Muon Energy Spectrum Research Articles

Omnidirectional borehole detector for muography: Design and performance evaluation

Muography using cosmic ray muons is a non-invasive and environmentally friendly imaging technique with comprehensive applicability across various fields such as mineral exploration, archaeology, and engineering, etc. Given characteristics of high penetration and broad energy spectrum of cosmic ray muons, three-dimensional density distribution of objects up to hundreds of meters can be well reconstructed. In mineral exploration and archaeology applications, conventional planar detectors are too large and usually deployed in spacious rooms like tunnels or outdoors, which seriously limits the deeper and broader applications of muography. A type of borehole muon detector is highly desired to address this. In the work, we introduce a novel borehole-type muography detector comprising annular and prismatic plastic scintillators, allowing for its deployment in boreholes. In the paper, the structural design of the detector is described in details and its performance is evaluated numerically and experimentally. Comprehensive investigation on components and on the system as a whole were conducted. According to our commissioning tests, the detector we propose has an omnidirectional field of view without blind spots, with an angular uncertainty of 27.4 mrad and a position uncertainty of 2.29 mm in the azimuthal direction, an angular uncertainty of 20.6 mrad and a position uncertainty of 10.31 mm in the zenithal direction. Detection efficiencies for both annular and prismatic scintillators were measured as 90.3 ± 0.53% and 92.27 ± 0.82%. In addition, an underground location was investigated, survival rate distributions being calculated from above-ground and underground measurements. The results indicate its capability to successfully address muography applications This novel borehole-type detector has the potential to address industry demand for lower-cost, more flexible muography solutions.

Reconstructing the Energy Spectrum of Cosmic Muons Measured with the Underground Detector of the Tien Shan High-Altitude Station

Reconstructing the Energy Spectrum of Cosmic Muons Measured with the Underground Detector of the Tien Shan High-Altitude Station

Monte Carlo simulation for background noise study of the Wudalianchi volcanic density imaging

In our muon radiography experiment on the Wudalianchi volcano in northeastern China, the muon flux was overestimated and the volcano density was underestimated due to the contamination by background noise. In our past simulation work on background noise, we did not construct the volcano model, we just simply used the volcanic high-resolution topographic map data and the cosmic ray particle source data to obtain the penetrating muon energy spectrum. In order to study the background noise and volcanic density more accurately and in detail, we used the GEANT4 tool to construct a virtual volcano and a virtual detector, and combined the cosmic ray shower library (CRY) to simulate the interaction between the volcano and cosmic ray particles. The results show that the background noise in volcano muon radiography is mainly composed of particles with low-energy (less than 1GeV). According to the elimination device to reduce the background particles, the volcano density map we obtained is closer to the simulated value than the map before eliminating. This research has implications for our next volcano experiments.

Evaluation of cosmogenic production of 39Ar and 42Ar for rare-event physics using underground argon

Underground argon (UAr) with lower cosmogenic activities of 39Ar and 42Ar has been planned as a detector in detecting scintillation light and charge collection using time projection chambers for dark matter searches and as a veto detector in suppressing backgrounds for neutrinoless double beta decay (0νββ) experiments. Long-lived radioactive isotopes, 39Ar and 42Ar, can also be produced on the surface when UAr is pumped out from a deep well. Understanding the production of long-lived isotopes in Ar is important for utilizing UAr for dark matter and 0νββ experiments in terms of its production, transportation, and storage. Ar exposure to cosmic rays at sea-level is simulated using Geant4 for a given cosmic ray muon, neutron, and proton energy spectrum. We report the simulated cosmogenic production rates of 39Ar, 42Ar, and other long-lived isotopes at sea-level from fast neutrons, high energy muons, and high energy protons. Total production rates of 938.53/kgArday and 5.81 × 10−3/kgArday for 39Ar and 42Ar are found from our simulation. Utilizing these production rates, we set a time limit of 954 days constrained by the production of 39Ar for UAr to be on the surface before it compromises the sensitivity for a dark matter experiment. Similarly, a time limit of 1702 days constrained by the production of 42Ar is found for a 0νββ experiment.

