Energy Distribution of Cosmic Ray Muons

1. Energy Distribution ofCosmic Ray Muons Paul Hinrichs With David Lee Advised by Phil Dudero

2. The Experiment • Cosmic rays are particles impingent on Earth from outer space • Appear at Earth’s surface mainly as muons • Goal of the experiment: measure the energy distribution of cosmic ray muons at Earth’s surface • References describe the muon energy spectrum as “almost flat below 1 GeV”

3. PMT A PMT B PMT C Discriminator Counters (6) Coincidence Logic Unit NIM-TTL Adapter PCI Timer/Counter Computer The Experiment • Three scintillation detectors: photomultiplier tube with plastic paddle • Absorber material slows or stops incoming muons; here, lead (r=11.4 g/cm³) • Electronics to process and read out PMT signal • Measure energy by varying the absorber thickness and examining the ratio of count rates

4. The Apparatus

5. The Apparatus

6. The Discriminator • PMT outputs a raw negative pulse, about 100mV high and lasting about 10ns • Discriminator cleans this raw signal up: whenever the PMT output goes below a threshold voltage, the discriminator outputs a NIM logic pulse of fixed length • Set threshold voltage to change sensitivity

7. The Discriminator

8. Coincidence Unit • Four-way coincidence unit: 4 selectable input channels • Buttons on the front allow independent selection of each channel • The coincidence unit pulses if all selected channels pulse simultaneously

9. Other Logic • Counters display number of counts since they were last reset • NIM-TTL adapter converts NIM pulses (negative true, about -1V) to standard TTL logic (positive true, +5V) • Adapter is needed to interface with computer, which only accepts TTL signals

10. Computer Data Collection • The computer collects data with a NI 6602 PCI counter and timer card • 3 input channels • The counting program, written by Kurt Wick and modified by us, counts for N periods of length T • Allows us to record and later analyze data over time: we have counts for each minute of data collection, not just totals

11. Calibration • PMTs first require calibration • More than one variable: • PMT drive voltage determines sensitivity, pulse height, noise • Discriminator threshold can cut out some noise, though not all • Usually, discriminator threshold is set low, and the coincidence unit discards uninteresting events

12. Calibration Procedure • Align all three paddles directly on top of each other • Set the coincidence unit to output coincidences on: • AC, the top and bottom panels • ABC, all three panels • Adjust the supply voltage and threshold voltage for B until the ratio ABC:AC is ~1 • Permute A, B, C and repeat for A and C

13. Muon Absorption • Need to know what particle energies are stopped by a given amount of lead • In this energy range, almost all energy loss is due to ionization • Use the Bethe-Bloch equation to predict energy loss of incoming muons, as a function of their current energy:

14. Muon Absorption • Use MATLAB to evaluate and plot –dE/dx:

15. Muon Absorption • Knowing –dE/dx, we can calculate the range R of a muon with energy E’: • Choosing Ecut sufficiently small (0.15 MeV here) means we can neglect it, and consider only the integral contribution • Integrate numerically with MATLAB to find the range of a muon with given energy • Can also solve numerically for Emingiven Rmax

16. Muon Absorption

17. Experimental Errors • Error in numerical computations is negligible • Bethe-Bloch equation, using the continuous stopping approximation, is only about 1–2% accurate in predicting muon range • Path length differences are only 0.1–0.2%, given the dimensions of our apparatus • Statistical error, proportional to ÖN

18. Practical Considerations • Maximum range: • About 130 cm available for lead • Theoretical maximum absorption ~1.7 GeV • Point Granularity • Each lead brick is 5 cm thick • Statistics • Low count rate: about 300 triple coincidences in 24 hours with no bricks

19. Preliminary Results • Data from a typical run: Totals: A – 1275 B – 232 C – 110 Per Minute: A – 0.885 B – 0.161 C – 0.076

20. Preliminary Results • Detector geometry means total flux through ABC, assuming no absorption, has the form FABC, Expected = K FAB • Use data collected with no absorber to determine K experimentally • We can then examine the ratio FABC, Measured / FABC, Expected to determine how much flux is being stopped

21. Preliminary Results

22. Preliminary Results

23. Future Work • Take more data • Try to calculate K analytically and compare with the measured value • Difference between expected and observed values give the efficiency of the detector • Refine computation of distribution function

24. References • Particle Data Group, Review of Particle Physics (2006). • Leo, William R., Techniques for Nuclear and Particle Physics Experiments,Springer-Verlag, Berlin, 1994. • Groom, D.E., Striganov, N.V., and Mokhov, S.I.; Muon Stopping Power and Range Tables 10 MeV–100 TeV, Atomic Data and Nuclear Data Tables 78, 183–356 (2001).

25. Questions? • Acknowledgements: • Phil, for general advice • Kurt Wick, for helping us set up the apparatus • Professor Michael DuVernois, for providing supplemental equipment, along with expertise • Michael Hamman and Timothy Weaver, who worked on this project during MXP last year • Peter Karn and Dave Kearsley, for general help and emotional support