Primary Nucleon Spectrum Research Articles

Testing of the EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 hadronic interaction models via help of the atmospheric vertical muon spectra

The recent results of the very precise measurements of the primary cosmic protons and helium nuclei energy spectra by AMS-02 and some rather accurate estimates of these energy spectra generated in SNR allow us to elaborate the new approximation of the pimary nucleon energy spectra. As the acuracy of this approximation is rather high we can use it to test various models of hadronic interactions with the help of atmospheric muon energy spectra. The atmospheric vertical muon energy spectra have been calcullated in terms of the EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 models in the energy range 102 ÷ 105 GeV with help of the CORSIKA package and this new approximation of the primary nucleon spectrum. The comparison of calculations with the muon spectra observed by collaborations L3+Cosmic, LVD and MACRO has shown that all models predict approximately two times lower intensity of the muon energy spectra. As these muons are products of decays of the most energetic π± and K± mesons in the atmosphere, we can conclude that production of these π± and K± mesons is underestimated by EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 models.

MUON FLUXES DERIVED FROM THE DIRECTLY MEASURED PRIMARY COSMIC RAY ELEMENTAL SPECTRA

The muon energy spectra at 0° and 89° have been estimated from the decay of nonprompt and prompt mesons created by the individual elemental primary cosmic ray groups during nucleus-air collisions in the upper atmosphere and the results are found to be fairly comparable with the measured muon fluxes obtained from the direct magnetic spectrograph results in Refs. 2–4, and also from the underground indirect measurements in Refs. 5–10. The muon spectrum derived from the single slope primary nucleon spectrum with a constant spectral index of value −2.73 is only slightly different from the present result for energies below 20 TeV. The present muon spectra at large zenith angle exhibit steeper spectral indices when compared to the expected results obtained from primary elemental groups by Parente et al.

Cosmic prompt-muon spectrum at super high energies estimated from the JACEE primary spectrum using recent charmed-particle production cross-sections

The prompt-muon flux generated directly from the decay of short-lived particles like D-mesons and Λc-hyperons produced during primary cosmic proton-air collisions has been estimated. The inclusive production cross-sections of charmed particles based on the recombination of quark parton model developed by Bugaevet al. and the primary-nucleon spectrum based on the latest JACEE balloon flight data have been used in this investigation. The derived direct muon spectrum has been compared with the earlier results of Elbertet al., Inazawaet al. Bugaevet al. and Allkofer and Bhattacharyya.

Sea level muon spectra at large zenith angles derived from the latest JACEE primary nucleon spectrum

Sea level muon energy spectra at large zenith angles have been derived from the latest JACEE primary spectrum using the Fermilab Single-Arm Spectrometer data on charged-meson production. The role of increasing total cross-section on the final result for the energy spectra has been investigated here with special emphasis. The inclusion of the rising total cross-section at cosmic range of energies, it is seen, has come into much use in explaining the observed data at very high energies.

Derivation of antiproton-proton flux ratio from the closed galaxy model

The antiproton-proton flux ratio has been estimated from the closed galaxy model of Peters and Westergaard by using the latest primary nucleon spectrum and\(pp \to \bar pX\) inclusive reaction accelerator results. The derived\(\bar p/p\) flux ratio is about three times higher than those expected from the leaky box model. The results have been compared with the previous estimates by different authors.

Derivation of the positron flux from the recent proton spectrum

The energy spectrum of cosmic-ray positrons has been estimated by using precise CERN and Fermilab accelerator data for pp→π+X inclusive reactions and the latest primary nucleon spectrum based on the directly measured data. The derived positron spectrum has been found in accord with the positron flux data registered near the top of the atmosphere.

Some comments on the asymptotic limit of antiproton-proton flux ratio at the top of the atmosphere

Using the leaky-box model the upper limit of the antiproton-proton flux ratio at the top of the atmosphere has been estimated from the latest primary nucleon spectrum and accelerator data on\(pp \to \bar pX\) inclusive reactions. The estimated value of\(\bar p/p\) flux ratio comes out to be (3.6±0.3)×10−4 is in accord with the previous results but still far from the measurements.

All particle primary nucleon spectrum derived from the latest jacee data

The all particle primary nucleon spectrum has been estimated on the basis of the latest Japanese American Emulsion Experiments on the balloon borne emulsion chamber measurements of the fluxes of p, He, C, N, O, Ne, Mg, Si, Fe and low energy fit extrapolated results have been found to follow the power law fit of the formN(E) dE=2·03E−2·7 dE (cm2 s sr GeV/nucleon)−1. The concept of nuclear fragmentation has been used to estimate the nucleon flux from nuclei spectra. The derived result agrees with the predicted primary spectrum after Yodh, Ellsworth, Stanev and Gaisser.