Muon radiography simulation for underground palace of Qinshihuang Mausoleum

Muon radiography is a nondestructive imaging technology based on the naturally existing cosmic ray muons. Because cosmic ray muons have the strong ability to penetrate, muon radiography in which the absorption of muons through matter is utilized, is especially suitable for the imaging of large-scale objects. While the traditional geophysical technologies used in archeology have some limitations, muon radiography is expected to become a powerful supplement in the nondestructive detection of large-scale cultural relics. Based on Monte Carlo simulation method Geant4, the muon radiography of the underground palace of Qinshihuang Mausoleum is studied in this work. A model of the underground palace of Qinshihuang Mausoleum is set up with GEANT4 program according to the data acquired by the previous archaeological study of Qinshihuang Mausoleum’s inner structure, as well as a reference model without these inner structure. By investigating the differences between the muon fluxes obtained from the two models, the muon radiography image of the inner structure of the model can be obtained. During the simulation, the cosmic ray muon source is generated by sampling according to an empirical formula summarized by Reyna, which can accurately describe the energy spectrum and angular distribution of cosmic ray muons at sea level. In addition, two viewpoints are selected in order to determine the three-dimensional position of the chamber. The simulation data are processed by using an image reconstruction algorithm which can be described as the following three steps. Firstly, the counts of muons in different directions are converted into muon flux. Secondly, the muon flux of the reference model is deducted from that of the Qinshihuang Mausoleum model, and the angular coordinates of the chamber walls are determined. Finally, combined with the wall’s angular coordinates obtained from the two viewpoints and the relative position between the two viewpoints, the chamber size and its position are reconstructed according to the geometric relationship. The errors of the reconstructed chamber center position and the length of chamber walls are both approximately 7%. In this article, we conduct only a preliminary study of muon radiography applied to the nondestructive detection of Qinshihuang Mausoleum, but the results show that muon radiography can be a promising tool for the archeological study of Qinshihuang Mausoleum. In the follow-up study, more factors will be taken into consideration, including the details of Qinshihuang Mausoleum model, and the improvement of image reconstruction algorithm.

Identification of the Ambient Response Relationship in Neutron Counting and Scintillation Measurement Systems

Radiation detection for nuclear security frequently employs neutron counting and scintillation systems simultaneously. One potential issue, particularly when searching a large area, is understanding the ambient (or background) response of these systems throughout the operation. This is easily mitigated for the scintillation system but remains a problem for neutron counting systems. Operational data and previous research have shown that a correlation appears between the neutron count rate and the count rate at high energies in the scintillation system (energies greater than 4 MeV) in background conditions. To understand the cause of the correlation, background measurements were performed using sodium iodide (NaI) and polyvinyl toluene (PVT) scintillation systems. These detectors were calibrated to high energy scales such that their spectra would show energies up to 70 MeV and 85 MeV, respectively. Results show that at least one statistical mode appeared in the spectra on these energy scales (particularly between 5 MeV and 60 MeV). The energy and maximum probability of these modes varied with orientation, and they were dependent upon the detector thickness with respect to the vertical axis and the detector area perpendicular to that axis, respectively. The modes’ energies also matched the expected energy deposition from background muons in the detectors with path lengths equal to one of the detectors’ dimensions. These data matched results from simulations of background muons interacting with these detectors calculated using MCNP, and they similarly matched muon energy spectra calculated from possible path lengths through the detectors using Python. These results indicate that scintillation measurements at energies higher than those employed in typical nuclear security operations are the result of background muons. Since these muons are produced similar processes as background neutrons, the count rate of these particles could potentially be applied to better characterize the background in neutron counting systems.

Expected Spectra of Muon-Induced Cascades in IceCube

The neutrino telescope IceCube is capable to reconstruct the energy spectrum of muons in very high energy region by means of measurements of muon-induced cascades. To compare with experimental data, the expected spectra of cascades were theoretically estimated. Calculations were performed for two variants of muon spectrum on the ice surface: a simple power-law energy spectrum with a differential slope index −3.7, and a composite spectrum combined of two power spectra with differential indexes −3.7 and −2.7. The differential spectra of cascades for different zenith angles and integral cascade spectra calculated for two variants of muon spectra are discussed.

Search for heavy neutrinos in π → μν decay

In the present work of the PIENU experiment, heavy neutrinos were sought in pion decays π+→μ+ν at rest by examining the observed muon energy spectrum for extra peaks in addition to the expected peak for a light neutrino. No evidence for heavy neutrinos was observed. Upper limits were set on the neutrino mixing matrix |Uμi|2 in the neutrino mass region of 15.7–33.8 MeV/c2, improving on previous results by an order of magnitude.

