Austin Park and Willie Dong 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 0.688 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 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 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 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