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

1979 ◽  
Vol 57 (3) ◽  
pp. 375-380
Author(s):  
A. K. Chakrabarti ◽  
A. K. Das ◽  
A. K. De
Keyword(s):  
Energy Spectrum ◽  
Sea Level ◽  
Critical Analysis ◽  
Muon Energy ◽  
Measured Spectrum ◽  
Muon Spectrum ◽  
Nucleon Spectrum ◽  
Good Agreement

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.

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

1979 ◽  
Vol 57 (7) ◽  
pp. 921-925 ◽  
Author(s):  
A. K. Chakrabarti ◽  
A. K. Das ◽  
A. K. De
Keyword(s):  
Sea Level ◽  
Pion Production ◽  
Spectral Shape ◽  
Muon Spectrum ◽  
Proton Proton ◽  
Absolute Value ◽  
Nucleon Spectrum ◽  
Scaling Models ◽  
The Mean ◽  
Good Agreement

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.

The rate of energy loss of high-energy cosmic ray muons

1963 ◽  
Vol 275 (1362) ◽  
pp. 391-410 ◽  
Keyword(s):  
Energy Spectrum ◽  
Energy Loss ◽  
Sea Level ◽  
Cosmic Ray ◽  
Nuclear Interaction ◽  
High Energy ◽  
Level Energy ◽  
Muon Spectrum ◽  
The Third ◽  
Muon Mass

The rate of energy loss of muons is examined by com paring the observed depth-intensity relation with that predicted from a knowledge of the sea-level energy spectrum of cosmic ray muons. The evidence for each of the parameters entering into the analysis is assessed and estimates are made of the sea-level muon spectrum up to 10000 GeV and the depth-intensity relation down to 7000 m.w.e. The effect of range-straggling on the underground intensities is considered and shown to be important at depths below 1000 m.w.e. Following previous workers the energy loss relation is written as -d E /d x =1.88+0.077 in E ' m / mc 2 + b E MeV g -1 cm 2 , where E ' m is the maximum transferrable energy in a /i-e collision and m is the muon mass. The first two terms give the contribution from ionization (and excitation) loss and the third term is the combined contribution from pair production, bremsstrahlung and nuclear interaction. The best estimate of the coefficient b from the present work is b = (3.95 + 0.25) x 10 -6 g -1 cm 2 over the energy range 500 to 10000 GeV, which is close to the theoretical value of 4.0 x 10 -6 g -1 cm 2 . It is concluded that there is no evidence for any marked anomaly in the energy loss processes for muons of energies up to 10000 GeV.

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

1977 ◽  
Vol 55 (7-8) ◽  
pp. 629-631
Author(s):  
Kalpana Sarkar ◽  
D. P. Bhattacharyya ◽  
D. Basu
Keyword(s):  
Energy Range ◽  
Sea Level ◽  
Energy Dependence ◽  
Space Flight ◽  
Muon Spectrum ◽  
Goddard Space ◽  
Pion Energy ◽  
Nucleon Spectrum

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.

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

1996 ◽  
Vol 11 (30) ◽  
pp. 2427-2433
Author(s):  
MALA MITRA ◽  
PRATIBHA PAL ◽  
D.P. BHATTACHARYYA
Keyword(s):  
Cosmic Ray ◽  
Upper Atmosphere ◽  
Energy Spectra ◽  
Muon Energy ◽  
Spectral Indices ◽  
Muon Spectrum ◽  
Indirect Measurements ◽  
Large Zenith Angle ◽  
Nucleon Spectrum ◽  
The Individual

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.

Das Impulsspektrum der Ultrastrahlungs-Muonen und das Ladungsverhältnis in 5200 m Höhe

1966 ◽  
Vol 21 (8) ◽  
pp. 1205-1210
Author(s):  
O. C. Allkofer ◽  
E. Kraft
Keyword(s):  
Sea Level ◽  
Cosmic Ray ◽  
Theoretical Models ◽  
Momentum Spectrum ◽  
Charge Ratio ◽  
Lead Absorber ◽  
Muon Spectrum ◽  
Total Spectrum ◽  
Good Agreement

The momentum spectrum of cosmic ray muons and the charge ratio at 5200 m above sea level have been measured. To separate the spectrum of muons from the total spectrum a lead absorber was used. From theoretical models the spectrum of muons is calculated. Good agreement is found between the calculated and measured muon spectrum.

Derivation of muon range spectrum under rock from the recent primary spectrum

1985 ◽  
Vol 63 (8) ◽  
pp. 1050-1060 ◽  
Author(s):  
Pratibha Pal ◽  
D. P. Bhattacharyya
Keyword(s):  
Cosmic Ray ◽  
Muon Energy ◽  
Energy Relation ◽  
Muon Spectrum ◽  
Primary Spectrum ◽  
Atmospheric Diffusion ◽  
Data Compilation ◽  
Scaling Hypothesis ◽  
Burst Data ◽  
Good Agreement

The muon range spectra under Mont Blanc Tunnel and Kolar Gold Field rocks have been calculated from the recently measured primary cosmic ray spectrum. The scaling hypothesis of Feynman has been used for the calculation of pion and kaon spectra in the atmosphere. The meson atmospheric diffusion equation has been solved by following the method of Bugaev et al. The derived muon energy spectrum has been found to be in good agreement with the measured data of the Kiel, Durham, DEIS, and Moscow University groups. The calculated muon energy spectra at large polar angles have been compared with the different experimental results. The integral muon spectrum up to 20 TeV supports the MARS burst data favourably. Using the procedure of Kobayakawa, the muon energy loss in rock due to ionization, pair production, and bremsstrahlung and nuclear interactions from Bezrukov and Bugaev, we have constructed the range–energy relation in Mont Blanc and Kolar Gold Field rocks. The estimated range spectra have been corrected for range fluctuations and have been compared with the Mont Blanc Tunnel data of Castagnoli et al., Bergamasco et al., and Sheldon et al. and the Kolar Gold Field data compilation by Krishnaswamy et al.

Pion production spectrum from primary cosmic ray spectrum and scaling constants

1977 ◽  
Vol 55 (2) ◽  
pp. 154-157 ◽  
Author(s):  
D. P. Bhattacharyya ◽  
R. K. Roy Choudhury ◽  
D. Basu
Keyword(s):  
Energy Spectrum ◽  
Sea Level ◽  
Satellite Data ◽  
Pion Production ◽  
Cosmic Ray ◽  
Muon Spectrum ◽  
Production Spectrum ◽  
Average Value ◽  
Scaling Hypothesis ◽  
Cosmic Muons

The scaling hypothesis of Dao et at. in p + p → π− + X reactions has been used to derive the sea level spectrum of cosmic muons from the satellite data of primary cosmic ray nucleons. It is found that the derived pion production spectrum depends on [Formula: see text], the average value of the Feynman variable x. Taking as input the energy spectrum of primary cosmic ray nucleons determined by Grigorov et al., as well as the sea level muon spectrum determined by Allkofer, Carstensen, and Dau, the value of [Formula: see text] at different pion energies has been estimated. A fit to the calculated results gives the following energy dependence of [Formula: see text]:[Formula: see text]

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