The muon intensity in the Felsenkeller shallow underground laboratory

The muon intensity and angular distribution in the shallow-underground laboratory Felsenkeller in Dresden, Germany have been studied using a portable muon detector based on the close cathode chamber design. Data has been taken at four positions in Felsenkeller tunnels VIII and IX, where a new 5 MV underground ion accelerator is being installed, and in addition at four positions in Felsenkeller tunnel IV, which hosts a low-radioactivity counting facility. At each of the eight positions studied, seven different orientations of the detector were used to compile a map of the upper hemisphere with 0.85∘ angular resolution. The muon intensity is found to be suppressed by a factor of 40 due to the 45 m thick rock overburden, corresponding to 140 m water equivalent. The angular data are matched by two different simulations taking into account the known geodetic features of the terrain: First, simply by determining the cutoff energy using the projected slant depth in rock and the known muon energy spectrum, and second, in a Geant4 simulation propagating the muons through a column of rock equal to the known slant depth. The present data are instrumental for studying muon-induced effects at these depths and also in the planning of an active veto for accelerator-based underground nuclear astrophysics experiments.

Testing of almost all the hadronic interaction models by comparing calculated muon energy spectrum with data

Uncertainties of the model energy spectra of the most energetic secondary charged mesons are discussed. Computer simulations of the partial energy spectra of the atmospheric vertical muons induced by primary cosmic particles with various fixed energies in terms of hadronic interactions models had been carried out with the help of the CORSIKA package. These partial spectra have been convolved with the contemporary spectra of the primary cosmic particles in the energy range 0.1-10 000 TeV. Results of simulations are compared with the contemporary data of the atmospheric vertical muon flux. Comparison shows that all models underestimate the production of secondary charged π±-mesons (and K±-mesons) by a factor of ~ 1.4 ÷ 2 at the highest energies. This underestimation induces a more rapid development of extensive air showers in the atmosphere and results in uncertainties in estimates of energy and composition of the primary cosmic particles.

Deconvolution in Measurements of Muon Neutrino Energy Spectra with IceCube

As the energy of an incident neutrino cannot be accessed experimentally, muon neutrino energy spectra have to be inferred from energy-dependent observables, using deconvolution algorithms. This paper discusses the challenges associated with the application of deconvolution algorithms and presents two examples of spectral measurements obtained using the IceCube neutrino telescope in the 59- and 79-string configuration.

Atmospheric Muons Measured with IceCube

IceCube is a cubic-kilometer Cherenkov detector in the deep ice at the geographic South Pole. The dominant event yield is produced by penetrating atmospheric muons with energies above several 100 GeV. Due to its large detector volume, IceCube provides unique opportunities to study atmospheric muons with large statistics in detail. Measurements of the energy spectrum and the lateral separation distribution of muons offer insights into hadronic interactions during the air shower development and can be used to test hadronic models. We will present an overview of various measurements of atmospheric muons in IceCube, including the energy spectrum of muons between 10 TeV and 1 PeV. This is used to derive an estimate of the prompt contribution of muons, originating from the decay of heavy (mainly charmed) hadrons and unflavored mesons. We will also present measurements of the lateral separation distributions of TeV muons between 150m and 450m for several initial cosmic ray energies between 1 PeV and 16 PeV. Finally, the angular distribution of atmospheric muons in IceCube will be discussed.

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.

Testing of the EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 hadronic interaction models via help of the atmospheric vertical muon spectra

The recent results of the very precise measurements of the primary cosmic protons and helium nuclei energy spectra by AMS-02 and some rather accurate estimates of these energy spectra generated in SNR allow us to elaborate the new approximation of the pimary nucleon energy spectra. As the acuracy of this approximation is rather high we can use it to test various models of hadronic interactions with the help of atmospheric muon energy spectra. The atmospheric vertical muon energy spectra have been calcullated in terms of the EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 models in the energy range 102 ÷ 105 GeV with help of the CORSIKA package and this new approximation of the primary nucleon spectrum. The comparison of calculations with the muon spectra observed by collaborations L3+Cosmic, LVD and MACRO has shown that all models predict approximately two times lower intensity of the muon energy spectra. As these muons are products of decays of the most energetic π± and K± mesons in the atmosphere, we can conclude that production of these π± and K± mesons is underestimated by EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 models.

