The muon energy spectrum at sea level from the intensities deep underground

The energy spectrum of muons at sea level is determined from the intensities deep underground. The following three points are different from past treatments: (1) From the energy-loss relation, −(dE/dt) = k(E) + b(E)E, including the effect of nuclear interaction and without the assumption that b is independent of E, the average range–energy relation is derived. (2) The reliable values of the factor which corrects for fluctuations in energy loss of muons passing through a great thickness of material are used. (3) Many authors measured the intensities under their respective rocks. The differences of these rocks are taken into account in the following way. The intensities are directly converted into the energy spectrum at sea level by using the appropriate average range–energy relations and correction factors. The resultant integral exponent of the energy spectrum in the vertical direction is β = 2.541 ± 0.190 with 95% confidence over the energy range 0.4–7 TeV having a weighted mean of 0.7 TeV.

Download Full-text

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

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1963.0176 ◽

1963 ◽

Vol 275 (1362) ◽

pp. 391-410 ◽

Cited By ~ 37

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.

Download Full-text

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

Canadian Journal of Physics ◽

10.1139/p79-049 ◽

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.

Download Full-text

Derivation of Muon Intensities in Sea-water Depths up to 1400 M.W.E. from a Recent Primary Cosmic Ray Spectrum

Australian Journal of Physics ◽

10.1071/ph840575 ◽

1984 ◽

Vol 37 (5) ◽

pp. 575 ◽

Cited By ~ 1

Author(s):

DP Bhattacharyya ◽

Pratibha Pal ◽

A Mukhopadhyay

Keyword(s):

Experimental Data ◽

Energy Loss ◽

Pair Production ◽

Sea Water ◽

Cosmic Ray ◽

Muon Energy ◽

Energy Relation ◽

Scaling Hypothesis ◽

Nuclear Interactions ◽

Water Depths

The muon intensities in sea-water depths up to 1400 M.W.E. have been derived from a recent primary cosmic ray spectrum. The scaling hypothesis of Feynman has been used in the calculation of meson spectra in the atmosphere. The range-energy relation for muons in sea water, used in the present work, accounts for the muon energy loss in sea water due to collisions, pair production, bremsstrahlung and nuclear interactions. The calculated muon range spectrum in sea water is well in accord with the experimental data obtained by Higashi et al. (1966), Davitaev et al. (1969), and Rogers and Tristam (1981, 1983

Download Full-text

Multiple interactions of muons in the NUSEX detector and muon energy spectrum deep underground

Astroparticle Physics ◽

10.1016/s0927-6505(96)00053-9 ◽

1997 ◽

Vol 6 (2) ◽

pp. 187-195 ◽

Cited By ~ 11

Author(s):

C. Castagnoli ◽

A. Castellina ◽

O. Saavedra ◽

T.M. Kirina ◽

R.P. Kokoulin ◽

...

Keyword(s):

Energy Spectrum ◽

Muon Energy ◽

Deep Underground ◽

Multiple Interactions

Download Full-text

Energy spectrum of hadrons in cosmic rays at sea level

Nature ◽

10.1038/256387a0 ◽

1975 ◽

Vol 256 (5516) ◽

pp. 387-388 ◽

Cited By ~ 19

Author(s):

F. ASHTON ◽

A. J. SALEH

Keyword(s):

Energy Spectrum ◽

Cosmic Rays ◽

Sea Level

Download Full-text

Energy spectrum of cosmic-ray muons at sea level

Il Nuovo Cimento ◽

10.1007/bf02732789 ◽

1964 ◽

Vol 32 (6) ◽

pp. 1524-1540 ◽

Cited By ~ 18

Author(s):

S. Miyake ◽

V. S. Narasimham ◽

P. V. Ramana Murthy

Keyword(s):

Energy Spectrum ◽

Sea Level ◽

Cosmic Ray

Download Full-text

Energy loss measurements of inclined muon bundles in the Cherenkov water detector

EPJ Web of Conferences ◽

10.1051/epjconf/201920808006 ◽

2019 ◽

Vol 208 ◽

pp. 08006

Author(s):

R.P. Kokoulin ◽

N.S. Barbashina ◽

A.G. Bogdanov ◽

S.S. Khokhlov ◽

V.A. Khomyakov ◽

...

