1. The Life and Times of Cosmic-ray Muons
December 12, 2007
Advanced Lab
Final Project
The Life and Times of Cosmic-ray Muons
Adam W. Bublitz
Summary
This experiment measures time dilation (T=γτ) by using scintillator to detect the decay of abundant cosmic-ray muons. Plagued by malfunctioning equipment, we were able to acquire good data with a little extra time and work. From this data we calculate the mean lifetime of a muon to be 2.09 µs with considerable error.
Experiment
The setup of the experiment consist of an signal traveling from the scintillator down optical fibers to a photo-multiplier tube (PMT). This converts the optical signal to an electrical signal that is passed through a discriminator. Two outputs travel from the discriminator to the computer. The computer runs a program to acquire data in which you manually set the width of a data collection window. Data is recorded if two events happen within the window, which should be a muon entering and decaying. The window is an attempt to prevent a second muon entrance from looking like the first muon decaying.
The graph below is the good data we finally obtained after discovering that none of the discriminators provided with the experiment worked. It was taken with a PMT voltage of 1800 V and discriminator voltage of 0.8 V. These parameters were found by trying to duplicate the theoretical muon flux through our dark box, which should have been muons/sec [2].
Error
As you can see, the graph of our data is extremely noisy. This is due to the PMT voltage being extremely high because the replacement discriminator we used had to be over 1500 V. Even this voltage was too slow at acquiring data so we ended up at 1800 V. This causes small differences in light level in the dark box or optical cable quality issues to provide larger errors than they would at lower PMT voltage that we initially tried to use.
Theory
High energy cosmic-rays from the sun collide with Earth’s upper atmosphere and create a pion shower. These pions quickly decay into muons and neutrinos. The muons decay at a relatively slower rate than the pions into primarily an electron, neutrino, and antineutrino. This experiment attempts to measure the mean lifetime of muons by detecting when muons enter our scintillator array and also when and if they decay in the array.
By taking an adequate amount of decay times for the muons, we can fit data to an exponential decay curve to find the mean lifetime of the muons coming from cosmic-rays. This will let us verify special relativity’s time dilation because we know that the muons are traveling near the speed of light. We also know that it takes ~50 microseconds[1] in the lab frame to travel down to where we are measuring them.
Conclusion
After collecting the data, we analyzed it by fitting it to a general exponential equation (Ae^(t/T)+B) in Mathematica. This gives us our result of T = 2.09 µs. I am not happy with this result because the experiment was so noisy that the error became huge. However, I do think that the data shows the general trend of this exponential decay. Also, this is much more accurate than the Gaussian “decay” curves that we obtained with the broken discriminators.
T = 2.09 µs
Sources
[1] Anonymous. “The Lifetime of Cosmic-ray Muons”, University of Rochester.
[2] Wolverton, Mark. “Muons for Peace,” Scientific American, Sept