Derivation of muon range spectrum at different polar angles in deep underground from primary nucleon spectrum

The energy spectra of sea-level muons at different zenith angles have been estimated from the latest JACEE primary spectrum using ISR results modified for p-nucleus interactions. The theoretical results have been compared with the experimental results. Using the recent modified range-energy relation after Kobayakawa along with the fluctuation correction procedure after Kiraly, Kiraly and Osborne, the muon range spectra in deep underground at different polar angles have been calculated. The derived results are well in agreement with the latest Mont Blanc data after Bergamascoet al., Battistoniet al. and Utah experiments after Bergessonet al.

Calculation of muon range spectrum under sea-water from the latest JACEE primary spectrum using the modified energy loss formulation after Kobayakawa

The muon range spectrum under sea-water has been estimated from the latest primary nucleon spectrum based on JACEE measurements. The hadronic-energy moments for p-nucleus collisions have been used for the calculation of meson production spectrum. The latest modified range-energy relation after Kobayakawa has been applied for the conversion of muon energy spectrum at sea-level to depth-intensity spectrum under sea. The calculated result has been compared with the measured data after Higashiet al., Davitaevet al. and Rogers and Tristam.

Cosmic ray sea level muon spectrum at large zenith angle derived from the latest JACEE primary spectrum

The sea level cosmic ray muon spectrum at 89° has been estimated from the primary nucleon spectrum estimated after the latest JACEE measurements. The p-A collision cross section has been considered for hadronic energy moments calculations. The meson atmospheric diffusion equations after Bugaev et al. have been used in this analysis. The calculated large zenith angle muon spectrum is well in accord with the latest MUTRON data for cosmic ray muons arriving at zenith angles 86° to 90°.

Sea Level Muon Spectrum Derived from the All Particle Primary Spectrum of GRIGOROV et al.

AbstractThe all particle primary spectrum of GRIGOROV et al. surveyed by HILLAS has been fitted by a power law fit of the form Iall particle(>E) = 1.3 E−1.65 (cm2 s sr)−1 where E is the energy in GeV/nucleus. Using our recently determined conversion factor for protonnuclei flux ratio of equal energies the primary proton spectrum has been calculated and the result agrees with the Goddard Space Flight Centre primary proton spectrum data satisfactorily. The primary nucleon spectrum has also been calculated and follows the form Nnucleons(E) dE = 2.664 E−2.75 dE (cm2 s sr GeV/nucleon)−1.Using this primary nucleon spectrum as the source of hadrons and accelerator data for various inclusive reactions viz. used for the estimation of hadronic energy moments in the frame work of FEYNMAN‐ Scaling, the differential meson spectra have been estimated. The meson atmospheric diffusion equation after Bugaev et al. has been considered for the derivation of sea level muon spectrum. The magnetic spectrograph data of Allkofer et al., Ayre et al., Green et al., and MUTRON group are in accord with the calculated muon spectrum.

Muon sea-level intensity and primary cosmic-ray nucleon spectrum in the (1÷100) TeV energy range from the Mt. Blanc underground experiment

We have measured the muon intensity underground up to 7100 hg/cm2 s.r. by means of a spark chamber apparatus. These intensities have been converted to a sea-level muon energy spectrum. An accurate description of the flux of hadrons and muons in the atmosphere allows us to derive the primary nucleon spectrum. If the validity of the superposition model and scaling in the fragmentation region is assumed, we find that the all nucleon spectrum is represented by a single exponent over the whole energy range (1°100) TeV and is given by the relationN(E)dE=(4.85±0.25)E −(2.79±0.04)dE.

Altitude variation of cosmic ray nucleons derived from feynman scaling hypothesis

The differential proton spectra at different atmospheric depths and the differential neutron spectrum at sea level have been calculated using the scaling hypothesis of Feynman for hadronic inclusive reaction at high energies. In evaluating such values we used the primary nucleon spectrum of Grigorov et al. It is found that the derived spectra fit well the experimental data given by different authors. The estimated neutron-proton flux ratio against atmospheric depths is in accord with the measured data surveyed by Aguirre.

