Measure Muon Lifetime
Demonstrate Relativistic Time Dilation
Measure Local Muon Flux
Measure Sea Level Muon Charge Ratio
Convenient Source of Genuinely Random Numbers
Create Simulated "Muons" and Measure their Lifetime
Study Processing of Photomultiplier Signal
The muon is one of Nature’s fundamental particles. Its discovery in 1937 by Carl Anderson marked a radical departure in physicists' understanding of the building blocks of matter. Although it was first assigned a place in theory of nuclear forces which was incorrect, it is now understood to be an important member of the lepton family of particles. TeachSpin, in collaboration with Thomas Coan and Jingbo Ye of Southern Methodist University, has made the first commercial teaching instrument for students to determine some of its physical characteristics.
The muon is produced copiously in Earth’s atmosphere by interactions between cosmic rays and atmospheric air molecules, and its flux at sea level is sufficient for student investigations. The muon’s lifetime can be measured with our apparatus using experimental techniques common to nuclear and particle physics. The stopping rate of muons, as a function of depth in the atmosphere, can be used as a demonstration of the time dilation effect of special relativity. Since the decay times of individual radioactive particles are randomly distributed, they are a convenient source of genuinely random numbers. These can be used to demonstrate common probability distributions.
With this new TeachSpin Apparatus You Can:
Measure Muon Lifetime
Measure Local Muon flux
Measure Sea-level Muon Charge Ratio
Demonstrate Relativistic Time Dilation
Convenient Source of Genuinely Random Numbers
Raw Data Accessible for Student Analysis
Detailed technical information and a copy of the user's manual for Muon Physics can be found at www.matphys.com.The website is maintained by Professors Thomas Coan and Jingbo Ye of Southern Methodist University, with whom TeachSpin collaborated in developing this exciting apparatus.
The complete instrument has three hardware components: a detector, readout electronics and user-supplied personal computer (PC). Control and data acquisition software are also included.
A 16.5 cm diameter by 36 cm tall black anodized aluminum cylinder houses the entire detector module including the plastic scintillator, photomultiplier tube (PMT), and high voltage supply (HV) as well as electronics for an imbedded light emitting diode (LED). The scintillator, a right circular cylinder, is optically coupled to a single 5 cm diameter 10-stage PMT. Because all of the circuitry for the PMT is mounted inside the aluminum cylinder, there are no exposed HV electrodes. The HV is manually controlled and monitored by external controls. The thickness of the scintillator assures that either muon passage through or decay within the scintillator produces a quantity of light well above the PMT threshold. The imbedded LED can be driven by the adjustable pulser to mimic muon decays and to test the readout electronics. Inside the aluminum cylinder, light tight wrapping on both the scintillator and PMT prevent light leaks.
Block Diagram for Muon Hardware
The electronics module houses all electronics needed to run the experiment. Connections on the front panel allow students not only to examine the PMT signal itself, but also to monitor that signal as it moves along the readout chain.
PMT pulses are first amplified and compared against an adjustable threshold. Pulses above threshold are sent to timing circuitry implemented in a field programmable gate array (FPGA) chip. The first flash of the scintillator starts the timing system. If a second flash occurs within 20 microseconds of the first, the readout electronics measures the time between the two flashes and passes that time to the lifetime display software.
If no second flash occurs within 20 microseconds, the pulse is simply recorded as a charged particle that has passed through the detector. Communication circuitry transfers the data to a PC or laptop through either a serial or USB port.
Data acquisition of muon decay times is computer controlled to eliminate the tedium of recording numbers and to permit extended data collection times. The decay time histogram is automatically updated with data from the readout electronics. Important display features like the histogram bin size and the logarithmic/linear axis type remain under user control. A password-protected built-in curve fitting algorithm allows for easy determination of the muon lifetime while still maintaining instructor control. Various rate monitors indicate quantities like the instantaneous and time averaged trigger rate, the total number of recorded muon decays and the elapsed time for data acquisition.
Raw data are written to disk files in a compact format so that students can export them to their own software package and not rely on the one provided. Simulation software allows the creation of decay time distributions with a user-adjustable muon lifetime. Source code for data acquisition, plotting and simulation is written in the Tcl/Tk scripting language and is provided free of charge so motivated students can modify the user interface or the built-in lifetime curve fitting algorithm.
The software is distributed on a CD and runs under Microsoft and Linux operating systems. The program requires 100 Mbytes of disc space and 32 Mbytes of memory. It was written to work well with an Intel 133 Mbyte processor. Free updates are available.
