Energy Distribution of
Cosmic Ray Muons
Paul Hinrichs
With David Lee
Advised by Phil Dudero
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”
The Experiment
Discriminator
Counters (6)
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
PMT A
Coincidence
Logic Unit
PMT B
NIM-TTL Adapter
PCI Timer/Counter
Computer
PMT C
The Apparatus
The Apparatus
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
The Discriminator
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
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
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
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
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
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:
2
Qmax
dE
Z 1  1 2me c 2  2 2Qmax
 (E)
C(E) 
2

K
ln
 
 2 2 4

2 2
2
dx
A 
I
2
 M c
Z 
Muon Absorption
Use MATLAB to evaluate and plot –dE/dx:
Muon Energy Loss in Lead
50
45
40
-dE/dx (x in cm)
35
30
25
20
15
10
5
0
0
200
400
600
800
1000
E (MeV)
1200
1400
1600
1800
2000
Muon Absorption
Knowing –dE/dx, we can calculate the range R
of a muon with energy E’:
E
dx
R  R( Ecut )  
dE
Ecut dE
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 Emin given Rmax
Muon Absorption
Muon Range in Lead
180
160
Maximum Range (cm)
140
120
100
80
60
40
20
0
0
200
400
600
800
1000
E (MeV)
1200
1400
1600
1800
2000
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 N
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
Preliminary Results
Data from a typical run:
Totals:
Counts over 24 hours, 24 Layers of Bricks (120 cm Pb)
9
Channel Counts
AB
AC
ABC
A – 1275
8
B – 232
7
C – 110
6
5
Per Minute:
4
A – 0.885
3
B – 0.161
2
C – 0.076
1
0
0
120
240
360
480
600
720
840
960
1080
Minute, from 11:50AM, April 12 to 11:50AM, April 13
1200
1320
1440
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
Preliminary Results
Muon Flux vs Maximum Energy Attenuated
1.2
1
Muon Flux Ratio
0.8
0.6
0.4
0.2
0
0
200
400
600
800
1000
Maxim um Energy Attenuated (MeV)
1200
1400
1600
1800
Preliminary Results
Observed Particle Energy Distribution
0.8
PDF
CDF
0.7
Probability of Observation
0.6
0.5
0.4
0.3
0.2
0.1
0
0
200
400
600
800
1000
Particle Energy, MeV
1200
1400
1600
1800
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
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).
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