l198 HALL LIND AND RISTINEN Evaluation gives (104)2(1.12×107sec)(25×10°sec/ serch 30.2 background counts/ch This agrees with the observed background of 31±2/ch Since a 695-h run is almost 29 days long, a much shorter run would be necessitated by the schedules of most instructional laboratory courses A 24-h run was made with a pha channel width of 0.0329+0.0009 usec/ch. to determine the quality of the data to be obtained in this time Figure 5 represents the results of this run. The background is less than one count/channel and FIG 3. Data from a 695-h run before subtracting back- has been ignored. The short time span of the spec ground. The time width of each channel is 0.112=0.003 trum also reduces the significance of any back- ground. A least squares fit of a straight line to these data gives a half-life of 1.64+0. 15 usec to obtain a background of 31=+2 counts. Sub- For a run of this short duration a more accurate time base determination is not needed as the traction of this background gives the time spec- largest error associated with the half-life is due squares fit of a straight line to these data gives to statistical variations in the data a half-life of 1.46_+0.04 usec.(It should be noted It is clear that aside from improving the time ase calibration, the greatest improvement in the that the accepted half-life of the free muon performance of the experimental setup would fact be under the accepted value because about occur if the anal yzing rate to discriminator trigger 45% of the muon flux is u- and 55% u+ 2 The w- rate ratio could be improved. For the 695-h run, particles have a reduced half-life relative to u+ articles in matter since the u particles are cap- tured into atomic orbitals which allow intel actions with the nuclei of the matter. Thus, the observed half-life might be expected to be some- what less than that of free muons, with the exact reduction in lifetime determined by the unknown probability with which a nuclear capture of a muon results in a discriminator pulse. In this work, we have chosen to approximate what may in fact be a complex decay curve by a straight line exponential decay. The background that was subtracted from the 695-h spectrum results from the rather high dis- criminator trigger rate of Since the analyzing rate was only 0.01/sec over-all, almost I of these discriminator pulses were random. CHANNEL NUMath Theoretically, the background per channel of the 695-h spectrum should be FIG. 4. Data from a 695-h run after subtracting 31 counts of background from each channel. The time width of ach channel is 0. 112- -0.003 usec. A computer fit of a Background =(discriminator rate)(time straight line to the data points has been drawn in. Its width of channel)(analyzing time slope represents a half-life of 1.46 usec