Author: Aryan Bharti
Cosmic rays are charged particles that, on entering the Earth’s upper atmosphere, react and form muons. Muons have varying energies and can be very potent particles. We can detect muons through a basic scintillator and photodetector combination. Since most muon detectors are expensive and not easily accessible, we will discuss a muon detector that is cheap and easy to assemble for high school students. The detector can also be used to measure the flux and direction of muons and the interaction of muons with different materials around us.
I Cosmic Rays
Cosmic rays are charged particles, moving through space at nearly the speed of light, raining onto the Earth from each point in the universe. Most cosmic rays are atomic nuclei stripped of their electrons. The vast majority are hydrogen nuclei, or protons, but heavier elements are also observed. The emission of cosmic rays is isotropic (within 1%), and no particular source of emission of these particles has been identified yet. The energies of these particles vary enormously, from (10 raised to the power of 9) electron volts to (10 raised to the power of 20) electron volts, and can be much higher than anything we can make in an accelerator.
Although there are several cosmic particles, we mostly receive muons on the Earth’s surface The mean life of a muon (𝜏) is 2*10^(-6) s, and they should only be able to travel about 600 m before decaying. But in reality, many muons manage to cross the Earth's atmosphere, which is about 8 km thick, before decaying. This is due to time dilation:
where ‘T’=dilated time, ‘t’=stationary time, ‘v’=speed of the particle and ‘c’=speed of light (this is an effect of the theory of special relativity, which states that the passage of time is distorted for objects that move at high speed).
II Scintillators and SiPM
What is a scintillator?
A scintillator is a device which emits light when a high energy radiation goes through it. It can detect both charged particles and photons. Scintillators can be gaseous, liquid or solid. After a charged particle enters the scintillator material, it excites a molecule of the scintillator. When the molecule deexcites, it emits light.
What is a photodetector?
A photodetector is a device which converts incident light into electrical signals.
What is a Silicon photomultiplier (SiPM)?
Silicon photomultipliers (SiPMs) are extremely sensitive, solid-state, high-performance photodetectors. They are made of arrays of multiple single-photon avalanche diodes (SPADs). Each cell (i.e., SPAD + resistor) is sensitive to single photons and provides a defined charge at the SiPM output when an avalanche is triggered. SiPMs have obtained growing attention as a cheap alternative to traditional photomultiplier tubes (PMTs), thanks to many advantages typical of solid-state detectors, such as compactness, ruggedness, ease of use, low operational voltage and insensitivity to magnetic fields.
III Cosmic Ray Detector
Consider a device that is cheap and easy to assemble and also capable of producing important measurements of the cosmic ray flux. The detector is modular, consisting of 12 repetitions of a basic photosensor unit. The photosensor consists of a square block of plastic scintillator (5 cm × 5 cm × 1 cm), which when crossed by a muon emits visible light - the emission spectrum peaks around 425 nm. The block is wrapped in reflective foil to contain the photons and prevent crosstalk with other units. On the lower edge of the block, however, contact is made with a SiPM (6 mm × 6 mm), which gets illuminated by the scintillation light and converts it into an electric signal; these electric pulses constitute the detection message to be processed by the electronic and logical modules (this includes an ATmega328 CH340G Arduino Nano). The twelve units are arranged in three horizontal layers (top, middle, and bottom); each layer hosts 4 units (as shown in figure 1), side by side.
Figure 1: Top view of the detector (single unit, dark squares in the middle are SiPMs)
The twelve channels are read independently and can be combined to form a time coincidence. The experiment is very safe as SiPM requires a low voltage to run.
In the simplest operation mode, the three layers are separated by the same vertical distance, so the detector volume is segmented into twelve cells. A perfectly vertical muon would activate three units lying on its path and produce a three-fold coincidence within 10 ns; this signal can be easily identified by the electronics; the three points characterize the trajectory of the muon, and the rate of such signals indicate the flux of vertical cosmic muons. Slanted trajectories will also activate three cells, which, however, do not lie on the same vertical line, so the rate for different incoming directions can also be reconstructed. The detector is also mounted on four wheels, which allows for easy transportation. Thus, one can relocate the detector in the open air, where it's exposed to the atmosphere, or, for instance, on the ground floor of a tall building, where the overburden of several floors will attenuate the rate of events.
The top and middle layers of the detector can be raised or lowered together through a pulley with counterweights in the four angular posts, while the bottom layer is fixed in position. Thus, empty space can be created between the layers and filled with targets of choice: this allows studying the interaction of muons with other systems. For instance, a classical experience is having a heavy (lead) target between the scintillators and measuring the muon decay. In this configuration, a cosmic muon entering from the top would cross two layers (giving two signals in coincidence) and then stop in the target; after slowing down and losing its relativistic boost, the muon will decay with a mean life of 2.2 microseconds and release an electron, which will subsequently produce a third signal in the detector. Thus, one can look for a two-fold (but not three-fold) time coincidence (the stopping muon) and then open a trigger to look for a third delayed hit within a few microseconds (the emitted electron); the distribution of delay times between muon and electrons will follow an exponential curve and provide a direct measurement of the muon mean life (𝜏)
It depends on 'm', the mass of the muon, and 'G', the so-called Fermi coupling constant; so, measuring 𝜏 you can actually measure the mass m of the muon. And of course, the detector is mounted on wheels which allows for easy transportation.
Figure 2: Complete detector with lead block in between
I thank my mentor, Dr. Federico Nova, and Pubali Chaudhury for their assistance. I would also give gratitude to the Cambridge Centre for International Research (CCIR) Future Scholar team for guiding us throughout this project.
 Stanev, T., 2021. High energy cosmic rays. 2nd ed. Cham: Springer.
 Latif, U., Anwar, M. and Younas, I., 2019. Measuring the lifetime of cosmic ray muons. PhysLab. Available at: <https://physlab.lums.edu.pk/images/f/f9/Man.pdf>.
 Lappetito, L., 2016. PSoC based Cosmic Muons Detector. PhysicsOpenLab. Available at: <https://physicsopenlab.org/wp-content/uploads/2016/09/PSoC_MuonDetector_ENG.pdf>.
 Acerbi, F., et al., 2017. Silicon photomultipliers and single-photon avalanche diodes with enhanced NIR detection efficiency at FBK. Elsevier. Available at: <https://www.sciencedirect.com/science/article/abs/pii/S0168900217313542>.
 Acerbi, F., et al., 2021. Single-Photon Detection Module Based on Large-Area Silicon Photomultipliers for Time-Domain Diffuse Optics. Instruments, MDPI. Available at: <https://www.mdpi.com/2410-390X/5/2/18>.