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Parameterization of Gamma, e^+/- and Neutrino Spectra Produced by p-p Interaction in Astronomical Environment
Astrophysics · Submitted 23 May 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The parametrized formulae predict that all secondary particle spectra be harder by about 0.05 in power-law indices than that of the incident proton and their inclusive cross-sections be larger than those predicted by p-p interaction models based on the Feynman scaling.
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The abstract, sentence by sentence
We present the yield and spectra of stable secondary particles (gamma, e^+/-, nu_e, nubar_e, nu_mu, and nubar_mu) of p-p interaction in parameterized formulae to facilitate calculations involving them in astronomical environments. The formulae are derived on the up-to-date p-p interaction model by [Kamae05] which incorporates the logarithmically rising inelastic cross-section, the diffraction dissociation process, and the Feynman scaling violation. To improve fidelity to experimental data in lower energies, two baryon resonance contributions have been added: one representing Delta(1232) and the other multiple resonances around 1600MeV/c^2. The parametrized formulae predict that all secondary particle spectra be harder by about 0.05 in power-law indices than that of the incident proton and their inclusive cross-sections be larger than those predicted by p-p interaction models based on the Feynman scaling.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present the yield and spectra of stable secondary particles (gamma, e^+/-, nu_e, nubar_e, nu_mu, and nubar_mu) of p-p interaction in parameterized formulae to facilitate calculations involving them in astronomical environments. | contribution 1.00 | 0.94 | 0.17 | asserted 0.99 |
| s1 | The formulae are derived on the up-to-date p-p interaction model by [Kamae05] which incorporates the logarithmically rising inelastic cross-section, the diffraction dissociation process, and the Feynman scaling violation. | method 0.99 | 0.56 | 0.04 | asserted 1.00 |
| s2 | To improve fidelity to experimental data in lower energies, two baryon resonance contributions have been added: one representing Delta(1232) and the other multiple resonances around 1600MeV/c^2. | method 0.89 | 0.86 | 0.04 | asserted 1.00 |
| s3 | The parametrized formulae predict that all secondary particle spectra be harder by about 0.05 in power-law indices than that of the incident proton and their inclusive cross-sections be larger than those predicted by p-p interaction models based on the Feynman scaling. | result 1.00 | 0.90 | 0.74 | asserted 0.98 |
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The paper
Original abstract
We present the yield and spectra of stable secondary particles (gamma, e^+/-, nu_e, nubar_e, nu_mu, and nubar_mu) of p-p interaction in parameterized formulae to facilitate calculations involving them in astronomical environments. The formulae are derived on the up-to-date p-p interaction model by [Kamae05] which incorporates the logarithmically rising inelastic cross-section, the diffraction dissociation process, and the Feynman scaling violation. To improve fidelity to experimental data in lower energies, two baryon resonance contributions have been added: one representing Delta(1232) and the other multiple resonances around 1600MeV/c^2. The parametrized formulae predict that all secondary particle spectra be harder by about 0.05 in power-law indices than that of the incident proton and their inclusive cross-sections be larger than those predicted by p-p interaction models based on the Feynman scaling.
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References
How later papers used it
74 later papers cite it
11 later papers by other authors are listed below: 9 used its method or tool, 1 used its data or values and 1 compared its own results with it. 1 more paper by the same authors is listed: 1 used its method or tool.
Uses its method or tool 10 of 27 papers with this label · 1 by the same authors
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Used the publicly available code of this paper as one of two numerical methods.
Multi-GeV Neutrino Emission from Magnetized Gamma Ray Bursts (2011) · 1.00 · paraphrased: the licence does not allow quoting
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Derived gamma-ray spectra using the models by this paper and others.
The Gamma-Ray Emission from the Supernova Remnant RX J1713.7-3946 Interacting with Two-phase Medium (2022) · 1.00 · paraphrased: the licence does not allow quoting
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We use the parametrization of [ref] for the secondary spectrum of $p-p$ interactions, and the exact formula for synchrotron emission given by [ref] to calculate the $144 MHz$ surface brightness and the $[200 MeV-300 GeV]$ $γ$-ray flux.
Coma cluster $\gamma$-ray and radio emission is consistent with a secondary electron origin for the radio halo (2024) · Model · 1.00
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Computed the differential inclusive cross-section for e^+/- production using the formulation of this paper.
Relativistic ions with power-law spectra explain radio phoenixes (2025) · 0.99 · paraphrased: the licence does not allow quoting
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Computed the local production and resulting emission in each cell from the local CR spectrum and ISM density, following this paper.
Reconciling the diffuse Galactic gamma-ray and the cosmic ray spectra (2017) · 1.00 · paraphrased: the licence does not allow quoting
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Derived gamma-ray spectra using the models by this paper and others based on n_H and n_CR.
Intrusion of MeV-TeV Cosmic-Rays into Molecular Clouds Studied by Ionization, the Neutral Iron Line, and Gamma-Rays (2020) · 1.00 · paraphrased: the licence does not allow quoting
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Derived gamma-ray spectra using the models by this paper and others.
