Angular Distribution Of Muons Research Articles

Mountain Muon Tomography Using a Liquid Scintillator Detector

Muon tomography (MT), based on atmospheric cosmic rays, is a promising technique suitable for nondestructive imaging of the internal structures of mountains. This method uses the measured flux distribution after attenuation, combined with the known muon angular and energy distributions and a 3D satellite map, to perform tomographic imaging of the density distribution inside a probed volume. A muon tomography station (MTS) requires direction-sensitive detectors with a high resolution for optimal tracking of incident cosmic-ray muons. The spherical liquid scintillator detector is one of the best candidates for this application due to its uniform detection efficiency for the whole 4π solid angle and its excellent ability to distinguish muon signals from the radioactive background via the difference in the energy deposit. This type of detector, with a 1.3 m diameter, was used in the Jinping Neutrino Experiment (JNE). Its angular resolution is 4.9 degrees. Following the application of imaging for structures of Jinping Mountain with JNE published results based on the detector, we apply it to geological prospecting. For mountains below 1 km in height and 2.8 g/cm3 in the reference rock, we demonstrate that this kind of detector can image internal regions with densities of ≤2.1 g/cm3 or ≥3.5 g/cm3 and hundreds of meters in size.

Microstructures and properties of CrxFeNi(3-x)Al high-entropy alloys

Muon tomography (MT), based on atmospheric cosmic rays, is a promising technique suitable for nondestructive imaging of the internal structures of mountains. This method uses the measured flux distribution after attenuation, combined with the known muon angular and energy distributions and a 3D satellite map, to perform tomographic imaging of the density distribution inside a probed volume. A muon tomography station (MTS) requires direction-sensitive detectors with a high resolution for optimal tracking of incident cosmic-ray muons. The spherical liquid scintillator detector is one of the best candidates for this application due to its uniform detection efficiency for the whole $4\pi$ solid angle and its excellent ability to distinguish muon signals from the radioactive background via the difference in the energy deposit. This type of detector, with a 1.3~m diameter, was used in the Jinping Neutrino Experiment~(JNE). Its angular resolution is 4.9~degrees. Following the application of imaging for structures of Jinping Mountain with JNE published results based on the detector, we apply it to geological prospecting. For mountains below 1~km in height and 2.8~${\rm g}/{\rm cm}^3$ in the reference rock, we demonstrate that this kind of detector can image internal regions with densities of $\leq$ 2.1~${\rm g}/{\rm cm}^3$ or $\geq$ 3.5~${\rm g}/{\rm cm}^3$ and hundreds of meters in size.

Monte Carlo characterization of the cosmic ray muon flux in shallow subsurface geological repositories intended for disposal of radioactive materials

Recent challenges in monitoring subsurface geological repositories intended for disposal of radioactive materials such as spent nuclear fuel call for new, innovative concepts that are facility independent, cost-effective, passive, and reliable. Once nuclear material is in place at these facilities, reverifying the inventory may no longer be feasible if continuity of knowledge is lost or unavailable to the inspectors. Using cosmic ray muons may present several potential advantages over conventional photon/neutron signatures, and their use in safeguards applications have only received attention in the past decade. However, there have been limited efforts to explore the integration of cosmic ray muons into repository safeguards and study potential gains, risks, and costs. This paper presents a Monte Carlo-based methodology to characterize the cosmic ray muon flux, including muon angular and energy differential distributions at depths representative of subsurface geological repositories. Since there have been limited measurements at these sites and a measurement made in one site is not always transferable to another site, the objective is to develop an efficient simulation method and useful parametrizations to provide a convenient tool for enabling muon simulations at any geological repository site. It is expected these results will provide a better understanding of how muons can be integrated into an existing geological repository safeguards framework.

Experimental Data of Muon Hodoscope URAGAN for Investigations of Geoffective Processes in the Heliosphere

Muon hodoscope URAGAN continuously detects the angular distribution of muons in a wide range of zenith angles and allows one to obtain information about variations, both in the intensity and in angular characteristics of the muon flux, caused by active processes in the heliosphere, the magnetosphere and atmosphere of the Earth. Various parameters of the muon flux anisotropy and methods of calculation of these parameters are discussed. Real-time processing of a continuous flow of multidimensional data from the muon hodoscope URAGAN is quite a challenge. In the article, methods of formation and primary analysis of the data, their processing in real time and obtaining time series of various parameters of integral counting rate and angular anisotropy of the muon flux, which are important for the physical analysis of modulation processes of cosmic rays in the heliosphere, are presented.

