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REVIEW 4 major objections 6 minor 48 references

New calculation of the geo-neutrino energy spectrum and its implication

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Recalculating the uranium-238 and thorium-232 geo-neutrino spectra with the latest nuclear data and forbidden-transition corrections, this paper finds the inverse-beta-decay yields are 3.47% and 9.00% lower than the 2005 reference flux.

desk verdict Useful update of geo-neutrino spectra, but the headline yield shifts rest on an unvalidated forbidden-transition model and need uncertainty propagation before they are taken as benchmarks. read the letter →

arxiv 2412.07711 v2 pith:SL5SN2IN submitted 2024-12-10 hep-ph nucl-exphysics.geo-ph

Yu-Feng Li , Zhao Xin This is my paper · ORCID
classification hep-phnucl-exphysics.geo-ph
keywords geo-neutrinospectruminversebetadecayyieldsummationmethodforbiddentransitionsENSDFnucleardatabaseKamLANDBorexinoradiogenicheat
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

Geo-neutrinos from the 238U and 232Th decay chains are the component of the terrestrial antineutrino flux that liquid-scintillator detectors can observe via inverse beta decay, and their energy spectrum connects measured event rates to the Earth's uranium and thorium inventory and radiogenic heat budget. This paper rebuilds those spectra with the summation method, using the latest ENSDF nuclear database, shape factors for first-forbidden Gamow-Teller transitions, and radiative, finite-size, and weak-magnetism corrections. The new flux model has inverse-beta-decay yields 3.47% lower for 238U and 9.00% lower for 232Th than the widely used 2005 reference flux. Refitting the KamLAND and Borexino data with the new spectra raises the fitted uranium contribution by about 10–20% and lowers the thorium contribution by a similar amount, while the inferred mantle signal rises slightly at both detectors.

What carries the argument

The summation method: the geo-neutrino spectrum of a chain is the production-weighted sum over every $\beta$ branch, $S_X = \sum_{ij} R_{ij} \sum_k I_{ij,k} S^{ij,k}_\nu$, where each single-branch spectrum is $S_\nu = K\,p_\nu E_\nu (E_0-E_\nu)^2 F(Z,E_\nu) C(Z,E_\nu)\,[1+\delta(Z,A,E_\nu)]$. The new elements are the shape factors $C(Z,E_\nu)$ for allowed Gamow-Teller, non-unique first-forbidden Gamow-Teller ($\Delta J^\pi = 0^-, 1^-$), and unique first-forbidden Gamow-Teller ($\Delta J^\pi = 2^-$) transitions, computed with exact relativistic Dirac wave functions, together with radiative, finite-size, and weak-magnetism corrections. These ingredients convert the updated ENSDF branching data into a flux that is systematically lower than the reference flux in the high-energy region where the IBD cross section is largest.

What would settle it

A high-precision measurement of the beta or antineutrino spectrum of 214Bi and 212Bi near the endpoint, sensitive to the shape of the non-unique first-forbidden transitions, would settle the claim: if the measured endpoint shape disagrees with the first-forbidden shape factor plus the allowed finite-size correction, the reported 3.47% and 9.00% IBD yield reductions would need revision.

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Extended reading notes

Core claim

The central claim is that the two-decade-old reference geo-neutrino spectrum overestimates the detectable flux at high energies. By combining the latest ENSDF evaluations (which add 77 new transitions in the 238U chain and 14 in the 232Th chain) with a beta-decay description that includes forbidden-transition shape factors and higher-order corrections, the authors obtain IBD yields that are lower than the reference flux by 3.47% for 238U and 9.00% for 232Th. Most of the thorium reduction comes from the non-unique first-forbidden decay of 212Bi; in the uranium chain the dominant forbidden contributor is 214Bi, whose high-Q branches shape the detectable spectrum. When the new fluxes are used to refit KamLAND and Borexino data, the fitted 238U signal increases by about 10% and 20% respectively and the fitted 232Th signal decreases by comparable fractions, with the total geo-neutrino rate nearly unchanged and mantle signals slightly higher.

