Muon Lifetime Studies
Austin Park and Willie Dong
Abstract
We used multiple scintillators and a circuit board (data acquisition) to determine the lifetime of a muon
particle. We formed a right trigonal prism with two scintillators on the outside of the box and a third diagonally
placed inside the box. The top side of the prism had an additional scintillator attached. We took continuous 24
hour runs of data for air and packing peanuts as materials of varying density within the box. We determined the
lifetime of a muon by measuring the window between the muon's entrance and the resulting electron's ejection.
Introduction and Background
Research
Most naturally occurring muons are created by cosmic rays, which consist mainly of protons, but also consist of
neutrons, neutrinos, and alpha particles (helium nuclei). When cosmic ray protons impact atomic nuclei in the
upper atmosphere, pions are created. These hadron-hadron impacts form pion showers, which decay quickly to
muon showers.
A muon falls through the atmosphere with an equal probability of decaying at all times. When it travels through the
top two scintillators the measurement of the lifetime starts. The muon decays into an electron, electron
antineutrino, and muon neutrino, by the weak force. Of these, the electron is the only one that is relatively easy to
record. It is ejected and runs into one of three scintillators. The lifetime of a muon is determined by the window
between the muon's entrance and the electron that is ejected. Most of the muons actually just fall straight through
our apparatus. These counts have windows on the order of nanoseconds and are filtered out of our data.
The muon has a reported mean lifetime of 2.2 µs. A muon does not emit much bremsstrahlung radiation
(electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged
particle). Because of this, it penetrates further into matter. When passing through matter, a muon loses kinetic
energy. When passing through matter, it is possible that negative muons can form muonic atoms by replacing an
electron in ordinary atoms. However, a muon's orbital is smaller and far closer to the nucleus than the atomic
orbitals of the electrons.
Procedures
First, the scintillators had to be calibrated, which mainly involved plotting a graph of counts (Hz) versus voltage
(V). We set one detector was to count at around 40 Hz and slowly turned up another detector's voltage from
around 0.5 V to 1.5 V in 0.05 V increments until the data displayed a plateau, or a portion of a graph that exhibits
little to no change. The optimal voltage, the voltage to which we calibrated the detector, was calculated 1/3 of the
way from the beginning of the plateau. We then used this detector to calibrate all of the others.
To setup the scintillators, a cardboard box was surrounded by two scintillators duct-taped on adjoint sides, with
another scintillator duct-taped on the inside of the box and touching the edges of the outer scintillators, forming a
right trigonal prism. Yet another scintillator on top of the top side scintillator. After the scintillators were set up, data
was collected with different filler material in the box: no filler material and packing peanuts .
Calibration Data
Detector A
Voltage (V) Frequency (Hz)
0.688
9.333
0.7
9.967
0.75
11.333
0.8
11.633
0.847
12.333
0.898
11.867
0.949
11.3
0.998
12
1.049
13.333
Detector B
Voltage (V) Frequency (Hz)
0.653
4.933
0.675
7.6
0.71
11.267
0.754
10.633
0.802
10.467
0.855
10.667
0.903
11.667
0.949
12
0.998
12.5
Detector C
Voltage (V) Frequency (Hz)
0.655
0.9
0.701
3.8
0.753
7.9
0.799
8.333
0.848
8.667
0.9
8.333
0.948
8.867
0.997
9.7
Detector D
Voltage (V) Frequency (Hz)
0.652
6.5
0.676
9.517
0.702
10.833
0.727
11.267
0.75
11.9
0.802
13.5
0.852
16.167
0.898
18.6
0.949
19.8
Scintillator A
Scintillator B
Scintillator C
Scintillator D
Optimal Voltages
Detector A: 0.799 V
Detector B: 0.758 V
Detector C: 0.802 V
Detector D: 0.718 V
Works Cited
Muon lifetime: Determination of the fundamental weak coupling constant. Informally published manuscript, Physics,
University of Notre Dame, Notre Dame, Retrieved from
http://isnap.nd.edu/Lectures/Laboratory/16_Muon_Lifetime.pdf
Thrasher, M. E. (1998). The measurement, simulation, and interpretation of the lifetime of cosmic ray muons. Informally
published manuscript, Physics, Harvard University, Cambridge, Retrieved from
http://web.mit.edu/rsi/www/pdfs/papers/98/mthrashe.pdf