Determination of local muon flux using astronomical Charge Coupled Device

As an abundant component of secondary cosmic rays at the Earth, muons carry significant data, such as information on mass number of primary particles producing extensive air showers. Anyhow, the total muon flux is an important observable in many phenomena, for example it is suggested that the muon flux is influenced by the level of solar activity at the Earth, while the neutrino anomaly and hadronic interaction models are studied through the products of muon decay. As a result a part of any cosmic ray detector is designed to observe muons, count and evaluate their energy and angular distribution. Thus a simple method was started in Research Institute for Astronomy and Astrophysics of Maragha, University of Maragheh, to study the recorded tracks of particles by an astronomical CCD at 1478 m above sea level. To analyze recorded data and determine the muon flux from experiments, the flux of secondary atmospheric muons simulated with CORSIKA code (version 6.9) to study the muon angular distribution for our geographical location (latitude: 46.2534°E, longitude: 37.3892°N). The data used here were gathered during a ground run on 4 months (of 2016 and 2017), at Maragheh, Iran. The paper presents numerical results of the muon’s flux obtained at 1478 m above sea level which is in good agreement with expected values from simulations. The results were compared with experimental data from different experiments.

Real-Time GSE Mapping of Muon-Flux Directional Variation with the URAGAN Hodoscope

Continuous monitoring of the muon flux over wide ranges of zenith and azimuth angles with the URAGAN detector (Moscow, 55.7° N, 37.7° E, 173 m AMSL) allows detection of variations in its intensity and angular distribution. A way of locating domains of anisotropy in the muon angular distribution is described, and they are mapped in matrix form in the GSE coordinate system. The maximum depth (height) of deformation, the zenith and azimuth angles of the center in the local system, and its GSE longitude and latitude are determined for each observed domain. The GSE longitudes of the detected domains of anisotropy are available on the Internet as functions of time and can be used to monitor the heliosphere’s activity.

Cosmic Ray Muons of High and Ultrahigh Energies

Muons are the main component of cosmic rays on the Earth’s surface and underground. The energy spectrum and angular distribution of muons in the atmosphere are related both to the mechanisms of their generation and to the basic characteristics of the primary cosmic rays—their energy spectrum and mass composition. Changes in the muon flux underground are determined by muon energy losses, and its measurements allow muon interaction processes to be studied. The history of extensive cosmic-ray muon investigations covers many decades. A retrospective overview of important directions of cosmic ray muon studies is presented, and analysis of the main experiments and results is given. Special attention is paid to the “muon puzzle”, that is, the muon excess increasing with the energy of primary particles, and to possible ways of solving it.

Measurement of cosmic muon angular distribution and vertical integrated flux by 2 m × 2 m RPC stack at IICHEP-Madurai

The 50 kton INO-ICAL is a proposed underground high energy physics experiment at Theni, India (9̂57′N, 77̂16′E) to study the neutrino oscillation parameters using atmospheric neutrinos. The Resistive Plate Chamber (RPC) has been chosen as the active detector element for the ICAL detector. An experimental setup consisting of 12 layers of glass RPCs of size 2 m × 2 m has been built at IICHEP, Madurai to study the long term stability and performance of RPCs which are produced on a large scale in Indian industry. In this paper, the studies on the performance of RPCs are presented along with the angular distribution of muons at Madurai (9̂56′N,78̂00′E and Altitude ≈ 160 m from sea level).

The EEE Project: a sparse array of telescopes for the measurement of cosmic ray muons

The Extreme Energy Events (EEE) Project is meant to be the most extensive experiment to detect secondary cosmic particles in Italy. To this aim, more than 50 telescopes have been built at CERN and installed in high schools distributed all over the Italian territory. Each EEE telescope comprises three large area Multigap Resistive Plate Chambers (MRPCs) and is capable of reconstructing the trajectories of the charged particles traversing it with a good angular resolution. The excellent performance of the EEE telescopes allows a large variety of studies, from measuring the local muon flux in a single telescope, to detecting extensive air showers producing time correlations in the same metropolitan area, to searching for large-scale correlations between showers detected in telescopes tens, hundreds or thousands of kilometers apart. In addition to its scientific goal, the EEE Project also has an educational and outreach objective, its aim being to motivate young people by involving them directly in a real experiment. High school students and teachers are involved in the construction, testing and start-up of the EEE telescope in their school, then in its maintenance and data-acquisition, and later in the analysis of the data. During the last couple of years a great boost has been given to the EEE Project through the organization of simultaneous and centralized data taking with the whole telescope array. The raw data from all telescopes are transferred to CNAF (Bologna), where they are reconstructed and stored. The data are currently being analyzed, looking at various topics: variation of the rate of cosmic muons with time, upward going muons, muon lifetime, search for anisotropies in the muon angular distribution and for time coincidences between stations. In this paper an overall description of the experiment is given, including the design, construction and performance of the telescopes. The operation of the whole array is also presented by showing the most recent physics results.