Load-bearing premise

The load-bearing premise is that the first-forbidden shape factors and the standard finite-size correction meant for allowed transitions correctly describe the beta spectra of 214Bi and 212Bi, the isotopes that dominate the detectable signal, even though the paper itself notes that a satisfactory finite-size correction for forbidden transitions does not yet exist.

Editorial extensions

If this is right

  • The IBD yields for the 238U and 232Th chains are 3.47% and 9.00% lower than the 2005 reference flux, so event-rate predictions in liquid-scintillator geo-neutrino detectors shrink by those amounts for the two chains.
  • Refitting the KamLAND and Borexino datasets with the new flux raises the fitted 238U contribution by roughly 10% (KamLAND) and 20% (Borexino) and lowers the fitted 232Th contribution by comparable amounts, leaving the total geo-neutrino event count almost unchanged.
  • Inferred mantle geo-neutrino signals increase slightly at both detectors under the new flux, but the tension between the KamLAND and Borexino mantle estimates persists at roughly the 1.5σ (1.2σ) level regardless of flux model or Th/U ratio treatment.
  • Next-generation experiments that adopt this flux model will predict fewer events from thorium and a reshaped uranium spectrum near the IBD threshold, affecting sensitivity projections for separating U and Th signals.

Reading between the lines

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

  • Beyond the paper: because the total fitted geo-neutrino event rate barely changes while the U/Th split shifts, the new flux mainly reshapes the relative spectral contributions; a shape-only fit of the prompt-energy spectra near the thorium endpoint could confirm this without relying on absolute rates.
  • Beyond the paper: the treatment of second- and third-forbidden transitions as allowed transitions is said to have negligible impact, but a dedicated calculation of the 214Bi and 210Tl high-Q branches would test whether the high-energy tail of the uranium spectrum is robust.
  • Beyond the paper: the persistent ~1.5σ KamLAND-Borexino mantle-signal tension under both flux models suggests the discrepancy is dominated by crustal-model or detector systematics rather than by the assumed geo-neutrino spectrum; next-generation data with lower statistical errors could separate these.
  • Beyond the paper: the missing finite-size correction for first-forbidden transitions, acknowledged in Appendix A, means the 3.47% and 9.00% numbers carry an unquantified systematic; a dedicated nuclear-theory calculation of that correction would attach a real error bar to the new flux.
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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

4 major / 6 minor

Summary. The manuscript presents a new summation-method calculation of the geo-neutrino energy spectra from the 238U and 232Th decay chains. The single-beta spectra include the Fermi function, forbidden-transition shape factors, and radiative, finite-size, and weak-magnetism corrections; the decay-branch inputs are taken from the latest ENSDF data. The paper reports that the resulting IBD yields are lower than the widely used Enomoto fluxes by 3.47% for 238U and 9.00% for 232Th (Table I), and it re-fits the KamLAND and Borexino geo-neutrino data with the new fluxes, finding upward shifts of roughly 10–20% in the extracted 238U contributions and comparable downward shifts in the 232Th contributions. The authors conclude that the new flux model has substantial implications for current and next-generation geo-neutrino experiments.

Significance. If the calculation is validated, a 3–9% shift in the IBD yields of the two dominant geo-neutrino chains is an important input for geo-neutrino analyses, and the re-analysis of KamLAND and Borexino data makes the consequence concrete. The paper has clear strengths: the summation framework is explicitly written down (Eqs. (1)–(3)), the decay-branch data are tabulated in detail, the decomposition of the yield change into database and beta-model effects is transparent, and the inclusion of forbidden transitions goes beyond the 2005 Enomoto treatment. The significance of the result is, however, presently limited by the absence of an uncertainty budget for the headline yield differences and by the unvalidated treatment of the dominant forbidden decays; the paper's own Appendix A concedes that no satisfactory finite-size correction for first-forbidden transitions is available, yet such transitions dominate the IBD signal. The manuscript therefore reports a potentially important new flux model, but the quantitative claims are not yet supported to the stated precision.

