AMERICAN JOURNAL OF PHYSICS VOLUME 38 NUMBER 10 OCTOBER 1970 A Simplified Muon Lifetime Experiment for the Instructional Laboratory Department y P, R. E.HALL, D. A. LIND, AND R. A. RIsTINEN hysics and Astrophysics, University of Colorado, Boulder, Colorado 80802 Received 27 April 1970) An experiment has been developed for the measurement of the half-life of cosmic by using a single scintillator detector. The associated electronies are much simp nventional cosmic ray muon lifetime measuring systems. It is this simplifie lakes the experiment well suited for the instructional laboratory. I INTRODUCTION II. APPARATUS AND ITS OPERATION Lifetime measurements of cosmic ray muons are The simplified system is shown in Fig. 2. Its commonly performed with some type of multiple operation is initiated when a muon traverses a detector telescope. 1 a typical arrangement is portion of the plastic scintillator and comes to shown in Fig. 1. With this system counters 1, 2, rest. The energy lost in the stopping process and 3 have their output signals routed such that ionizes the plastie and gives rise to a pulse of the time-to-amplitude converter(TAC)is started light which is transformed into an electrical pulse only by muons that pass through l and 2 but not 3. and amplified by the photomultiplier tube. The Because of the geometry of this arrangement, a signal for the discriminator is brought directly tart signal to the TAC indicates that a charged off the anode of the photomultiplier tube by a particle has stopped in the absorber. If the stopped 50-02 cable and is proportional in amplitude to the particle was a muon, the subsequent decay into intensity of the light pulse. As a result, if the in an electron plus a neutrino pair sends a stop pulse cident muon traverses enough of the scintillator to the TAC, and an output pulse representing plastic, the electrical pulse delivered to the dis- the start-stop time is recorded by a pulse height criminator will cause it to trigger. The triggered analyzer(PHA). Since the half-life of a free discriminator sends out a 4-nsec wide pulse which muon i8 1.53 usee, corresponding to a mean life is then equally divided between two 50-4 cables of 2.21 usec, the chance of a decay occurring per which drive the start and stop inputs of the TAC. interval of time decreases by half after each 1.53 The cable to the start input of the TAc is ap- usec of time. Therefore, the TAC pulses stored proximately 8 ft longer than the cable to the stoy in successive channels of the PHA will represent input. In its normal state, the TAC is ready to an exponential decay curve. By plotting the accept only a start pulse. It ignores the stop pulse, successive channel accumulations on semilog- and the start pulse starts a timing run. The delay rithmic graph paper, a straight line of negative of the start pulse relative to the stop pulse by the slope is produced. The straight line nature of the 8 ft of additional cable assures that the stop input graph indicates that a radioactive decay phenom- is no longer activated when the pulse gets to the enon is indeed being observed, and by fitting a start input. Failure to include this delay time straight line to the semilog graph of the data would mean that the TAC would be unable to points, one may easily extract the half-life of the accept the start pulse. It should be noted that muon the 8-ft cable extension subtracts approximately While this experimental setup for measuring 8 nsec from the time to which each PHA channel the cosmic ray muon half-life is logical in arrange- would normally correspond. This does not change ment and has worked well for a number of ex- the shape of the spectrum stored in the PHA, perimenters with various modifications, it is rela- and the half-life obtained from the slope of the tively complex and expensive. In this paper we spectrum will be unchanged discuss the development of a simplified apparatus A muon that started the Tac timing run ma which yields essentially the same lifetime measure- be stopped in the scintillator and decay at, some ments as the multiple detector arrangement just later time. The neutrinos from the decay leave described the scintillator without any further effect. The