Measurement of cosmic-ray muons with the Distributed Electronic Cosmic-ray Observatory, a network of smartphones

Solid-state camera image sensors can be used to detect ionizing radiation in addition to optical photons. We describe the Distributed Electronic Cosmic-ray Observatory (DECO), an app and associated public database that enables a network of consumer devices to detect cosmic rays and other ionizing radiation. In addition to terrestrial background radiation, cosmic-ray muon candidate events are detected as long, straight tracks passing through multiple pixels. The distribution of track lengths can be related to the thickness of the active (depleted) region of the camera image sensor through the known angular distribution of muons at sea level. We use a sample of candidate muon events detected by DECO to measure the thickness of the depletion region of the camera image sensor in a particular consumer smartphone model, the HTC Wildfire S. The track length distribution is fit better by a cosmic-ray muon angular distribution than an isotropic distribution, demonstrating that DECO can detect and identify cosmic-ray muons despite a background of other particle detections. Using the cosmic-ray distribution, we measure the depletion thickness to be 26.3 ± 1.4 μm. With additional data, the same method can be applied to additional models of image sensor. Once measured, the thickness can be used to convert track length to incident polar angle on a per-event basis. Combined with a determination of the incident azimuthal angle directly from the track orientation in the sensor plane, this enables direction reconstruction of individual cosmic-ray events using a single consumer device. The results simultaneously validate the use of cell phone camera image sensors as cosmic-ray muon detectors and provide a measurement of a parameter of camera image sensor performance which is not otherwise publicly available.

Developing a cosmic ray muon sampling capability for muon tomography and monitoring applications

In this study, a cosmic ray muon sampling capability using a phenomenological model that captures the main characteristics of the experimentally measured spectrum coupled with a set of statistical algorithms is developed. The “muon generator” produces muons with zenith angles in the range 0–90° and energies in the range 1–100GeV and is suitable for Monte Carlo simulations with emphasis on muon tomographic and monitoring applications. The muon energy distribution is described by the Smith and Duller (1959) [35] phenomenological model. Statistical algorithms are then employed for generating random samples. The inverse transform provides a means to generate samples from the muon angular distribution, whereas the Acceptance–Rejection and Metropolis–Hastings algorithms are employed to provide the energy component. The predictions for muon energies 1–60GeV and zenith angles 0–90° are validated with a series of actual spectrum measurements and with estimates from the software library CRY. The results confirm the validity of the phenomenological model and the applicability of the statistical algorithms to generate polyenergetic–polydirectional muons. The response of the algorithms and the impact of critical parameters on computation time and computed results were investigated. Final output from the proposed “muon generator” is a look-up table that contains the sampled muon angles and energies and can be easily integrated into Monte Carlo particle simulation codes such as Geant4 and MCNP.

Investigation of the zenith angle dependence of cosmic-ray muons at sea level

Angular distribution of cosmic-ray muons at sea level has been investigated using the Geant4 simulation package. The model used in the simulations was tested by comparing the simulation results with the measurements made using the Berkeley Lab cosmic ray detector. Primary particles’ energy and fluxes were obtained from the experimental measurements. Simulations were run at each zenith angle starting from θ = 0° up to θ = 70° with 5° increment. The angular distribution of muons at sea level has been estimated to be in the form I(θ) = I(0°) cosn (θ), where I(0°) is the muon intensity at 0° and n is a function of the muon momentum. The exponent n = 1.95±0.08 for muons with energies above 1 GeV is in good agreement, within error, with the values reported in the literature.

Study of atmospheric muons using a cosmic ray telescope

The charge ratio of cosmic muons holds important information for both the atmospheric neutrino anomaly and hadronic interaction models. In this paper we measured the muon charge ratio () in the cosmic ray flux in the momenta range 0.76–1.60 GeV/c by using a cosmic ray telescope. The delayed coincidence method is used based on the reduced mean lifetime of negative muons due to nuclear capture in matter. The systematic time-dependent effects of the muon charge ratio are considered by grouping the decay data into different time intervals. We compared the experimental data with the predictions of CORSIKA simulations using a high energy interaction model (QGSJET-II) and two low energy interaction models (UrQMD and GHEISHA) in the energy range 1011–1016 eV for primary particles. In addition, by considering the muon flux in different zenithal and azimuthal angles, the muon angular distribution is obtained as I(θ) = I(0)cos nθ with average n = 1.91 ± 0.07. Dependence of the muon flux on the azimuth angle (the East–West effect) is also observed, due to the influence of the geomagnetic field in particular on low energy muons.

