Life Time of Muons
The purpose of this experiment is to measure life time of muons decaying at rest. Muons, produced in the atmoshere bombarded by high energy cosmic radiation, are passing through the system of two detectors located one above the other one. A coincidence of signals from these two detectors (signals occuring in both detectors within 100ns) marks a particle entering the muon telescope from above and serves as a filter rejecting many noninteresting signals from background radiation. Some particles, with appropriate energies, will end their flight in the lower detector (proper amount of lead between both detectors ensures that many of them will be muons). If a stopped particle is muon, it will decay after some time producing electron. The time interval between signals from the muon entering the lower detector and the electron emerging after its decay is converted by a time-to-amplitude converter into amplitude of signal fed to the CAMAC analog-to-digital converter (ADC) controlled by the computer. The spectrum of time intervals is displayed in the figure below. The expected distribution should be exponential with the exponential time constant being the average life time of muon. The full range of the spectrum (about channel 2000) corresponds to the time interval of about 25 microsecond. There are not many muons with such energies that they will end their path exactly in the lower detector (usually they will pass both detectors and will be stopped in somewhere in the ground), so counting rate is rather low. To collect a reasonable number of events, the experiment has to be run a number of days.
Distribution of muon decay times collected over the period of 8 days (experiment was started on Wednesday, April 22, 1998 and terminated on Thursday, April 30, 1998)
The data were evaluated using previously performend time calibration of the CAMAC analog-to-digital converter. It was done using precise time calibrated digitizing scope and a variable delay generator feeding start and stop inputs of the time-to-amplitude converter. The calibartion yielded 0.01293 microseconds per the ADC channel. To increase statistics in each channel the data were compressed to 50 channels that were in turn converted to time units. The data were fitted with the exponential line plus constant background. The three parameter fit gave value of the average muon life time (2.02+-0.08) microseconds. The final data with the fitted line are presented in the figure below. The obtained value is lower than the accepted value of (2.19703+-0.00004) microseconds by slightly more than 2 sigma. This difference may reflect an influence of medium on the decay rate of negative muons.
The compressed data and exponential decay line fitted to the data.