Primary Cosmic-ray Nucleon Spectrum Research Articles

Estimation of Sea Level Muon Energy Spectrum at High Latitude from the Latest Primary Nucleon Spectra Near the Top of the Atmosphere

The vertical muon energy spectra at sea level have been estimated from directly measured primary cosmic-ray nucleon spectrum. The hadronic energy moments have been calculated from the CERN LEBC EHS data on the Lorentz invariant cross-section results on pp → π±X and pp → K±X inclusive reactions and are duly corrected for A–A collisions. Finally, the sea level muon energy spectra have been calculated from the decay of conventional mesons, using standard formulation. The estimated muon spectra are found to be in good agreement with the directly measured muon spectra obtained from the different experiments.

Estimation of the Sea Level Muon Spectra at Different Zenith Angles below 10 TeV Energy

The moderate energy primary cosmic ray nucleon spectrum has been calculated from the direct measurements of Webber et al., Seo et al., and Menn et al. along with the other results surveyed by Swordy. Using these directly measured primary mass composition results all particle primary nucleon energy spectrum has been constructed using superposition model to estimate the energy spectra of muons from the decay of the cosmic ray non-prompt and prompt mesons in the atmosphere. The Z-factors have been estimated from the CERN LEBC-EHS on the Lorentz invariant cross section results on pp → π±X and pp → K±X inclusive reactions and FNAL data on π±p → π ±X reactions, and duly corrected for A--A collisions. Using these Z-factors the meson energy spectra in the atmosphere have been calculated. The sea level muon energy spectra at zenith angles 0°, 45°, 72°, and 75° have been derived from the decay of non-prompt mesons by adopting standard diffusion equation of hadronic cascades. The contribution of charmed mesons to muon spectrum has also been accounted by adapting the conventional procedure. The derived differential sea level muon energy spectra for energies ≤10 TeV have been found to follow the power law fits of the form N μ(E)≈ const. E -γ. Our estimated muon energy spectra at zenith angles ≤75° have been found comparable with the global spectrograph muon flux results of MARS, DEIS, and MSU groups.

Super-high-energy neutrino spectra in the atmosphere derived from the latest JACEE, MSU, SOKOL and CRN primary spectrum usingZ-factors for p-air collisions estimated from Fermi national accelerator data

The absolute spectra of atmospheric neutrinos in the vertical direction and at large zenith angle have been estimated directly from the primary cosmic-ray nucleon spectrum based on the latest JACEE, MSU, SOKOL and CRN data surveyed by Swordy. The Fermi National Accelerator Laboratory results for pp→K±X, pp→K±X and pp→pX inclusive reactions have been used for theZ-factor calculations for meson production and these were modified for p-air and A-A collisions. The derived muon and electron neutrino spectra at 0° and 89° from non-prompt meson decay are found comparable with the results of Volkova and Zatsepin, and Butkevichet al. An estimate of the prompt muon neutrino spectra at 0° and 89° fromtthe charmed-meson decay has been given along with the earlier results of different authors. The present result for muon neutrino spectra at zenith angles 0° and 89° is found in approximate agreement with the EAS-TOP results of the Gran Sasso group.

Calculation of absolute intensity of muons under standard rock at depths >2000 hg cm-2

Using the latest estimation of the primary cosmic-ray nucleon spectrum and the data on hadron-nucleus collisions, the absolute vertical muon energy spectrum at sea level has been calculated. This spectrum has been converted to a depth-intensity spectrum under standard rock by analytic as well as Monte-Carlo methods. The spectrum from the analytic method has been corrected for range fluctuations. The absolute muon energy spectrum at sea level and the intensity of muons under standard rock have been compared with the respective experimental results.