Keyword(s):

Energy Loss ◽

Average Energy ◽

Cosmic Ray ◽

Muon Energy ◽

Single Experiment ◽

Muon Component ◽

Energy Deposit ◽

Tracking Detector ◽

Wide Range ◽

Muon Bundles

An experiment on the measurements of the energy deposit of inclined cosmic ray muon bundles is being conducted at the experimental complex NEVOD (MEPhI). The complex includes the Cherenkov water calorimeter with a volume of 2000 m3 and the coordinate-tracking detector DECOR with a total area of 70 m2. The DECOR data are used to determine the local muon densities in the bundle events and their arrival directions, while the energy deposits (and hence the average muon energy loss) are evaluated from the Cherenkov calorimeter response. Average energy loss carries information about the mean muon energy in the bundles. The detection of the bundles in a wide range of muon multiplicities and zenith angles gives the opportunity to explore the energy range of primary cosmic ray particles from about 10 to 1000 PeV in the frame of a single experiment with a relatively small compact setup. Experimental results on the dependence of the muon bundle energy deposit on the zenith angle and the local muon density are presented and compared with expectations based on simulations of the EAS muon component with the CORSIKA code.

Download Full-text

GOM20: A Stable Geodetic Reference Frame for Subsidence, Faulting, and Sea-Level Rise Studies along the Coast of the Gulf of Mexico

Remote Sensing ◽

10.3390/rs12030350 ◽

2020 ◽

Vol 12 (3) ◽

pp. 350

Author(s):

Guoquan Wang ◽

Xin Zhou ◽

Kuan Wang ◽

Xue Ke ◽

Yongwei Zhang ◽

...

Keyword(s):

Gulf Of Mexico ◽

Sea Level Rise ◽

Sea Level ◽

Reference Frame ◽

Time Window ◽

Tide Gauge ◽

Vertical Direction ◽

Geodetic Reference Frame ◽

Regional Reference ◽

And Sea Level

We have established a stable regional geodetic reference frame using long-history (13.5 years on average) observations from 55 continuously operated Global Navigation Satellite System (GNSS) stations adjacent to the Gulf of Mexico (GOM). The regional reference frame, designated as GOM20, is aligned in origin and scale with the International GNSS Reference Frame 2014 (IGS14). The primary product from this study is the seven-parameters for transforming the Earth-Centered-Earth-Fixed (ECEF) Cartesian coordinates from IGS14 to GOM20. The frame stability of GOM20 is approximately 0.3 mm/year in the horizontal directions and 0.5 mm/year in the vertical direction. The regional reference frame can be confidently used for the time window from the 1990s to 2030 without causing positional errors larger than the accuracy of 24-h static GNSS measurements. Applications of GOM20 in delineating rapid urban subsidence, coastal subsidence and faulting, and sea-level rise are demonstrated in this article. According to this study, subsidence faster than 2 cm/year is ongoing in several major cities in central Mexico, with the most rapid subsidence reaching to 27 cm/year in Mexico City; a large portion of the Texas and Louisiana coasts are subsiding at 3 to 6.5 mm/year; the average sea-level-rise rate (with respect to GOM20) along the Gulf coast is 2.6 mm/year with a 95% confidence interval of ±1 mm/year during the past five decades. GOM20 provides a consistent platform to integrate ground deformational observations from different remote sensing techniques (e.g., GPS, InSAR, LiDAR, UAV-Photogrammetry) and ground surveys (e.g., tide gauge, leveling surveying) into a unified geodetic reference frame and enables multidisciplinary and cross-disciplinary research.

Download Full-text