Measurements of the Angular Distributions of Muons fromΥDecays inpp¯Collisions ats=1.96 TeV

The angular distributions of muons from Upsilon(1S,2S,3S) to mu+mu- decays are measured using data from proton anti-proton collisions at sqrt(s)=1.96 TeV corresponding to an integrated luminosity of 6.7 /fb and collected with the CDF II detector at the Fermilab Tevatron. This analysis is the first to report the full angular distributions as functions of transverse momentum pT for the Upsilon mesons in both the Collins-Soper and s-channel helicity frames. This is also the first measurement of spin alignment of Upsilon(3S) mesons. Within the kinematic range of Upsilon rapidity |y|<0.6 and pT up to 40 GeV/c, the angular distributions are found to be nearly isotropic.

Measurement of Angular Distributions of Drell-Yan Dimuons inp+dInteractions at800 GeV/c

We report a measurement of the angular distributions of Drell-Yan dimuons produced using an 800 GeV/c proton beam on a deuterium target. The muon angular distributions in the dilepton rest frame have been measured over the kinematic range 4.5<m{mu mu}<15 GeV/c{2}, 0<p{T}<4 GeV/c, and 0<x{F}<0.8. No significant cos2phi dependence is found in these proton-induced Drell-Yan data, in contrast with the situation for pion-induced Drell-Yan data. The data are compared with expectations from models which attribute the cos2phi distribution to a QCD vacuum effect or to the presence of the transverse-momentum-dependent Boer-Mulders structure function h{1}{perpendicular}. Constraints on the magnitude of the sea-quark h{1}{perpendicular} structure functions are obtained.

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.

Atmospheric neutrino oscillations from upward throughgoing muon multiple scattering in MACRO

The energy of atmospheric neutrinos detected by MACRO was estimated using multiple Coulomb scattering of upward throughgoing muons. This analysis allows a test of atmospheric neutrino oscillations, relying on the distortion of the muon energy distribution. These results have been combined with those coming from the upward throughgoing muon angular distribution only. Both analyses are independent of the neutrino flux normalization and provide strong evidence, above the 4σ level, in favour of neutrino oscillations.

Study of atmospheric neutrinos with the MACRO detector

The MACRO experiment detected different categories of atmospheric muon neutrinos. We describe in this paper the energy estimate of upward throughgoing muons by using the multiple coulomb scattering. Combining the results of such analysis with the upgoing muon angular distribution, both not using the absolute ν flux normalization informations, an evidence above 4σ for atmospheric neutrino oscillation is found.

Inconsistencies in interpreting the atmospheric neutrino anomaly

We note a discrepancy between the value ofR expected on the basis of the muon neutrino angular distribution and the value actually observed. The energy independence ofR leads to a fine-tuning problem. This may be indicative of some unaccounted for new physics.

Muonic cascades in isolated low-Zatoms and molecules

Muonic x-ray cascades in B, C, N, O, and Ne following muonic atom formation in ${\mathrm{B}}_{2}{\mathrm{H}}_{6},$ ${\mathrm{CH}}_{4},$ ${\mathrm{C}}_{2}{\mathrm{H}}_{6},$ ${\mathrm{C}}_{4}{\mathrm{H}}_{10},$ ${\mathrm{N}}_{2},$ ${\mathrm{O}}_{2}$, and Ne were investigated. The densities of the different target gases were low enough to prevent any contact of the atom or molecule on which the formation takes place with surrounding atoms or molecules during the cascade. Using semiconductor detectors, the yields of transitions in several series with energies between 1.5 keV and 300 keV were measured. Cascade calculations were performed in order to explain the observed transition yields. The cascades could be reproduced by variation of only two parameters: the number of electrons and the muon angular momentum distribution at the starting point of the calculation. The cascade of $\ensuremath{\mu}\mathrm{Ne}$ formed in monoatomic neon was described best. Moreover, muonic carbon cascades were found to differ according to the sort of hydrocarbon, demonstrating the influence of the capturing molecule's structure on the muonic cascade. By varying the number of initially available electrons, the molecular effects could be described with the cascade program.