major comments (4)
  1. [Table I and Eq. (3)] The headline IBD yield differences are quoted to two decimal places without any uncertainty. Table VI lists intensity uncertainties δI_{ij,k} for the branches that dominate the IBD signal, and the text states that a 21 keV Q-value shift in the 234Pa^m branch changes the 238U IBD yield by +3.31%; neither Q-value uncertainties nor beta-model systematics are propagated into Table I. Without an uncertainty budget, the claimed 'significant deviation' and the 10–20% implications for KamLAND and Borexino cannot be quantitatively assessed. Please add at least the database-driven uncertainties and a model systematic for the beta-spectrum treatment.
  2. [Appendix A, Table III] The shape factors for the non-unique first-forbidden transitions (the 0− and 1− rows of Table III) are written as functions of electron kinematics and are attributed to the 'exact relativistic calculation' of the Dirac wave function. For non-unique forbidden decays, however, the relative weights of the nuclear matrix elements enter the shape factor, and the manuscript does not state the assumed matrix-element ratios or the approximation used. This is load-bearing because 214Bi contributes about 47% of the 238U IBD signal and 212Bi is the only forbidden contributor above threshold in the 232Th chain. Please state the assumption (e.g., ξ-approximation or a specific multipole-dominance limit) and propagate the resulting uncertainty into the yield differences.
  3. [Appendix A, Eq. (A8)] The finite-size correction of Eq. (A8) is derived for allowed Gamow-Teller transitions, and the text explicitly concedes that 'a satisfactory FS correction for first-forbidden transitions has yet to be established.' Applying this allowed correction to all branches, including 214Bi and 212Bi, directly affects the endpoint region that is most relevant to the IBD signal. The paper's own caveat that the exact-relativistic treatment 'may result in an underestimation in the high-energy region compared to allowed transitions' means that the sign and size of this systematic are unknown. Please provide a sensitivity estimate, for example by varying the finite-size treatment or by comparing with measured beta spectra, before the −3.47% and −9.00% shifts can be taken as quantitative.
  4. [Appendix A and B, validation] No comparison is made with measured electron or beta spectra of 214Bi and 212Bi, nor with independent calculations for these dominant forbidden branches. Since the text's own decomposition of Table I shows that the headline differences from Enomoto are dominated by the beta-decay model rather than by the database update, a direct spectral comparison is the most natural test of the model. Please include such comparisons, or explicitly state that the quoted shifts are model-dependent and not yet benchmarked against measured spectra.
minor comments (6)
  1. [Conclusion] The conclusion states that 'the IBD yields for 235U and 232Th geo-neutrinos have been underestimated using the previous geo-neutrino fluxes'; this should read 238U, and 'underestimated' contradicts Table I and the earlier statement that the new fluxes are lower than Enomoto's. The previous fluxes appear to overestimate the IBD yield.
  2. [Table VI] Table VI lists R_{ij} = 1.0000 for 234Pa^m → 234U, which is inconsistent with Table IV's value of 0.9984 for the same production weight. Please clarify how the 0.0016 branch to the 234Pa ground state is handled in the IBD calculation.
  3. [Figure 1 and text] The text near Figure 1 says the red lines 'fall below the black and blue lines', but the figure contains black dashed, black solid, and red solid lines, with no blue line. Please correct the description.
  4. [Reference [1]] Reference [1] is dated 2023, while the text says the Enomoto evaluation is from 2005; the thesis year should be corrected to the version actually used.
  5. [Introduction] The introduction contains 'the Coulomb interactions between between the emitted electron and daughter nucleus' with a duplicated 'between', and the phrase 'namely, i.e.' is redundant.
  6. [Table VI] The transition-type column in Table VI contains typographical errors: '2 rd' and '3 rd' should be '2nd' and '3rd'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the new geo-neutrino flux is a summation of external ENSDF branch data with a prior independent beta-spectrum framework, and the KamLAND/Borexino refits are downstream consequences rather than fitted inputs.