Cosmogenic activation of germanium used for tonne-scale rare event search experiments

We report a comprehensive study of cosmogenic activation of germanium used for tonne-scale rare event search experiments. The germanium exposure to cosmic rays on the Earth’s surface are simulated with and without a shielding container using Geant4 for a given cosmic muon, neutron, and proton energy spectrum. The production rates of various radioactive isotopes are obtained for different sources separately. We find that fast neutron induced interactions dominate the production rate of cosmogenic activation. Geant4-based simulation results are compared with the calculation of ACTIVIA and the available experimental data. A reasonable agreement between Geant4 simulations and several experimental data sets is presented. We predict that cosmogenic activation of germanium can set limits to the sensitivity of the next generation of tonne-scale experiments.

Discovering intermediate mass sterile neutrinos through τ−→π−μ−e+ν(orν¯) decay

Distinguishing the Dirac and Majorana nature of neutrinos remains one of the most important tasks in neutrino physics. By assuming that the $\tau^- \to \pi^- \mu^- e^+ \nu$ (or $\bar{\nu}$) decay is resonantly enhanced by the exchange of an intermediate mass sterile neutrino $N$, we show that the energy spectrum of emitted pions and muons can be used to easily distinguish between the Dirac and Majorana nature of $N$. This method takes advantage of the fact that the flavor of light neutrinos is not identified in the tau decay under consideration. We find that it is particularly advantageous, because of no competing background events, to search for $N$ in the mass range $m_e + m_{\mu} \leqslant m_N \leqslant m_{\mu} + m_{\pi}$, where $m_X$ denotes the mass of particle $X \in \{ e, \mu, \pi, N \}$.

Atmospheric muon and electron neutrino energy spectrum measured by first year of IceCube-86 detector

The flux of atmospheric neutrinos is the main background for searches for cosmic neutrinos. Precise measurement of its spectrum allows us to reduce uncertainty of any kind of signal analysis. A unified analysis of atmospheric neutrinos using data collected with the full IceCube detector between May 2011 and May 2012 is presented in which both muon and electron flavors are included in a single framework.

A new air-shower observable to constrain hadronic interaction models

The energy spectrum of muons at ground level in air showers is studied and a new observable is proposed to constrain hadronic interaction models used in air shower simulations. An asymmetric Gaussian function is proposed to describe the muon ground energy spectrum and its parameters are studied regarding primary particle, energy and hadronic interaction models. Based on two realistic measurements of the muon density at a given distance from the shower axis, a new observable (rμ) is defined. Considering realistic values of detector resolutions and number of measured events, it is also shown rμ can be successfully used to constrain low and high energy hadronic interaction models. The study is focused in the energy range between 1017.5 and 1018.0 eV because of the importance of this interval for particle physics and astrophysical models. The constraining power of the new observable is shown to be large within current experimental capabilities.

Calculating vertical atmospheric muon energy spectra for energies ranging from 102 to 105 GeV

New calculations of the atmospheric vertical muon energy spectra for energies ranging from 102 to 105 GeV are performed using an original approach and the CORSIKA 7.4 software package. The intensity of the atmospheric muon flux calculated using the SIBYLL 2.1 and QGSJET II-03 models for muon energies of ~(103–105) GeV is 1.7 times lower than the intensity predicted by L3+Cosmic, MARO and LVD collaborations on the basis of experimental data. For the energy range of ~(102–103) GeV, this reduction is as high as ~2.2 for the QGSJET II-03 model; for the SIBYLL 2.1 model, it falls to 2.1. If we assume that the first generation of charged π± and K ± mesons makes the greatest contribution to the most energetic muon flux, the generation of mesons is underestimated by 1.7 times in the abovementioned models.

Production rate calculations for cosmic-ray-muon-produced 10Be and 26Al benchmarked against geological calibration data

First, I benchmark existing methods of calculating subsurface 26Al, 10Be, and 14C production rates due to cosmic-ray muons against published calibration data from bedrock cores and mine excavations. This shows that methods based on downward propagation of the surface muon energy spectrum fit calibration data adequately. Of these methods, one that uses a simpler geographic scaling method based on energy-dependent attenuation of muons in the atmosphere appears to fit calibration data better than a more complicated one that uses the results of a global particle transport model to estimate geographic variation in the surface muon energy spectrum. Second, I show that although highly simplified and computationally much cheaper exponential function approximations for subsurface production rates are not globally adequate for accurate production rate estimates at arbitrary location and depth, they can be used with acceptable accuracy for many exposure-dating and erosion-rate-estimation applications.