Sea Level Muon Spectrum Research Articles

Altitude profile of atmospheric muons in a location with relatively high cut-off rigidity

We have investigated the differential and integrated muon fluxes, muon charge ratios and the zenith angle dependence of the integrated muon intensities at sea level and various depths in the atmosphere of Tsukuba, Japan, for muons with momenta below 400GeV/c using the Geant4 simulation package. The simulated sea level muon spectrum and charge ratio have been seen to be in good agreement, throughout the momentum interval of the interest, with those from the measurements made by the BESS-TeV spectrometer. Integrated muon intensities have been found to increase as the atmospheric depth decreases up to slightly above 200g/cm2, and then they have a trend to decrease at lower atmospheric depths. Muon charge ratios at each of the atmospheric depth of interest have been shown to have a very similar behavior with the one at sea level. Simulation results for the zenith angle dependence of muon intensity have been quite compatible with the existing information in the literature for sea level. It has also been shown that the zenith angular dependence of muon intensity has a tendency to disappear (to obey the secθ distribution) as the atmospheric depth decreases for muons with relatively low (high) momenta.

Sea-level muon spectrum in the energy range 1–10 TeV from the data of underground experiments

Within an adjoint approach, the properties of the muon component in various types of rock and in water are calculated with allowance for fluctuations of energy losses in all muon-interaction processes. The behavior of the muon spectrum at sea level is established on the basis of a comparison of the muonabsorption curves obtained in this way and experimental data from underground facilities. It is shown that the deficit of the calculated muon flux obtained with the aid of data from direct measurements of the spectra of primary nuclei and Reggeon models of nuclear interactions is not less than 50% in the energy range 1–10 TeV.

Cosmic muon flux at shallow depths underground

We consider the cosmic muon background for the installations located at shallow depths. We suggest a relatively simple formula for the sea-level muon spectrum, which allows calculate dependencies of the vertical muon intensity and integral muon flux density on overburden. Muon flux dependency on the zenith angle at overburden of 10 to 100 meters of standard rock shows that muon angular distribution practically does not change in this interval. We present muon angular distributions for three typical apparatus locations in measurements on the surface and at shallow depths. It is shown that for such installations the active shielding "umbrella" should overlap a zenith angle of \theta ~ 80^o to remove the cosmic muon background.

The cosmic ray muon spectrum and charge ratio in CosmoALEPH

The ALEPH experiment at the LEP e +e − storage ring at CERN has been used to measure the momentum spectrum of cosmic ray muons. ALEPH is located at a vertical depth of 320 m.w.e. underground close to the Jura mountains. The high resolution of the time projection chamber (TPC) of ALEPH allows to reconstruct muon tracks with momenta up to the TeV region. The measured muon momentum spectrum and the charge ratio in the range from 80 to 2500 GeV are presented. After corrections for energy loss in the overburden the sea level muon spectrum at nearly vertical incidence is obtained. The experimental data are compared to theoretical expectations and results from other experiments.

Parametrization of atmospheric muon angular flux underwater

The analytical expression for angular integral flux of atmospheric muons in matter with the explicit relation of its parameters with those of the sea level spectrum is obtained. The fitting formula for the sea level muon spectrum at different zenith angles for spherical atmosphere is proposed. The concrete calculations for pure water are presented. Fluctuations of muon energy losses are taken into account by means of parametrized correction factor calculated using survival probabilities resulted from Monte Carlo simulations. Parametrizations of all continuous energy losses are obtained with using the most recent expressions for muon interaction cross-sections. The corresponding parametrization errors and field of method application are comprehensively discussed. The proposed formulae could be useful primarily for experimentalists processing data of arrays located deep under water or under ice.

Atmospheric muon flux at sea level, underground, and underwater

The vertical sea-level muon spectrum at energies above 1 GeV and the underground/underwater muon intensities at depths up to 18 km w.e. are calculated. The results are particularly collated with a great body of the ground-level, underground, and underwater muon data. In the hadron-cascade calculations, the growth with energy of inelastic cross sections and pion, kaon, and nucleon generation in pion-nucleus collisions are taken into account. For evaluating the prompt muon contribution to the muon flux, we apply two phenomenological approaches to the charm production problem: the recombination quark-parton model and the quark-gluon string model. To solve the muon transport equation at large depths of homogeneous medium, a semi-analytical method is used. The simple fitting formulas describing our numerical results are given. Our analysis shows that, at depths up to 6-7 km w. e., essentially all underground data on the muon intensity correlate with each other and with predicted depth-intensity relation for conventional muons to within 10%. However, the high-energy sea-level data as well as the data at large depths are contradictory and cannot be quantitatively decribed by a single nuclear-cascade model.

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.

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°.