full rationale

The derivation chain is transparent: ENSDF decay data (Ref. [23]) enter Eq. (2)/(B1); the single-branch beta spectra use the universal formula Eq. (1)/(A1), with shape factors and corrections from the cited method framework; Eq. (3) converts the summed spectrum to an IBD yield; Eqs. (C1)-(C7) then refit KamLAND and Borexino event numbers with the new spectral shapes. The only overlapping-author citation is Ref. [27] (Y.-F. Li and D. Zhang), used for the beta-spectrum description in Table III and Appendix A. That cited calculation is an independent prior result whose stated assumptions do not include the geo-neutrino IBD yields or the KamLAND/Borexino data used here; the present paper applies it to new decay-chain inputs, so the central yield differences are not defined in terms of the conclusions they support. Table I further separates the database-only change ('Flux with new database') from the model change ('New Flux'), and the fitted N_U and N_Th values are outputs of a likelihood fit to fixed external data, not inputs disguised as predictions. The Appendix A admission that 'a satisfactory FS correction for first-forbidden transitions has yet to be established' and the unquantified matrix-element ratios in non-unique first-forbidden shape factors are genuine accuracy and robustness limitations, but they are approximations acknowledged by the authors, not reductions of the result to its own premises. The self-citation in Ref. [27] is load-bearing methodologically but is independent support under the review rules, and no equation equates the final IBD-yield shift to an input by construction. Therefore the paper shows no significant circularity.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

No free parameters are fitted in this paper; the inputs are ENSDF nuclear data and published beta-decay theory. The load-bearing approximations are the uniform first-forbidden GT shape-factor treatment and the use of the allowed-GT finite-size correction for forbidden transitions, both stated in Appendix A. No new entities are introduced.

assumptions (6)
  • standard math The Fermi description of beta decay in Eq. (1)/(A1) with the listed corrections correctly describes single-beta spectra.
    Background from Refs. [26-31]; not re-derived here.
  • domain assumption ENSDF data for the 238U and 232Th chains are accurate and complete.
    All branching ratios, Q-values, and intensities come from ENSDF [23] without independent check.
  • ad hoc to paper All forbidden transitions can be treated as first-forbidden GT transitions using the shape factors of Table III, and the allowed-GT finite-size correction of Eq. (A8) applies to all transitions.
    Appendix A states no satisfactory finite-size correction for first-forbidden transitions exists, yet Eq. (A8) is applied universally; this affects the dominant 214Bi and 212Bi branches.
  • ad hoc to paper Second- and third-forbidden transitions can be approximated as allowed with negligible impact.
    Appendix B applies this approximation for high-spin 210Tl branches; authors assert negligible effect without quantification.
  • domain assumption The IBD cross sections of Refs. [15,16] and the official KamLAND/Borexino detector response, efficiencies, and background tables are correct.
    Used to convert spectra to yields and in the chi-square fits; taken from the experimental papers.
  • domain assumption The reference crustal models (Table IX), originally computed with the Enomoto flux, can be rescaled by the new yield differences to derive mantle signals.
    Appendix C derives mantle signals by subtracting scaled crustal models; assumes the scaling captures shape changes.

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Pith. "Pith review of New calculation of the geo-neutrino energy spectrum and its implication." pith.science (2026). https://pith.science/paper/SL5SN2IN

@misc{pith2026241207711,
  author       = {Pith},
  title        = {Pith review of: New calculation of the geo-neutrino energy spectrum and its implication},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SL5SN2IN}},
  note         = {Machine review of arXiv:2412.07711}
}
read the original abstract

