1 Purpose of This Lab Exercise:

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Physics 4796 - Experimental Physics
Temple University, Spring 2010-11
C. J. Martoff, Instructor
J. Tatarowicz, TA
Physics 4796 Lab Writeup
Particle Physics with Cosmic Rays
1
Purpose of This Lab Exercise:
Acquaint you with some apparatus used to study the behavior of elementary particles (cosmic ray muons). Study radioactive decay and measure
fundamental Weak Interaction quantities (the muon lifetime and the Fermi
Coupling Constant) using a least-squares fit to decay data. Understand the
uncertainties in least-squares fitting.
1.1
Specific Goals
• Calculate energy loss of stopping muons and decay electrons using
Bethe-Block theory.
• Understand why the lifetime measurement is independent of the muons’
history before entering the apparatus.
• Measure performance characteristics of the TeachSpin Muon Physics
apparatus.
• Obtain a low-background muon decay time spectrum by correctly adjusting the high voltage and threshold of the apparatus.
• Fit the time spectrum to determine the muon lifetime and its random
and systematic uncertainties.
Approximate time needed: Two to four lab sessions.
1
1.2
Suggested References:
1. Coan and Ye, “TeachSpin Muon Physics Manual” (on course website).
Page 27ff contains many more interesting and some historic references
to related topics. Operating instructions start on page 28.
2. Coan and Ye, “A Compact Apparatus for Muon Lifetime Measurement
and Time Dilation Demonstration in the Undergraduate Laboratory”,
Am. J. Phys. 74, 161 (2006) (on course website).
3. Knoll, Radiation Detection and Measurement (in Paley).
4. Horowitz and Hill, The Art of Electronics App. A
2
Preparation:
Carefully read pages 1-26 of the “Muon Physics Manual”. Pay particular
attention to Figure 5. Answer the Prelab questions in writing and discuss
your answers with the instructor.
This is a highly integrated apparatus (otherwise known as a “black box”),
but it does provide a few opportunities to peer inside it.
The brains of the apparatus is labeled “FPGA Timer” in Figure 5. FPGAs (Field Programmable Gate Arrays) are not quite computers, but they
are so fast and capable of so much computer-like analysis without any overhead of disk drives, memory boards and operating systems that they have
become essential to many sophisticated electronic devices. They’re even described on YouTube!
www.youtube.com/watch?v=L2wsockKwPQ.
Just one big FPGA manufacturer (Xilinx) had $1.6 billion in revenues last
year. However, learning about FPGA’s will have to be left as an exercise
for the interested student. (You could start at
http://www.xilinx.com/support/education-home.htm).
3
Lab Activities
To get a feel for what’s inside the box, go to page 31 of the Manual and do
Student Exercises 1 (skip the frequency response part), 2, 3, 4, 5, 7, 8, 9,
10. Skip 6, 11, 12. BUT- READ NOTES BELOW before plowing through
these exercises.
Notes:
• While doing Student Exercise 5, use the software to get a spectrum of
decay times rather than a digital scope. Answer the following additional question:
We are supposed to believe that the two pulses in the sequences measured by the apparatus are causally related- the first is supposed to be
a muon stopping and the second is supposed to be that muon decaying.
But we know that there are background counts occurring randomly in
2
time, due to naturally occurring radioactivity in the room, for example. The “raw muon’ count rate tells us the rate of these background
counts for our chosen discriminator setting. If all the counts were
background occurring randomly in time with the measured rate, what
would be the probability of getting a pulse sequence that “looks like” a
muon decay? Hint- see question 4 on the Prelab and the discussion of
radioactive decay in your Modern Physics textbook. A pulse sequence
will “look like” a muon decay if one pulse occurs, followed within 20
microseconds (not after 20 microseconds) by a second pulse.
• Multiply your calculated probability by the “raw muon” rate. This
is an estimate of the rate of background counts in the muon decay
spectrum. Verify that your settings are such that the calculated background is less than 1/10 of the “Decay Rate” indicated on the “Monitor” panel in the data acquisition software. Discuss these results with
the instructor before proceeding.
• Before you take the actual data (Student Exercise 8), have the instructor check your settings. Take data at least overnight.
For the lifetime fit, use the built-in fit program first. The code word
is “muon”.
Next, use the “sift” program provided by the manufacturer to export
your data into a file you can import into EXCEL or OpenOfficeCALC.
Use the FREQUENCY function in the spreadsheet to plot your data
and the built-in fitter result. Calculate χ2 for the fit and look up in a
χ2 table the probability that your data is actually represented by this
fit function. Estimate the uncertainty in the fitted lifetime by varying
it by hand and watching the effect on χ2 .
It is beyond the scope of this course to implement a full nonlinear leastsquares fit, which could fit this data without the heuristic approach of
the built-in fitter. This could be done using algorithms like LevenbergMarquardt (see Press et al, Numerical Recipes- The Art of Scientific Computing),
as in certain commercial software packages like ORIGIN.
Model your lab report after Eckhause, M. et al., Phys. Rev. 132, 422
(1963) (find this article through the Temple Libraries’ Journal Finder service).
3
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