extracted from the same data set, once normalized, can be compared with photoabsorption results to test the spin-independence assumption.

Reading between the lines

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

  • If the spin-independence assumption holds, a future measurement of the gamma-ray strength function from a low-spin photoexcitation on the same target should match the normalized strength function used here; a mismatch would directly probe the assumption's validity.
  • The divergence from the Skyrme model, if it persists across neighboring tellurium isotopes, may signal missing correlations or pairing effects in the microscopic calculation rather than a single-nucleus anomaly.
  • Applying the same photonuclear normalization to existing particle-gamma coincidence data on other nuclei could yield a systematic, model-independent set of level densities, and could be tested by comparing the resulting gamma-ray strength functions with photoabsorption data.
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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 / 4 minor

Summary. This paper reports the extraction of the nuclear level density (NLD) of 128Te using the Oslo method applied to (p,p'γ) data measured with the ELI-NP/IFIN-HH setup. The three-parameter ambiguity (A, B, α) of the Oslo method is resolved by normalizing the γ-ray transmission coefficient to the photonuclear γ-ray strength function of Ref. [43] (fixing B and α) and the NLD to known discrete levels (fixing A), rather than to constant-temperature (CT) or Fermi-gas (FG) parameterizations. The resulting NLD is presented for excitation energies from 0 to 5.8 MeV and compared to CT, FG, and a Skyrme-based microscopic model. The paper finds that the experimental NLD lies between the CT and FG expectations and clearly deviates from the Skyrme prediction. Statistical and systematic uncertainties are propagated separately, with the 27% statistical / 73% systematic split resulting from χ²/NDF scaling.

Significance. If the underlying assumptions hold, this is a valuable new NLD measurement for 128Te and demonstrates a normalization route for the Oslo method that does not rely on CT or FG models, which is of interest for nuclear reaction rate calculations and for testing statistical-model input. The paper benefits from a clear presentation of the uncertainty propagation, including the χ²/NDF scaling and an explicit statistical/systematic decomposition. The central result, however, rests on the unverified spin-independence of the γ-ray strength function between the J^π≈1± ensemble probed by photon absorption and the broader spin distribution populated in (p,p'γ); this is load-bearing for the normalization and is acknowledged but not quantitatively addressed.

major comments (2)
  1. [Section 3, Eq. (3)-(5)] The normalization of B and α to the photoabsorption γSF of Ref. [43] assumes that the γSF is independent of the initial spin and parity, so that the J^π≈1± states probed by photon scattering are equivalent to the higher-spin states (up to J≈8, as shown in Fig. 4) populated in (p,p'γ). The slope and absolute scale of the extracted NLD are directly tied to α and A through Eq. (3), so a violation of spin-independence would bias the NLD and affect the comparison to CT, FG, and Skyrme models. The paper states this assumption explicitly in Section 3 and acknowledges it in the Conclusion, but it does not quantify the resulting uncertainty or exploit the HPGe-derived spin distribution to test it. I request a quantitative estimate of the systematic error in ρ(Ex) from a plausible spin-dependent γSF, or an explicit propagation of the measured spin distribution into the normalization; without this, the claim of model independence is stronger than the evidence supports.
  2. [Section 3, Eq. (5)] The χ² minimisation of the γSF normalization returns a reduced χ²/NDF = 2.65, yet the reported uncertainty σα/α = 3.4% is not scaled to χ²/NDF = 1 as is done for the Oslo-method fit in the same section. Since α and B set the NLD slope and scale via Eq. (3), an under-scaling of these uncertainties would propagate directly into the NLD error bars, particularly at the highest excitation energies. Please apply the same χ² scaling procedure to the photonuclear fit, or explain why the residual mismatch (χ²/NDF = 2.65) can be considered already consistent with the quoted uncertainties without inflation.
minor comments (4)
  1. [Section 3, Table 1] The NLD table lists energies down to -0.2875 MeV, which is unphysical for a level density. Please clarify whether this is an artifact of the binning or the first-generation subtraction, and consider truncating the table at Ex ≥ 0 to avoid confusion.
  2. [Section 3, last paragraph before Section 4] The sentence 'under the assumption that for at theγSF is independent of the initial spin' contains a typo and should read 'under the assumption that the γSF is independent of the initial spin'.
  3. [Section 4, Eq. (6)] The spin distribution from Eq. (6) is described as 'subtracted and normalised', but the normalization condition (e.g., sum to unity) is not specified. Please state the normalization explicitly so that the comparison with the models in Fig. 4 is reproducible.
  4. [Figure 3] The labels in the left panel of Figure 3 are small and some overlap; a larger font or a separate legend table would improve readability, as the comparison between data and the three theoretical γSF model curves is central to the discussion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Oslo-method normalization is anchored to external photoabsorption and discrete-level data, and the only non-independent comparison is explicitly disclaimed.