The energy spectrum of geo-neutrinos plays a vital role in the experimental measurement of geo-neutrinos that have profound implications for both particle physics and earth sciences. In this letter, we present a state-of-the-art calculation of the energy spectrum of geo-neutrinos originating from the beta decay of Uranium-238 and Thorium-232. Our calculation is underpinned by the latest updates in the nuclear database, accounts for previously overlooked forbidden transitions, and incorporates advanced corrections for the beta decay. This brand new geo-neutrino flux model, compared to the widely-used estimates from Enomoto, reveals notable distinction in the energy spectrum shape because of our comprehensive approach. When considering the inverse beta decay (IBD) detection process, our findings show a significant deviation in the predicted IBD yield of around 4% for Uranium-238 and 9% for Thorium-232 decay chains. The implications of using the new geo-neutrino flux model for the experimental analysis are substantial, potentially affecting the analysis results of geo-neutrino measurements of KamLAND and Borexino by around 10% to 20%. Our study represents a significant advancement in geo-neutrino research, establishing a new benchmark for accuracy and reliability in the field.

Figures

Figures reproduced from arXiv: 2412.07711 by the authors.

Figure 1
Figure 1. FIG. 1: The geo-neutrino energy spectra from the decay [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Profiles of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Note that the backgrounds listed in Table VII are [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (1 more)
Figure 3
Figure 3. Figure 3: FIG. 3: The observed event spectra (data points) and the best fits (histograms) for different components of the geo-neutrino [PITH_FULL_IMAGE:figures/full_fig_p011_3.png]

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Works this paper leans on

48 extracted references · 40 canonical work pages

  1. [1]

    Enomoto, Neutrino Geophysics and Observation of Geo- Neutrinos at KamLAND , Ph.D

    S. Enomoto, Neutrino Geophysics and Observation of Geo- Neutrinos at KamLAND , Ph.D. thesis, Tohoku University (2023)

    work page 2023

  2. [2]

    Eder, Nuclear Physics 78, 657 (1966)

    G. Eder, Nuclear Physics 78, 657 (1966)

    work page 1966

  3. [3]

    Javoy, Geophysical Research Letters 24, 177 (1997), https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/96GL03931

    M. Javoy, Geophysical Research Letters 24, 177 (1997), https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/96GL03931

    work page doi:10.1029/96gl03931 1997

  4. [4]

    Discriminating among Earth composition models using geo-antineutrinos

    H. Nunokawa, W. J. C. Teves, and R. Zukanovich Funchal, JHEP 11, 020 (2003), arXiv:hep-ph/0308175

    work page Pith review arXiv 2003

  5. [5]

    Marx, Czech

    G. Marx, Czech. J. Phys. 19, 1471 (1969)

    work page 1969

  6. [6]

    Radioactive heat production of six geologically important nuclides

    T. Ruedas, Geochem. Geophys. Geosyst. 18, 3530 (2017), arXiv:1710.06721 [astro-ph.EP]

    work page Pith review arXiv 2017

  7. [7]

    Geophysical and geochemical constraints on geoneutrino fluxes from Earth's mantle

    O. Sramek, W. F. McDonough, E. S. Kite, V . Lekic, S. Dye, and S. Zhong, Earth Planet. Sci. Lett. 361, 356 (2013), arXiv:1207.0853 [physics.geo-ph]

    work page Pith review arXiv 2013

  8. [8]

    Neutrinos and Energetics of the Earth

    G. Fiorentini, F. Mantovani, and B. Ricci, Phys. Lett. B 557, 139 (2003), arXiv:nucl-ex/0212008

    work page Pith review arXiv 2003

Show all 48 references
  1. [9]

    Fiorentini, M

    G. Fiorentini, M. Lissia, F. Mantovani, and R. Vannucci, Earth Planet. Sci. Lett. 238, 235 (2005), arXiv:physics/0508019

    2005 arXiv

  2. [10]

    Dye, Rev

    S. Dye, Rev. Geophys. 50, 3007 (2012), arXiv:1111.6099 [nucl- ex]

    2012 arXiv

  3. [11]

    W. F. McDonough, O. ˇSr´amek, and S. A. Wipper- furth, Geochem. Geophys. Geosyst. 21, e2019 (2019), arXiv:1912.04655 [physics.geo-ph]

