Reference: Melissinos, Experiments in Modern Physics (p.399-409)
I. Introduction
The surface of the earth is constantly struck by cosmic ray particles arriving from high in the atmosphere. Most of the surface flux is due to muons resulting from the decay of pions produced by high altitude interactions of the primary cosmic rays (mostly protons) with atmospheric nuclei. The muon (mass = 105.6 MeV/c**2, lifetime about 2 microsec) is a lepton like the electron but much heavier. It is unstable, decaying into an electron and two (why?) neutrinos. In this experiment you will use a “telescope” constructed of plastic scintillator to detect cosmic ray muons, measure their flux and determine the lifetime of muons stopped in a block of scintillator. The major steps in the experiment are:
A. Plateau and time the counters. (Check for functionality with a radioactive source).
B. Measure coincidence rates and calculate the flux at 4-5 vertical separations between the counters.
C. Observe the time distribution of decays of stopped muons and measure the muon lifetime.
D. Make a rough measurement of the zenith angle dependence of the cosmic ray flux.
II. Counters
The three flat scintillators must be plateaued to yield good efficiency for throughgoing muons. Using a reasonable discriminator threshold (30-100 mV) make a plateau curve for each tube and determine the proper operating voltage.
DO NOT EXCEED – 2000 VOLTS ON THESE TUBES !
You may wish to make a pulse height spectrum from one or more of the tubes as an aid to understanding the plateau curves. The expected muon counting rates are about 10 Hz for the larger counters. What would you expect for the counting rate of the small counter?
In order to compensate for differences in the phototubes and their positions in the equipment it will be necessary to adjust cable lengths and possibly use the delay boxes to “time the counters”. Using fairly long cables, connect each counter to a properly adjusted discriminator. Connect the outputs from all of the discriminators into a coincidence unit. Choose a particular counter as your reference and make delay curves for the other counters with respect to the reference. Set the delay for each counter to the center of its delay curve.
III. Vertical Muon Flux
Measure the coincidence rate between the top two counters for five different vertical separations. Determine the accidental coincidence rate both by calculation from the singles rates and the resolving time and by direct measurement with a large delay. Subtracting the accidental rates, calculate the vertical flux of cosmic ray muons (# muons/sec/area/steradian) for each position.
You may try placing the bottom flat counter into the coincidence to reduce the accidental rate. Being completely sure that the bottom counter does not affect the solid angle, compare the rate with the subtracted muon rate measured above.
You should find that the flux is approximately constant as a function of the vertical separation of the two counters if you have corrected properly for the changes in solid angle.
IV. Muon lifetime
To measure the muon lifetime you must trigger on muons that pass through the top two counters but stop in the large block of scintillator. Make a coincidence between the top two counters and add the bottom counter in anticoincidence. To ensure that the anticoincidence (or veto) pulse arrives before the other signals, shorten the relative delay of the bottom counter by about 5 ns (starting from the value that places it in coincidence with the top two counters.) The width of the veto pulse should be enough so that it fully overlaps the other pulses. The output of the coincidence unit (A .and. B .and. not D) will provide the start signal to the TAC.
Calibrate the TAC/PHA on the appropriate scale for a muon lifetime measurement. (Question: how can you generate a sufficiently long delay for this calibration ?).
Estimate the relative size of the PMT signal from the large block of scintillator for through muons and for electrons from muon decay. The rate of energy loss in plastic scintillator is 1.95 MeV/(gm/cm**2) and the density is 1.032 gm/cm**3. Apply high voltage to the 5 inch PMT and examine the pulse height spectrum.
D0 NOT EXCEED -2500 VOLTS ON THIS TUBE
Using a reasonalbe discriminator threshold (30-50 mV) make a plateau curve and select an operating voltage for counter C. In order to be sure the counter is sensitive for the smaller pulse from the decay electron, reduce the discriminator setting, taking into account the relative energy deposit for through muons and decay electrons. Send the discriminator output into the stop input of the TAC and adjust the relative timing so that the prompt signal arrives slightly before the start pulse.
Check on the oscilloscope that you can observe a muon decay.
After you have verified the logic and calibrated the TAC, record a time spectrum for data. Rebin the data time spectrum into 7-8 bins. Perform a fit to the binned distribution using an exponential function and a flat background function. Obtain the muon lifetime.
V. Using only two counters again, measure the zenith angle dependence of the cosmic ray flux (including solid angle factors and correction factors). Compare the flux at vertical and horizontal orientations and two zenith angles in between (a total of 4 measurements).
VI. Technical notes:
A) To see a clear threshold in the plateau curve, perform the HV plateauing in the muon telescope. Otherwise, muons clipping the edges will become more efficient as the HV increases and distort the curve.
B) The discriminator threshold for the new phototube used in counter A should be 50 mV or less.
C) Use the following logic for the lifetime measurement: 1 .AND. 2 .AND. (.not. 4) for the TAC start and 3 for the TAC stop.
D) To avoid signals for double-pulsing do not set the gain for phototube 3 too high. Note that the time-associated with double pulsing is around 2 micro-sec, close to the muon lifetime.
E) To avoid background from through-going muons, place counter 1 in the uppermost position and counter 2 close to counter 3. This configuration minimizes background but will have somewhat lower rates.
F) Use the pulser to calibrate the delay box and TAC/MCA. Make a copy of the signal with the NIM discriminator. Move the start a little later than the stop and then adjust for the 10 microsec range.
G) The high end of the TAC range (channel no > 1500) does not work well. There may also be a problem with some channels at the start of the range.
VII. Self Test
1. Estimate the mean decay path for a muon of momentum 1 GeV, 10 GeV, 100 GeV. Compare your results with the “height” of the atmosphere.
2. For each of the muon momenta in 1., estimate the fraction of the muons produced at the scale height of the atmosphere that reach the surface of the earth before decaying.
3. What is the travel time between the top and bottom counters in the muon decay apparatus? Assume particles traveling near the speed of light and a separation of approximately 110 cm.
4. What is the rate of energy loss for a muon in plastic scintillator material in MeV/cm? What is the total energy loss in the large block of scintillator (height=20 cm) for a vertical muon? Compare this with the maximum total energy of the electron in the decay of a muon to an electron and two neutrinos.
5. Explain why a muon does not decay into an electron and one neutrino. (Hint: Think about conservation laws)
6. Explain why we use the following logic for the lifetime measurement: 1. AND. 2 .AND. (.not. 4) for the TAC start and 3 for the TAC stop.
7. What is the time distribution of real muons in 1 and 2 and random pulses in 3 ? How can you minimize this background ?
8. How do you calibrate the TAC for a 10 microsec or 20 microsec range ? (the delay box or long cables will not work).
9. What is the expected zenith angle dependence of the muon cosmic ray flux ?
10. Why must you make a correction for muonium formation in your lifetime measurement ?
11. In some experiments (e.g. QUARKNET muon detectors) coherent noise from cell-phones produces coincidences. How can you check for this type of background ?
Last updated January 1, 2015
Tom Browder (teb#phys.hawaii.edu)