An accurate measurement of the sea-level muon spectrum within the range 4 to 3000 GeV/c

The differential and integral spectra of muons moving in the near-vertical direction have been measured at Nottingham using a solid iron magnetic spectrometer. This instrument utilised an automatic recording system for data collection which allowed the range of muon momenta covered by this investigation to extend from 4 to 3000 GeV/c, the lower limit being set by the magnet itself. The diffusion model for particle propagation through the Earth's atmosphere was used to provide the muon momentum spectrum incident upon the instrument.

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.

Sea Level Muon Spectrum Derived from Bugaev Model Using the Primary Cosmic Ray Energy Spectrum of Grigorov et al

AbstractIn a recent paper BHATTACHARYYA has derived the pion and kaon production spectra in the atmosphere using a form of the primary nucleon energy spectrum of the measurements of GRIGOROV et al. and the interaction model of BUGAEV et al. The sea level muon spectrum derived from these meson spectra agrees with the magnetic spectrograph data of ALLKOFER et al. and AYRE et al.In this report a critical analysis of the paper has been made and some obvious mistakes in the formulation have been pointed out. The formulation of BUGAEV et al. and the data of GRIGOROV at al. have been misinterpreted by BHATTACHARYYA. The corrected results have been properly interpreted in this report.

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.

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.

Kaon-pion ratio derived from dynamical model and the spectral shape of the muon spectrum

The kaon-pion ratio, estimated from the theoretical model based on the structural aspects of hadrons, has been applied to the diffusion model ofBull et al. The derived spectral shape of the sea level muon spectrum is in accord with the magnetic spectrograph data of Kiel and Durham Groups.

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.

Sea Level Muon Spectrum and Muon Charge Ratio derived from CERN Results for Nucleon?Nucleus Inelastic Interactions

The sea level cosmic ray spectrum and muon charge ratio have been estimated by using the energy moments of the cross section for proton-air inelastic collisions. These energy moments have been determined by interpolation from CERN results for proton-nucleus inelastic interactions in pion production. The derived results are compared with previous work.

Dao Scaling Model and Sea Level Cosmic Ray Muon Spectrum from Goddard Space Flight Group Measured Primary Proton Spectrum

AbstractA new type of scaling model for p + p → π− + X inclusive reactions, proposed by DAO et al., is applied to derive the sea level muon spectrum. The nucleon spectrum data of Goddard Space Flight Group were taken as input. It is found that the sea level muon spectrum depends explicitly on the average value of the FEYNMAN variable x whose most probable value is estimated to be 0.18.

Kaon‐pion Ratio from ISR Results and the Derived Sea Level Muon Spectrum from MAEDA'S Model

Kaon‐Pion‐Verhältnis nach ISR (CERN)‐Resultaten und reduziertes Myonspektrum nach MAEDA'S ModellVarious authors have estimated the production spectrum of particles in the nuclear interactions of primary protons with air nuclei. In general pions have been considered by them as the parents of muons and kaon contribution to muon flux is neglected.Recently THOMPSON and WHALLEY [1] have studied the data of AYRE et al. [2] on 2 × 105 muons above 20 GeV which provided the impetus for the authors to consider and include muons produced as the result of kaon decay along with muons produced from the decay of pions. Later DAU et al. [3] have calculated the production spectrum of muons using the experimental results of the Kiel Group (ALLKOFER et al. [4]) and MAEDA'S [5] model. It is found from their investigation that the calculated results are not in fair agreement with the observed data for vertical incidence of muons. The adopted value of the kaon‐pion ratio in their calculations was 15% which is somewhat higher than the value obtained from the machine measurements by the CERN Intersecting Storage Ring Group (ANTINUCCI et al. [6]).In the present work we have used the kaon‐pion ratio from the CERN ISR data and calculated the spectral shape of the sea level muon spectrum from MAEDA'S [5] model. The derived spectrum is fitted to the magnetic spectrograph data of the Kiel and Durham Groups [2, 4]. χ2‐test has been performed to obtain an idea about the significance of the fit with the measured data.

Effect of Solar Modulation on the Low Energy Sea Level Muon Spectrum Near the Geomagnetic Equator

A study is made of the influence of long-term solar modulation on the low energy sea level muon spectrum near the geomagnetic equator. Recent experimental data are compared with theoretical results calculated from the phenomenological model of Allkofer and Dau. It is suggested that the observed enhancement in the muon intensity is mainly due to a shift in the solar potential.

Sea level muon spectrum derived from the Goddard Space Flight Centre measured nucleon spectrum using the Cocconi–Koester–Perkins model

The sea level muon spectrum is estimated from the Goddard Space Flight Centre group measured nucleon spectrum by using the model of Cocconi, Koester, and Perkins (CKP). The derived muon spectrum agrees well with the magnetic spectrograph data of Ayre, Baxendale, Hume, Nandi, Thompson, and Whalley when the energy dependence of pion inelasticity (Kπ) in the CKP model is assumed in the pion energy range 10–500 GeV. Above 50 GeV pion energy (Eπ) the pion inelasticity follows the relation Kπ = 0.1 ln Eπ.