    2019 arXiv

  4. [12]

    Bellini, K

    G. Bellini, K. Inoue, F. Mantovani, A. Serafini, V . Strati, and H. Watanabe, Riv. Nuovo Cim.45, 1 (2022), arXiv:2109.01482 [physics.geo-ph]. 6

    2022 arXiv

  5. [13]

    Domogatsky, V

    G. Domogatsky, V . Kopeikin, L. Mikaelyan, and V . Sinev, Phys. Atom. Nucl. 69, 1894 (2006), arXiv:hep-ph/0411163

    2006 arXiv

  6. [14]

    C. G. Rothschild, M. C. Chen, and F. P. Calaprice, Geophys. Res. Lett. 25, 1083 (1998), arXiv:nucl-ex/9710001

    1998 arXiv

  7. [15]

    Ricciardi, N

    G. Ricciardi, N. Vignaroli, and F. Vissani, JHEP 08, 212 (2022), arXiv:2206.05567 [hep-ph]

    2022 arXiv

  8. [16]

    Strumia and F

    A. Strumia and F. Vissani, Phys. Lett. B 564, 42 (2003), arXiv:astro-ph/0302055

    2003 arXiv

  9. [17]

    R. W. King and J. F. Perkins, Phys. Rev. 112, 963 (1958)

    1958

  10. [18]

    F. T. Avignone, S. M. Blakenship, and C. W. Darden, Phys. Rev. 170, 931 (1968)

    1968

  11. [19]

    V ogel, G

    P. V ogel, G. K. Schenter, F. M. Mann, and R. E. Schenter, Phys. Rev. C 24, 1543 (1981)

    1981

  12. [20]

    Tengblad, K

    O. Tengblad, K. Aleklett, R. V on Dincklage, E. Lund, G. Ny- man, and G. Rudstam, Nuclear Physics A 503, 136 (1989)

    1989

  13. [21]

    Jeff and eff projects,

    “Jeff and eff projects,” http://www.nndc.bnl.gov/ ensdf

  14. [22]

    Endf/b-viii reference paper,

    “Endf/b-viii reference paper,” Nucl. Data Sheets148(2018)

    2018

  15. [23]

    Evaluated nuclear structure data file (ensdf),

    “Evaluated nuclear structure data file (ensdf),” http://www. nndc.bnl.gov/ensdf

  16. [24]

    Abe et al

    S. Abe et al. (KamLAND), (2022), 10.1029/2022GL099566, arXiv:2205.14934 [physics.geo-ph]

    2022

  17. [25]

    Agostini et al

    M. Agostini et al. (Borexino), Phys. Rev. D101, 012009 (2020), arXiv:1909.02257 [hep-ex]

    2020 arXiv

  18. [26]

    Fermi, Z

    E. Fermi, Z. Phys. 88, 161 (1934)

    1934

  19. [27]

    Li and D

    Y .-F. Li and D. Zhang, Phys. Rev. D 100, 053005 (2019), arXiv:1904.07791 [hep-ph]

    2019 arXiv

  20. [28]

    Sirlin, Phys

    A. Sirlin, Phys. Rev. 164, 1767 (1967)

    1967

  21. [29]

    Sirlin, Phys

    A. Sirlin, Phys. Rev. D 84, 014021 (2011), arXiv:1105.2842 [hep-ph]

    2011 arXiv

  22. [30]

    A. C. Hayes, J. L. Friar, G. T. Garvey, G. Jungman, and G. Jonkmans, Phys. Rev. Lett. 112, 202501 (2014), arXiv:1309.4146 [nucl-th]

    2014 arXiv

  23. [31]

    X. B. Wang, J. L. Friar, and A. C. Hayes, Phys. Rev. C 94, 034314 (2016), arXiv:1607.02149 [nucl-th]

    2016 arXiv

  24. [32]

    Araki et al., Nature 436, 499 (2005)

    T. Araki et al., Nature 436, 499 (2005)

    2005

  25. [33]

