Muon Decay Experiment
John Klumpp
And
Ainsley Niemkiewicz
What Are Muons?
• Fundamental particles
• Carry charge of +/- 1
• Essentially heavy
electrons
• Inherently unstable
• Decay into electrons
and neutrinos


  e  e  
Where Do They Come From?
• Cosmic rays collide
with matter in the
upper atmosphere
• Many fundamental
particles produced
• Only muons make it
to the surface. Why?
-High mass
-Time dilation
What Does Relativity Have To Do
With It?
•
•
•
•
Muons only survive about 2.2μs in lab frame
2.2μs * Speed of Light = .66 meters
But the muons are not in the lab frame
From the lab frame their clocks run slower, so
they live longer
• From the muon’s reference frame the distance is
shorter
• Measuring lifetimes confirms theory of relativity
How Do We Detect Them?
• Muons captured in scintillation detector
• Flash of light produced when muons are
stopped
How Do We Measure Lifetime?
• Another flash of light is produced by detector
when muon decays
• Time between capture flash and decay flash is
the muon lifetime
How Do We Calculate Mean
Lifetime
• Muons decay randomly, so many samples
are needed
• Collect samples for 48 hours
• Fit data to exponential decay equation
Data
• Calibration  40 channels = 1.28 μs
• Compress data from 512 channels to 64
channels. This helps MatLab’s Gaussian
approximation work better
•  10 channels = 1.28 μs
• Trial 1 (48 hour trial):
F(x) = 172.9e-x/71.41 + 16.19 channels
• Trial 2 (12 hour trial):
F(x) = 109.4e-x/74.37 + 9.655 channels
Fit Curve
Where’s The Mean Lifetime?
• The exponential decay equation is
x / b
f(x)  ae
c
• In this equation, b is the average lifetime.
• In trial 1,
b = 71.41 channels*1.28µs/40 channels = 2.38±0.13µs
• Similarly, in trial 2,
b = 74.37*1.28/40 = 2.29±0.13µs
Sources of Uncertainty
•
•
•
•
Background radiation
Some muons don’t decay
Some decays may not be detected
Deletion of first fifteen channels
Conclusion
• Simple, accurate experiment
• Demonstrates random nature of particle
decay
• Confirms relativistic time dilation