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:

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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.