    M. C. Chen, Earth Moon Planets 99, 221 (2006)

    2006

  26. [34]

    Bellini et al

    G. Bellini et al. (Borexino), Phys. Lett. B 687, 299 (2010), arXiv:1003.0284 [hep-ex]

    2010 arXiv

  27. [35]

    Strati, M

    V . Strati, M. Baldoncini, I. Callegari, F. Mantovani, W. F. Mc- Donough, B. Ricci, and G. Xhixha, (2014), arXiv:1412.3324 [physics.geo-ph]

    2014 arXiv

  28. [36]

    Han, Y .-F

    R. Han, Y .-F. Li, L. Zhan, W. F. McDonough, J. Cao, and L. Ludhova, Chin. Phys. C 40, 033003 (2016), arXiv:1510.01523 [physics.ins-det]

    2016 arXiv

  29. [37]

    McDonough and S

    W. McDonough and S. s. Sun, Chemical Geology 120, 223 (1995), chemical Evolution of the Mantle

    1995

  30. [38]

    A. C. Hayes and P. V ogel, Ann. Rev. Nucl. Part. Sci. 66, 219 (2016), arXiv:1605.02047 [hep-ph]

    2016 arXiv

  31. [39]

    X. B. Wang and A. C. Hayes, Phys. Rev. C 95, 064313 (2017), arXiv:1702.07520 [nucl-th]

    2017 arXiv

  32. [40]

    ˇStef´anik, R

    D. ˇStef´anik, R. Dvornick ´y, and F. ˇSimkovic, AIP Conf. Proc. 1894, 020022 (2017)

    2017

  33. [41]

    T. A. Mueller et al. , Phys. Rev. C83, 054615 (2011), arXiv:1101.2663 [hep-ex]

    2011 arXiv

  34. [42]

    G. L. Fogli, E. Lisi, A. Palazzo, and A. M. Rotunno, Phys. Rev. D 82, 093006 (2010), arXiv:1006.1113 [hep-ph]

    2010 arXiv

  35. [43]

    Fiorentini, G

    G. Fiorentini, G. L. Fogli, E. Lisi, F. Mantovani, and A. M. Ro- tunno, Phys. Rev. D 86, 033004 (2012), arXiv:1204.1923 [hep- ph]

    2012 arXiv

  36. [44]

    Gando et al

    A. Gando et al. (KamLAND), Phys. Rev. D88, 033001 (2013), arXiv:1303.4667 [hep-ex]

    2013 arXiv

  37. [45]

    Takeuchi, K

    N. Takeuchi, K. Ueki, T. Iizuka, J. Nagao, A. Tanaka, S. Enomoto, Y . Shirahata, H. Watanabe, M. Yamano, and H. K. M. Tanaka, Phys. Earth Planet. Interiors 288, 37 (2019), arXiv:1901.01358 [physics.geo-ph]. 7 Appendix A: The analytical method for beta transition The geo-neutri...

    2019 arXiv

  38. [46]

    [24], which are divided into three distinct periods

    Geo-neutrino analysis of KamLAND data In our analysis of the KamLAND data, we referred to the observations presented in Ref. [24], which are divided into three distinct periods. Given that the detector responses vary across these periods, we structure our total χ2 as the sum o...

    1994

  39. [47]

    [25], which corresponds to an exposure of 3262.74 days

    The geo-neutrino analysis for Borexino data For the Borexino data, we utilized the dataset released in Ref. [25], which corresponds to an exposure of 3262.74 days. The χ2 function is constructed in a manner similar to that used for the KamLAND data, with the only difference be...

  40. [48]

    The reference crustal contributions for Kamioka and Gran Sasso, used for KamLAND and Borexino, respectively, are detailed in Table IX

    The mantle study The mantle geo-neutrino signal is derived by subtracting the expected signals from the crustal model from the total signal. The reference crustal contributions for Kamioka and Gran Sasso, used for KamLAND and Borexino, respectively, are detailed in Table IX. R...

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