Derivation of Absolute Depth‐Intensity Spectrum under Standard Rock from the Recently Estimated Primary Cosmic Ray Spectrum

AbstractUsing the recently derived primary cosmic ray nucleon spectrum from JACEE and GSFC balloon flight data and Fermilab results for pp → π± + X anything inclusive reaction data in the light of Feynman scaling the depth‐intensity spectrum under standard rock has been estimated. A precisely constructed range‐energy relation has been applied in this analysis. The derived spectrum when corrected for range fluctuation agrees approximately with the experimental data under standard rocks measured by MIYAZAKI, BARTON, CASTAGNOLI et al., MEYER et al., BERGAMASCO et al., SHELDON et al. and BASCHIERA et al.

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.

Primary cosmic-ray nucleon spectrum from the sea-level muon spectrum using the scaling model

Using three values of the differential exponent, namely 2.65, 2.70 and 2.75, of the primary cosmic-ray nucleon spectrum, the scaling model of high-energy N-N collisions parametrised from the recent ISR data and a realistic model for the propagation of cosmic rays through the atmosphere, the sea-level vertical muon spectra in the energy range 0.5-103 GeV have been derived. By comparing the results with the recent muon data of Allkofer et al. (1971) it can be concluded that the primary cosmic-ray nucleon spectrum may be represented by a single exponent over the whole energy range 5-104 GeV, and is given by the relation D(EN)dEN=2.48EN-2.70dEN. This conclusion is not in agreement with the results of some recent similar calculations.

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.

Bose-type distribution and primary cosmic ray nucleon spectrum from sea-level muon spectrum

The recent CERN Intersecting Storage Ring cross section data on the p+p to pi +or-+X inclusive reactions have been analysed using the Bose-type distribution of the form E(d3 sigma )/(d3p)=(Axs12/)/(exp( epsilon ( lambda )/T)-1) proposed by Hoang (1973). This formula has been used to derive the cosmic ray primary nucleon spectrum from the sea-level muon spectrum. It is found that the primary spectrum obeys the following relation: N(Ep)dEp=2.06Ep-2.64dEp. The result has been compared with the recent experimental data and theoretical predictions given by different authors.

Sea level cosmic ray proton spectrum and rising of proton-air collision cross section from Yekutieli model

The sea level proton spectrum has been calculated from the satellite data on primary cosmic ray nucleon spectrum using Yekutieli's nucleon cascade model (see abstr. A65035 of 1974). The interaction parameters yield the absorption cross section of p-air interaction which is in agreement with measured EAS experimental results in the spectral energy range 106-109 GeV/c.

Pion production spectra in the atmosphere derived from scaling hypothesis and CE model

The pion production spectra have been derived from the CE model and scaling hypothesis. It is found that the pion spectra derived from the primary cosmic ray nucleon spectrum using the CE model agrees well with the sea level muon spectrum if one assumes the energy dependence of pion inelasticity (Kpi ) in the energy band 3-1000 GeV. The CE model fits with the experimental data better than that expected from the scaling hypothesis.

The production spectrum of charged cosmic ray pions and the primary cosmic ray nucleon spectrum

The production spectrum of charged pions and the primary cosmic ray nucleon spectrum have been derived from the experimental muon spectrum determined near the geomagnetic equator at the zenith angles 45 degrees W and 60 degrees W. The derived pion spectrum follows the relation P(Epi )dEpi =(0.22+or-0.03)Epi -(2.65+or-0.12) dEpi and the primary spectrum agrees with the relation N(Ep) dEp=2.9Ep-2.65 dEp. The results have been compared with the values expected from the vertical muon spectrum.

Primary cosmic ray nucleon spectrum from sea-level muon spectrum and scaling hypothesis parameters

Based on the measured sea-level muon energy spectrum and the fitted parameters of Feynman’s scaling hypothesis that describe high energy collisions, we have deduced the primary cosmic ray nucleon spectrum in the energy range 50 GeV < E < 5000 GeV. It is shown that the statistical errors in the resulting nucleon spectrum are among the lowest that exist now and any residual systematic uncertainties in the evaluated flux can be reduced further by using accurate high energy collision data of nucleons and pions in light nuclei at current accelerator energies.