X-Ray Emission from the PeVatron-candidate Supernova Remnant G106.3+2.7 (2021) · 1.00 · paraphrased: the licence does not allow quoting
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Calculated the injection of the secondary e^+/- backgrounds using the parameterized cross section presented in this paper.
A dark matter model that reconciles tensions between the cosmic-ray $e^\pm$ excess and the gamma-ray and CMB constraints (2017) · 0.98 · paraphrased: the licence does not allow quoting
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Used the method of this paper to calculate the gamma-ray spectrum due to the decay of neutral pions produced in proton-proton collisions.
The multi-wavelength view of shocks in the fastest nova V1674 Her (2023) · 1.00 · paraphrased: the licence does not allow quoting
By the same authors
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Used two pp to gamma interaction models, one by this paper, to infer the CR proton spectrum from the measurement.
Inferred cosmic-ray spectrum from ${\it Fermi}$-LAT $\gamma$-ray observations of the Earth's limb (2014) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Uses its data or values 1 of 10 papers with this label
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Used the cross section in this paper in its pi^0 decay model.
Detection of the Characteristic Pion-Decay Signature in the Molecular Clouds (2018) · 0.81 · paraphrased: the licence does not allow quoting
Compares with it 1 of 7 papers with this label
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Compared its own results for the p+p channel with this paper.
New determination of the production cross section for secondary positrons and electrons in the Galaxy (2022) · 0.97 · paraphrased: the licence does not allow quoting
How the literature uses it
46 arXiv papers cite this in 80 sentences
Papers citing it · 47 sentences without a confident label
Contests it 1 paper
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The widely used parametrizations for this cross section in astrophysics e.g. [ref] , do not fit well these two data points.
Parametrization of gamma-ray production cross-sections for pp interactions in a broad proton energy range from the kinematic threshold to PeV energies · Discussion and Conclusions · contest 0.91
Uses its method or tool 14 papers
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To infer the CR proton spectrum from the measurement, we use two $pp→γ$ interaction models, one by [ref] (Kamae model) and the other by [ref] (K&O model).
Inferred cosmic-ray spectrum from ${\it Fermi}$-LAT $\gamma$-ray observations of the Earth's limb · Introduction · 1.00
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The differential inclusive cross-section $dσ_e(E_i,E)/dE$ for $e^±$ production is computed using the formulation of [ref] .
Relativistic ions with power-law spectra explain radio phoenixes · Hadronic phoenix model · 0.99
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The most commonly used cross section parametrization relies on a customized implementation of Pythia 6 by Kamae [ref] .
New determination of the production cross section for $\gamma$ rays in the Galaxy · Introduction · 0.89
Uses its data or values 5 papers
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We calculate the flux of secondary background $e^-$ and $e^+$ from the Solar-demodulated flux of GCR protons as derived from the BESS data [ref] and model the cross-sections according to Ref. [ref] .
Cosmic ray backgrounds for dark matter indirect detection · Secondary electrons and positrons from propagation · 0.92
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The energy loss timescale due to $pp$ interactions can be estimated as [equation] where the cross section $σ_pp∼3×10^-26 cm^2$ for $10^10-12$ eV [ref] and the inelasticity $κ_pp≈0.5$.
High Energy Gamma Rays from Nebulae Associated with Extragalactic Microquasars and Ultra-Luminous X-ray Sources · X-ray Source Embedded Bubbles in the local Universe · 1.00
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In the $π^0$ decay model, we use the cross section in [ref] and the relation that $σ_pH_2=2 σ_pp$ [ref] .
Detection of the Characteristic Pion-Decay Signature in the Molecular Clouds · Discussion · 0.81
Compares with it 5 papers
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We compare our results for the $p+p$ channel with [ref] (labeled Kamae) and [ref] (labeled AAfrag).
New determination of the production cross section for secondary positrons and electrons in the Galaxy · Results on the $e^+$ production cross section and source spectrum · 0.97
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Figure [ref] shows some examples of the $γ$-ray production differential cross section calculated from the experimental $π^0$ spectrum data and compares them with the low energy models from [ref] .
Parametrization of gamma-ray production cross-sections for pp interactions in a broad proton energy range from the kinematic threshold to PeV energies · Gamma-ray spectra for $T_p^th ≤T_p <1$ GeV · 1.00
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In order to estimate the impact of our results on the diffuse Galactic emission at Fermi-LAT energies, we show in Fig. [ref] a comparison between our cross section and the one derived by Kamae et al. [ref] that is used in the Fermi-LAT official Galactic interstellar emission model [ref] .
New determination of the production cross section for $\gamma$ rays in the Galaxy · Results on the $γ$ ray production cross section and emissivity · 1.00
Cites it as background 2 papers
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Parametrisations for meson production are discussed in Refs. [ref] and an overview of nuclear spallation cross section models is given in Ref. [ref] and references therein.
Cosmic ray backgrounds for dark matter indirect detection · Galactic propagation · 0.87
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Until recently, the only parametrizations available for the integral cross-section and photon emission spectra were either only applicable to limited energy ranges [ref] , or were given as extensive numerical tables [ref] .
naima: a Python package for inference of relativistic particle energy distributions from observed nonthermal spectra · Pion Decay · 0.81
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