Advanced Physics Laboratory: Measuring Muon Lifetime at University of Michigan, Lab Reports of Physics

Download Advanced Physics Laboratory: Measuring Muon Lifetime at University of Michigan and more Lab Reports Physics in PDF only on Docsity! University of Michigan Physics 441-442 January, 2006 Advanced Physics Laboratory Measurement of the Muon Lifetime – Addendum Both PMTs are working, and it is desirable to require a “coincidence” between them in order to reduce the background from processes other than muon decays significantly. First set the HV supply to +1400 V. Hook up a fast oscilloscope to the two signal outputs on the “converter” box with one output to Channel 1 and the other to Channel 2 on the scope. Since the pulses from the PMTs vary considerably in amplitude, it is best to use one of fast analog scopes, rather than a fancy digital one. Trigger on Channel 1 and observe both channels. You are looking for negative-going pulses from the phototubes that are about 20 ns long with ampli- tudes ~40 mV. If you trigger on Chan. 1, you should see the Channel 1 pulses and at about the same time, a group of pulses on Chan. 2 for which comparable numbers of photons are seen by each PMT. Ideally, the pulse heights should be comparable on both channels. You can trigger on Chan. 2 to see what the other combination looks like. See the note below about "afterpuls- ing". Trigger the scope on large pulses and look for pulses ~1 µs later. Next, run the pulses from the PMTs to two channels of the LeCroy octal NIM discriminator module as shown in the schematic below. [See the Glossary for some explanation of terms.] The thresholds of these should be set to about 50 mV. This is done by a small screw adjustment. The threshold can be monitored by looking at the voltage at the jack next to the threshold con- trol. It reads ten times the actual threshold. Hook up Chan. 1 and Chan. 2 of the scope to out- puts of the two discriminators. You should see “NIM” pulses ~0.75 V and about 20 ns long. Again you should see a grouping of coincident pulses. Check that the pulses on both channels come at the same time. If not, adjust cable lengths so that the outputs overlap when they arrive at the logic unit. If necessary, you can adjust the discriminator output widths to be certain that the pulses from the two sources overlap. Next, run the two discriminator outputs to 2 inputs of the LeCroy Logic circuit, and set it up to require coincident pulses from the two channels. Check the output of the coincidence circuit and run it into the scaler. You should see coincidence rate ~10 Hz. Run the coincidence output through about 64 ns of cable to the TAC start and through a short cable to the stop. [The cable delay is about 1.5 ns/foot.] Set up the TAC and the Pocket MCA as described in the long writeup. Once you start recording data, take short runs with the HV at 1300, 1400, and 1500 V and meas- ure the counting rate at each HV setting. Note that if the HV is too high and/or the discriminator threshold is too low, you may see an artifact in the time distribution near 1 µs due to "afterpuls- ing" in the phototubes. Do not exceed 1500 V. Note that there is no "correct" HV to run at. The higher voltages give higher rates if the afterpulsing artifact is not a problem. Experiment with different Range setting on the Time-to-Pulse-Height converter to make sure you understand how it works. It is best to take data out to 10 µs so you can understand the back- ground due to random pulses. The recommended MCA settings are: Threshold = 40, "ADC Gain" = 2048. Once you under- stand how everything works, take your long data run(s) and do your time calibration as described 1/17/06 2 Muon Lifetime below. To determine the muon lifetime, it is best to fit the curve to an exponential plus a constant background, or possibly a linear background. The safest way to fit the time spectrum is to print it out on a semilog scale and do an “eyeball” fit to an exponential plus a constant background. Use the time calibration to convert the slope to microseconds. Once you understand this, you can copy the spectrum files (which are text files) into Igor to do a proper fit and estimate the un- certainty. Note that the error assigned to each point should be the square root of the number of counts in that channel; otherwise you will get rather nonsensical fits. To understand the shape of the background due to random pulses causing a "stop", you can take a run with the "start" pro- vided by the pulser (set at say 1 kHz), and the "stop" provided by the usual coincidence. When you leave the MCA running overnight, it is probably best to disconnect the computer from the network. Otherwise, the UM update may run and force the computer to restart and terminate your run. Be sure to hook it back up to the network when you are done with your run so that it can be updated properly. Time Scale Calibration To calibrate the time scale on the Time-to-Amplitude converter (TAC), you can use the Ortec 480 pulser and the Ortec 427A Delay Amplifier. Set the pulser for negative output. Trigger the scope externally with one output, and feed the other to the Delay Amplifier input and then through a tee to the TAC “Start”. Feed the Delay Amplifier output through a tee to the scope and the TAC “Stop”. Observe the delayed pulses on the scope as you vary the delay with the switches. Check the delays using the time base of the scope. Take pulse height data for the largest range of delays possible and use these data to cali- brate the time scale of the TAC. Questions (1) Does your lifetime agree with the accepted value? Discuss effects that might cause the lifetime to be low. What effects might cause the lifetime to appear high? (2) Calculate the weak coupling constant GF from your measured lifetime. (See page 2 of the writeup. Be careful about units.) (3) Look up articles on the behavior of stopped muons in materials such as liquid scintillator (e.g., Phys. Rev. C35, 1987). Why might the lifetime for negative muons be different from that for positive muons? How much could this affect your result? [If you have very good data, you can try to fit your data to the sum of two exponentials plus a constant background.] (4) Use your muon lifetime measurement to calculate the weak coupling constant Gf. (See equation in main writeup.) (5) The rate at which muons stop in the barrel and decay is pretty much constant. Explain why the event rate depends on the photomultiplier high voltage. (6) As mentioned above, "afterpulsing" in the phototube can cause a fake bump in the time spectrum near 1 µs. Explain how the afterpulses are produced in the photomultiplier and why they can cause a bump. [There's some interesting physics here.] (7) Did you find that the background due to random stops is consistent with being constant? (8) Explain why the Start to the time-to-pulse height converter is delayed ~64 ns.