This report presents the design, characterization, and application of a high-sensitivity optical detection system based on plastic scintillators coupled to Multi-Pixel Photon Counters (MPPCs). The primary objective was to evaluate the performance of MPPCs (Silicon Photomultipliers) as robust, low-voltage alternatives to traditional photomultiplier tubes for detecting faint scintillation light. The optoelectronic properties of the sensors were analyzed, including single-photoelectron gain calibration and dark count rate measurements, to optimize the signal-to-noise ratio. By embedding wavelength-shifting fibers to enhance light collection efficiency, the system was configured into a three-fold coincidence telescope. The angular distribution of the cosmic ray muon flux was measured to validate the detector's stability and geometric acceptance. Fitting the experimental data to a $\bm{\cos^n(θ)}$ distribution yielded an angular exponent of $\bm{n = 1.44 \pm 0.06}$, consistent with literature values. These results demonstrate the efficacy of the MPPC-scintillator coupling for precise photon counting and timing applications in high-energy physics instrumentation.
E ARTH is under constant bombardment by cosmic rays, a flux of highly energetic charged particles originating from outer space . This primary radiation, composed of approximately 89% protons, 9% helium nuclei, 1% electrons and 1% heavier nuclei, is thought to be accelerated to relativistic speeds by powerful galactic events such as supernovae [1]. Upon entering the upper atmosphere, these primary particles collide with air molecules, initiating a cascade of lighter, secondary particles known as an extensive air shower. In these initial interactions, unstable mesons-primarily pions (π) and kaons (κ)-are produced. The charged pions are of particular importance, as they decay almost instantaneously into the particles that are the focus of this study: muons [2] refer figure 1.
The muon (µ) is a fundamental lepton, similar to an electron but approximately 200 times more massive [3]. This significant mass is the key to its highly penetrating power. While muons are unstable, with a short intrinsic lifetime of only 2.2 microseconds , those created in the upper atmosphere possess enough energy to travel near the speed of light [4]. Due to the effects of relativistic time dilation, their lifetime in our frame of reference is extended, allowing a significant
e + e -e + e - Fig. 1. Schematic representation of a cosmic ray air shower. The primary proton p initiates the cascade. The Muons (µ) are highlighted in red as they are the penetrating particles detected in this setup.
fraction to survive the journey to the ground [4]. Unlike the electromagnetic and hadronic components of the air shower, which are quickly absorbed by the atmosphere, the muonic component is “penetrating.” As a result, the energetic particle flux at sea level is overwhelmingly dominated by these secondary muons, which arrive with a mean energy of about 4 GeV [4]. The directionality of this flux is not uniform; it is known to be most intense from the vertical (zenith) and decreases at larger angles [3], a key property that will be investigated in this work.
In this experiment, the naturally occurring flux of cosmic muons is used to characterize and validate a prototype muon telescope. The primary objective is to conduct a comprehensive, multi-part investigation into the properties of these particles using a custom-built, three-fold coincidence detector. The first phase of the work involves the complete characterization of the detector system, including optimizing the operating threshold by analyzing the detector’s response to background and signal, and experimentally verifying the penetrating power of the detected particles. The main scientific goal is to then use this validated instrument to perform a precise measurement of the muon flux as a function of zenith angle, θ. The resulting angular distribution will be analyzed by performing a comparative fit to several prominent theoretical models, allowing for a quantitative measurement of the physical parameters that govern the muon flux at ground level.
A. Theoretical Principles 1) Muon Interaction with Matter and Energy Loss: When high-energy charged particles travel through matter, two primary effects occur: the particle loses energy and it is deflected from its initial direction. If the charged particles are heavysuch as the muons in our case -these effects are primarily due to inelastic collisions with the atomic electrons in the material. Although the energy transfer in a single collision is small, in a dense medium the interaction cross-section is significant. Consequently, many collisions occur per path length, resulting in a substantial cumulative energy loss [4].
This specific energy loss (stopping power) is described quantum-mechanically by the Bethe-Bloch formula, shown in Equation 1 [1]: where:
• N a : Avogadro’s number Since cosmic ray muons travel at relativistic speeds at ground level, they typically behave as MIPs. This means their energy deposition per unit distance traveled is nearly constant; a common approximation for this value is 2 MeV/(g/cm 2 )
This distinct physical signature is the key to reliably counting cosmic muons while rejecting background noise. Because sea-level muons act as MIPs, they deposit a relatively constant and predictable amount of energy as they pass through the scintillator [5]. The fundamental principle of scintillation detection states that the amplitude of the output electrical pulse is directly proportional to the energy deposited [4].
Taken together, these principles form the basis of our triggering strategy. Since muons deposit a consistent, substantial amount of energy, they produce a distinct class of large-amplitude pulses. Conversely, background events (such as detector dark counts) correspond to single-photoelectron events and produce consistently small-amplitude pulses [5]. This clear separation allows for the effective use of a fixedlevel (Leading Edge) discriminator. By performing a threshold scan, we can experimentally identify the bo
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