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.

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