Dan Olson, Ryan Stiefvater, and Mark Hotovy

Cosmic Ray Observatory Project

 

 

The Muon

 

 

 

                Discovered in 1937, the muon is a fairly recent find in physics.  First hypothesized by Hideki Yukawa, the muon was discovered in 1937 by J. C. Street and E. C. Stevenson in a cloud chamber. The discovery was published in "New Evidence for the Existence of a Particle Intermediate Between the Proton and Electron" in the Physics Review, and solidified Yukawa’s theory, which would account for what seemed a violation of conservation of energy and momentum.  After Yukawa hypothesized the existence of an intermediate mass "meson" that could possibly be responsible for the nuclear strong force, the muon seemed a strong candidate.  The muon was eventually discovered to be a product of the decay of Yukawa’s particle, the pion.  The muon is a lepton, one of the lightest class of particles, and has 207 times the mass of an electron.  The muon has a charge of -1, decays into an electron or positron, and can interact with matter mainly through ionization.  Produced mainly by the decay of pions originating as cosmic rays, muons have a lifetime of 2.20 microseconds.  Muons constitute approximately half of the cosmic radiation at sea level, and are therefore central to the observation and study of cosmic rays.  Although velocities of muons vary greatly, their kinetic energies are large enough to manifest significant relativistic effects.  (A minimal value, used in the below example, is 2 GeV)  The relativistic effects on muons extend the range from a mere 660 meters to a much larger 13,860 meters.

                Created in cone-shaped showers spreading from an initial point of collision, muons travel at high speeds (close to the speed of light), but generally remain within 1 degree of the primary particle’s path.  The muon is a weakly reacting fermion, and therefore does not experience any strong attraction toward the nuclear particles.  Because of this, the majority of interaction is through ionization of passing particles.  Muons generally lose energy at a rate of 2 MeV per gm-cm2 as they travel due to ionization, meaning those created in the upper atmosphere will lose around 2 GeV of energy before reaching sea level.  This property of ionization allows fairly easy detection of muons through the use of a scintillator panel and photo multiplier tube (PMT), which produces an electrical charge whenever an ionized particle is detected.

 

                In any study of cosmic rays, the study of muons is invaluable, as they are much more easily detected than their “cousins” the neutrinos, due to their greater tendencies toward interaction with particles through ionization.  In addition, the high energies of most muons make them readily distinguishable from background radiation through the use of simple discriminators.  As muons are now being studied throughout the world with various detector apparatuses, they seem to hold great promise in solving the mystery of anomalous high energy cosmic rays, currently at the forefront of modern physics research.

The Muon Lifetime Experiment

                To determine the mean lifetime of a muon, it is necessary for a detector to catch the decay of a muon.  To do so we use a set of 3 detectors each consisting of a scintillator panel mounted with photo multiplier tubes.  Suppose a muon passes through the first panel, but stops in the

                                                                                         Diagram 1

second (Diagram 1).  When this occurs, it is signaled as a coincidence between the top 2 detectors and nothing seen by the third.  This is known as a two-fold coincidence.  Such an event is used to trigger a delay.  If within this time delay the second detector sees a flash of light, most likely the decay of the muon, it sends a signal to the logic unit, creating a count.  The pulse that the second detector sees is a photon emitted by the decay of the muon.    To determine the muon’s lifetime, the probability for decay of the muon at different time intervals must be determined.  The probability of the muon living to a certain time, and then dying in the next time interval is p(1-p)N where N is the time interval and p is the probability at N = 0.  When the probability of a muon surviving is plotted versus increasing time interval, the probability goes to zero.  To determine the average lifetime of a muon, we use the equation:

                                                                                 .

                If we graph the number of counts on the vertical axis versus the time of the delay, we


should expect to get a graph that resembles the graph of the probability of the muon having                                                                                      

                                                                                        Diagram 2

decayed (Diagram 2).  When we take the natural log of the results and graph them, the slope of the line should be a measure of the average lifetime of a muon.  The accepted mean value for a muon is about 2.2 nanoseconds.  The experiment is not 100% efficient.  For example, one must account for accidentals, which occur certain situations.  For example, the path of a muon may take it through the top two detectors, but cause it to miss the third.  This mimics a muon stopping in the second detector.  If a second muon then enters the second detector, one could get a false muon decay signal.

The Muon Lifetime Experiment Data

                To date, our measurements, designed to detect the decay of a muon within a detector panel, have yielded the following data:

                               

                                Time (ns)               Trial 1                     Trial 2                     Trial Avg.

                                     20                           1                               1                                1

                                     40                           0                               0                                0

                                     60                           1                               0                                .5

                                     80                           0                               2                                1

                                    100                          0                               0                                 0

 

Conclusion

                The data we have collected does not correspond to the expected results.  This indicates some difficulty in our experiment.  A first possibility is a difficulty with the detectors.  The detectors became less sensitive as the experiment progressed.  We do not know why.  A second possibility is a lack of stability of the high voltage power supply.  A third possibility is that we did not have the logic units properly wired.