Detailed technical information and a copy of the user's manual for Muon Physics can be found at www.matphys.com. The website is maintained by Professors Thomas Coan and Jingbo Ye of Southern Methodist University, with whom TeachSpin collaborated in developing this exciting apparatus.
Mean Muon Lifetime
Straightforward determinations of average muon lifetime can be made using the curve fitting software provided. More advanced students can be asked to create their own curve fitting algorithms.
Finding the Muon Lifetime
The form for the decay time distribution for muons stopped in the scintillator is characteristic of the decay of radioactive substances with some background counts.
Additional background counts can be easily induced by bringing a 1 micro-Curie Cs-137 source close to the detector. After measuring and plotting the distribution of times between successive scintillator flashes, students can fit the exponential-like distribution and extract the mean muon lifetime (t) in matter, using either our curve fitting algorithm or their own. (The data can be exported to third-party software.) The figure below is a screen capture from the included software and shows a fit to actual student data. Note that the central value for the muon’s lifetime is less than the free space value t = 2.197 ± 0.001 µsec. This correctly indicates the effect of nuclear interactions between protons and negative muons.
Once the muon lifetime is measured, a value of the Fermi coupling constant GF, characterizing the strength of the weak interactions, is easily determined from the relation:
Accounting only for statistical error, the student data shown in this brochure yields
GF = (1.18 ± 0.01) x 10–5 GeV–2, which is consistent with more precise measurements.
Sea-level Charge Ratio
With this instrument, the muon lifetime measured in matter (i.e., plastic scintillator) is an average over negatively and positively charged muons. Negatively charged muons have nuclear interactions that slightly lessen their mean lifetime in matter. Therefore, using the lifetime of negative muons in carbon taken from the literature (tau = 2.043 ± 0.003 µsec), the sea-level charge ratio of positive to negative muons at low energy , Eµ = 200 MeV, can be easily determined. The student data included in this brochure yields a sea-level charge ratio f+/f– = 1.08 ± 0.01 (32.5° latitude), which is consistent with published values.
Time Dilation Effect of Special Relativity
Once the muon lifetime is measured, the stopping rate as a function of elevation above sea level can be used to distinguish between the predictions of classical mechanics and special relativity, providing evidence for the time dilation effect of special relativity. Although the instrument is not optimized for this measurement, the simplicity of the measurement is appealing since it requires no lead shielding. For example, after measuring the muon stopping rate to a statistical precision of 2% at two locations vertically separated by 1985 meters, the ratio of these stopping rates (0.55 ± 0.02) agrees well with a straightforward calculation (0.56 ± 0.05) that accounts for time dilation, muon energy loss in the atmosphere and the differential muon momentum spectrum at sea level.
Predictions of Probability Theory
The decay times of individual muons are an excellent source of genuinely random numbers. Once the exponential form of the probability distribution for these times is measured, students can make predictions about the outcomes of corresponding binomial experiments. Taking a new data set then allows a direct comparison between actual data and the predictions of probability theory.
Cosmic Ray Background Radiation
Included rate monitors measure both the stopping rate of muons and the combined total charged particle flux (which includes both muons and electrons) that pass through the scintillator. This data can be used to monitor variations in cosmic radiation at the geographic location of the observer.
Explore Processing of Photomultiplier Signal
Probe points are provided along the entire electronic signal chain so that students can examine the waveforms of the photomultiplier signal, either real or simulated, at various stages of processing. The photomultiplier high voltage, the amplifier gain, the threshold setting and the FPGA timing characteristics are easily measured with an oscilloscope or voltmeter.
Diameter: 16.5 cm
Height: 35.5 cm
Overall mass: 5 kg
10-stage bialkali photocathode
Diameter: 5.1 cm
Readout electronics size: 11x7.5x3 inches
Bin Size (resolution): 20 ns
Dynamic Range: 20 µsec
Timing clock frequency: 50 MHz ±100 ppm
Power consumption (excluding PC): 25 Watts
Typical detected muon decay rate: 1 event/minute
Supported operating systems: Microsoft Windows 95, 98, ME, 2000, XP and Linux
Supported I/O port protocols: Serial and USB
Free updates of user interface and lifetime curve fitting software
Recommended minimum PC performance
Processor: Intel 133 MHz
Disk space: 100 Mbytes
Memory: 32 Mbytes
Altimeter: -450 – +6300 meters, 1 m resolution.
Automobile power inverter: 150 Watts, +12 V DC to 110 V AC, 60 Hz
Mountain: User supplied
Detailed technical information and a copy of the user's manual for Muon Physics can be found atwww.matphys.com. The website is maintained by Professors Thomas Coan and Jingbo Ye of Southern Methodist University, with whom TeachSpin collaborated in developing this exciting apparatus.