Graduate Physics Laboratory Handbook: Lifetime of the Cosmic Ray Muon
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2.4.1 Lifetime of the Cosmic Ray Muon

The muon is considered by many to be a "heavy" electron. (The mass of the muon is 205 times that of the electron). It is unstable and is known to have an intrinsic lifetime of several microseconds. Its decay is explained in the weak interaction theory in which it is used as a basic parameter.

Pions, with a mass 273 times that of the electron, are created in the upper atmosphere in nuclear interactions produced by high-energy cosmic-ray protons. These decay into a muon and a neutrino with a relatively shorter lifetime of a few tens of nano seco nds. The muons that are so produced, due to their longer lifetime and almost complete absence of nuclear interaction, are the principle components of penetrating particles produced by cosmic rays that are observed at sea level. Both µ⁺ and µ^- are observed at sea level. On coming to rest both µ⁺ and µ^- decay but the lifetime of the µ^- is altered due to weak interaction with the atomic nucleus when captured to form a mesic atom.

The purpose of this experiment is to measure the intrinsic lifetime of the muon. The equipment for this purpose is available in the Graduate Laboratory. A description of one method of performing the experiment is described in a Graduate Laboratory Note. T he difficulty with this method lies in the small volume of the described detector and the limited solid angle possible of the cosmic-ray telescope. Another method is described below but the experimenter may choose to devise his own.

The principal problem is the dearth of muons that can actually be made to come to the end of their ranges in any finite detector. This number should be estimated to understand the problem. There is, however, a large activated mineral-oil scintillation cou nter (8" x 8" x 24") available in the lab. It has no wide angle telescope to define the cosmic-ray beam but can be used without it by using a coincidence between two photomultiplier tubes which look at the scintillator volume. In this way, a muon is detec ted by a coincidence pulse and, if it stops and decays, a second coincidence pulse detects its decay. The time interval between these two pulses is measured with a time-to-pulse height converter which, when converted with a pulse height analyzer, can be u sed to measure the frequency of decay times. From this frequency distribution the mean life for the cosmic ray muon can be determined and from this the intrinsic muon lifetime.

In this brief description a number of statements of a general nature have been made. They are meant to serve only as a guide for a more detailed and thorough study which will climax, with diligence, in an experiment (and paper) which quantitatively measur es and discusses the muon lifetime.

References

1. E. U. Condon and H. Odishaw, Handbook of Physics, New York: McGraw Hill (1967). See page 9-159 for overview of muon nuclear capture.
2. R. E. Hall, D. A. Lind, and R. A. Ristinen, "A Simplified Muon Lifetime Experiment for the Instructional Laboratory", Am. J. Phys. 38, 1196 (1970).
3. A. A. Bartlett, "Student Experiment on the Observation of a Cosmic-Ray Shower Transition Curve", Am. J. Phys. 23, 286 (1955).
4. A. Owens and A. E. MacGregor, "Simple Technique for Determining the Mean Lifetime of the Cosmic Ray Mu-Meson", Am. J. Phys. 46, 8 (1978).
5. D.H. Frisch and J.H. Smith, "Measurement of the Relativistic Time Relation Using µ-Mesons", Am. J. Phys. 31, 342 (1963).
6. G. C. Kyker, "Resolving Time Effect on Counting Statistics", Am. J. Phys. 49, 561 (1981).
7. E. A. Bogomolov, et al., "Investigation of the Cosmic Ray East-West Asymmetry", Can. J. Phys. 46, 805 (1968).
8. P. S. Freier and C. J. Waddington, "Electrons, Hydrogen Nuclei, and Helium Nuclei observed in the Primary Cosmic Radiation during 1963", J. Geophys. Res. 70, 5753 (1965).
9. J. R. Winckler and K. Anderson, "Geomagnetic and Albedo Studies with a Cerenkov Detector at 40 Degrees Geomagnetic Latitude", Phys. Rev. 93, 596 (1954).
10. M. A. Shea and D. F. Smart, "A Study of Vertical Cut-Off Rigidities Using Sixth Degree Simulations of the Geomagnetic Field", J. Geophys. Res. 70, 4117 (1965).
11. J. R. Winckler, et al., "A Directional and Latitude Survey of Cosmic Rays at High Altitudes", Phys. Rev. 79, 656 (1950).
12. J. B. Birks, The Theory and Practice of Scintillation Counting, New York: Pergamon Press Ltd. (1964). QC787.C6B53.
13. Glenn F. Knoll, Radiation Detection and Measurement, New York: John Wiley (2000).  To be added to GL library 10/00.
14. William R. Leo, Techniques for Nuclear and  Particle Physics Experiments, New York: Springer Verlag (1996).   QC793.L46  Modern treatment of devices and techniques.
15. B. Rossi, High Energy Particles, New York: Prentice Hall, (1952). QC721.R828.
16. E. Segre, Nuclei and Particles, New York: W. A. Benjamin, (1964). Grad Lab #25. QC721.S4475.
17. A. Wolfendale, Cosmic Rays, New York: Philosophical Library (1963). QC485.W6.
18. A. E. Sandstrom, Cosmic Ray Physics, Amsterdam: North Holland Publishing Co. (1965). Grad Lab #88. QC485.S3.
19. B. Rossi and N.  Neison, Phys. Rev. 62, 417 (1933), 64, 199 (1935).
20. Photomultiplier Handbook, (Burle Industries, Inc.,Lancaster, Pa., 1989). This is a complete guide to the understanding of photomultiplier tubes. Note the temperature dependence of photomultiplier tubes.