full rationale

The paper's derivation chain is self-contained with respect to circularity. The Oslo-method fit (Eq. 1) yields a one-parameter family of (rho, T) solutions; the three-parameter ambiguity (A, B, alpha) introduced in Eqs. (3)-(4) is resolved by external data: B and alpha are fixed by fitting the unnormalized transmission coefficient to the photonuclear gammaSF of Ref. [43] via Eq. (5), and A is fixed by complete discrete-level spectroscopy in the 2-3 MeV region from Ref. [46]. Neither of these anchors is the constant-temperature or Fermi-gas parametrization, so the abstract's claim of avoiding CT/FG normalization is accurate in the narrow sense stated. The comparison in Section 4 of the extracted gammaSF with the photoabsorption data is not presented as an independent prediction; the paper explicitly says 'since the photoabsorption cross-section was used to normalise the absolute magnitude and the total slope of the γSF, only the relative shapes can be used to evaluate the consistency.' The main physical caveat, the spin-independence/Brink-Axel assumption that equates the J^pi approximately 1+/- photoabsorption gammaSF with the gammaSF governing decays of the broader spin distribution in (p,p'gamma), is acknowledged in the Conclusion as a remaining uncertainty and is a limitation, not a circular reduction: the NLD values in Table 1 are not equal to any input by construction. The self-citations to Refs. [16] and [43] involve overlapping authorship (J. Isaak), but the cited photonuclear data are an external, published, independently falsifiable measurement, so they constitute real evidence rather than a load-bearing self-citation chain. No equation is shown to reduce to its own input, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. The three Oslo-method constants A, B, alpha are resolved by external data (photoabsorption cross-section and complete discrete levels), so the NLD is not equivalent to a fitted model, but it inherits the listed assumptions about spin independence, dipole dominance, first-generation subtraction, level-scheme completeness, and detector response.

free parameters (3)
  • Oslo-method normalization constant A = not quoted; fixed by matching known levels at 2-3 MeV
    Absolute scale of the NLD, set from complete discrete-level spectroscopy in Section 3.
  • Oslo-method normalization constant B = not quoted; fixed by chi2 fit to photoabsorption cross-section
    Absolute scale of the transmission coefficients T(E_gamma), set by photonuclear data in Section 3.
  • Oslo-method slope parameter alpha = not quoted; sigma_alpha/alpha = 3.4% after chi2/NDF = 2.65
    Slope of the gammaSF and NLD ambiguity, fixed by photonuclear data in Section 3.
assumptions (5)
  • domain assumption The gamma-ray strength function is independent of excitation energy and initial spin (Brink-Axel), so the gammaSF from J about 1 photonuclear states can be used to normalize the gammaSF from higher-spin states.
    Invoked in Section 3 after Eq. (5) and again in the Conclusion; load-bearing for the B and alpha normalization.
  • domain assumption Dipole radiation with L=1 dominates the decay, so Eq. (2) can be applied with L=1.
    Stated in Section 3 before Eq. (2), supported by Reference [41] but not verified in this data set.
  • domain assumption The first-generation subtraction correctly removes cascade gamma rays so the remaining decay probability follows Eq. (1).
    Foundation of the Oslo method, cited from References [2,4,5] and applied in Section 3.
  • domain assumption The known discrete level scheme of 128Te is complete up to 3.345 MeV, so the cumulative count at 2-3 MeV sets the absolute NLD scale.
    Used in Section 3 to fix A, following RIPL-3 recommendations from Reference [47].
  • domain assumption The Geant4-based detector response used in the iterative unfolding is accurate enough that residual response errors are covered by the chi2/NDF scaling.
    Unfolding in Section 3 relies on GROOT [40]; the uncertainty scaling is derived from this assumption.

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Cite this review

Pith. "Pith review of Nuclear level density of ${}^{128}$Te from $(\mathrm{p},\mathrm{p}'\gamma)$ scattering and complementary photonuclear data." pith.science (2026). https://pith.science/paper/KT3HBUKI

@misc{pith2026250109360,
  author       = {Pith},
  title        = {Pith review of: Nuclear level density of $^128$Te from $(\mathrmp,\mathrmp'\gamma)$ scattering and complementary photonuclear data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KT3HBUKI}},
  note         = {Machine review of arXiv:2501.09360}
}
abstract

We have extracted the nuclear level density of ${}^{128}$Te from a $(\mathrm{p},\mathrm{p} '\gamma)$ scattering experiment using the large-volume \labr\ and \cebr\ detectors from ELI-NP at the 9~MV Tandem facilities at IFIN-HH. The decay data were normalised using photonuclear data, resulting in nuclear level densities without intrinsic model dependencies from the constant temperature or Fermi gas models. The deduced nuclear level density follows in between the expectations from these two models, but we observe a clear divergence from a microscopic model based on the Skyrme force.

Figures

Figures reproduced from arXiv: 2501.09360 by the authors.

Figure 1
Figure 1. Raw (left), unfolded (middle) and first generation (right) matrices for 128Te. The area selected for further analysis of the first-generation matrices is shown as a black outline. been highlighted and subtracted in the unfolding step, discussed later in this text. Note that these γ-ray spectra also contain the response function of the LaBr3:Ce and CeBr3 detectors and, as we are working in the quasi-continuum region,… view at source ↗
Figure 2
Figure 2. Experimental (top left) and best fit (top right) of the probability matrix. The bottom panels show two projections of the best fit (red line) compared with the experimental data (black circles) in the energy ranges 3.61-3.71 MeV and 5.31-5.41 MeV. For comparison, the best fit of the data without the aluminium contamination subtracted (blue dotted line) is also shown. The error bars include both statistical uncertain… view at source ↗
Figure 3
Figure 3. (Left) Experimental γ-ray strength functions of 128Te obtained from this work (ELI-NP/IFIN-HH), the photoabsorption cross-section from Reference [43] (TU Darmstadt/HIγS), and (γ, n) cross-section data from Reference [44] (Saclay). For comparison, three typical parametrisations, as implemented in the TALYS code, are shown as solid lines for electric dipole strength and dashed lines for magnetic dipole strength. (Righ… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: (Left) HPGe spectrum showing the low-lying transitions in the yrast band, highlighted in red, from cascade γ rays, and identified non-yrast transitions, with an excitation energy gate around the neutron separation threshold. (Right) Intrinsic nuclear spin distribution …

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