Correlation between the sea level muon spectrum and the primary nucleon spectrum using the Cocconi–Koester–Perkins model

Using the recent ISR data of proton–proton interactions on the inclusive production of pions and nucleons, realistic values of the mean pion inelasticity Kπ and the mean nucleon inelasticity KT have been estimated. These values have been used for the derivation of the sea level differential muon spectrum from the primary nucleon spectrum and vice versa using the CKP model as an extension of the work presented in an earlier article. It is found that none of the measured primary nucleon spectra of Ryan, Ormes, and Balasubrahmanyan and Grigorov, Rapoport, and Shestoperov fit any of the precisely measured muon spectra of Ayre, Baxendale, Hume, Nandi, Thompson, and Whalley and Allkofer, Carstensen, and Dau in spectral shape or the absolute value. On the other hand good agreement between the derived muon spectra and the spectra of Allkofer et al. and Ayre et al. is found if the primary nucleon spectra of the forms, N(Ep) = (1.38 ± 0.08)Ep−2.59 and N(Ep) = (1.00 ± 0.10)Ep−2.55, respectively, are assumed. The first form is comparable with that obtained by Brooke, Hayman, Kamiya, and Wolfendale following more approximate but similar procedure. It is also not unjustified when compared with the measured primary all nuclei spectrum of Grigorov et al. in the light of suggestions made by Ellsworth, Ito, Macfall, Siohan, Streitmatter, Tonwar, Vishwanath, Yodh, and Balasubrahmanyan. By comparing the pion production spectra derived from the same primary nucleon spectrum but using the CKP and the scaling models, it is concluded that the results are sensitive to the model assumed for the collisions.

Energy spectra of secondary gamma rays at different atmospheric depths

The CERN Intersecting Storage Ring (ISR) data for p + p → π0 + X inclusive reaction have been used to derive the spectrum of secondary gamma rays at the top of the atmosphere. The measured primary nucleon spectrum of the Goddard Space Flight Group has been taken as a nucleon source spectrum. Using the cascade theory, the gamma ray spectra at the atmospheric depths 540, 650, and 735 g cm−2 have been calculated. The results are approximately in accord with the emulsion chamber data at Mt. Chacaltaya, Mt. Norikura, and Mt. Fuji in the spectral range 0.2–4 TeV.

Sea level muon spectrum derived from the primary nucleon spectrum using the Cocconi–Koester–Perkins model

In a recent paper Sarkar, Bhattacharyya, and Basu have derived the sea level muon energy spectrum from the measured nucleon spectrum of Ryan, Ormes, and Balasubrahmanyan using the Cocconi–Koester–Perkins model. They have found good agreement between this muon spectrum and the precisely measured spectrum of Ayre, Baxendale, Hume, Nandi, Thompson, and Whalley. In this report a critical analysis of the paper has been made and it is found that there are some obvious mistakes both in the formulation and in the calculation. The corrected results do not agree with the Ayre et al. spectrum. The unjustified values of some of the parameters used in their work are discussed.

Neutron‐Proton Ratio at Different Atmospheric Depths and Sea Level Neutron Spectrum Derived from the Primary Nucleon Spectrum

AbstractThe differential neutron spectrum at sea level has been calculated using the conventional phenomenological model after ASHTON. The energy dependence of nucleon‐air nucleus inelastic interaction cross section is assumed in these calculations. The derived sea level neutron spectrum from the satellite measured primary nucleon spectrum of GRIGOROV et al. fits well the experimental neutron spectrum of ASHTON and COATS. The neutron‐proton ratios calculated for different atmospheric depths is in accord with the measured data (AGUIRRE).

Primary cosmic-ray nucleon spectrum from the atmospheric gamma-ray and muon data

The available experimental inclusive cross-sections for single-pion and kaon production in proton-proton collisions between 0.01 and 2 TeV incident-proton laboratory energy have been used to determine a phenomenological form for the inclusive cross-sections. This has been used together with the recent high-precision measurements of atmospheric gamma-ray and single-muon spectra between 0.002 to 50 TeV to derive the primary nucleon spectrum in the formI(E)=I0E-γ up to the primary energy ≥100 TeV. The parametersI0 and γ, vary in the range 1.75┌2.7 and 2.63┌2.78, respectively.

Vertical sea level meson-neutrino spectrum derived from the Goddard Space Flight Center measured nucleon spectrum

The vertical sea level meson neutrino spectrum has been derived from the measured primary nucleon spectrum of Goddard Space Flight Centre Group by using the model of Pal and Peters. The calculated result agrees with the work of Osborne et al. at high energies.