Lead Shielding and Muons
1
BY DEREK H. AND
YAZMEEN T.
Purpose
2
TO DETERMINE HOW LEAD
THICKNESS AFFECTS THE
MUON COUNT RATE
The Experiment
3
 The Question: How is muon flux affected by lead shielding?
 From the captured data, we want to see if there is a correlation between
lead thickness and count rate.
 Energies of muons will be looked at to help understand this correlation;
a loss of lower energy muons in lead will affect count rate.
Hypothesis
4
 The majority of low energy muons will ionize and interact
with more atoms in the lead bricks than in air, causing
them to be slowed down or completely stopped. We expect
to see a substantial decline in the count rate due to the lead
bricks.
Calibration/Plateauing
• This is done to achieve the maximum signal to noise ratio
100
90
80
70
60
CPS A:2
50
CPS B
40
CPS C
CPS D
30
20
10
0
0.5
0.6
0.7
0.8
0.9
5
1
1.1
1.2
1.3
Experiment Set-Up
6
Detector A
40cm
Lead
Bricks
Detector B
Detector C
Detector D
Procedure
7
• Run a control to find the muon count-rate
• Calculate sky (solid) angle:
Angle: 0.455 steradians
Percent of entire sky: 3.26%
• Shield with lead bricks in intervals of three
• Perform a 24 hour run for each layer of thickness
• Look how the flux varies with lead thickness
8
Flux vs.
Thickness of
Lead
We tried an
exponential fit to
show the
relationship between
the flux and lead
thickness
700
600
500
400
Counts/min
Flux
(Counts/min)
300
With an increase of
thickness=decrease
in flux
Expon.
(Counts/min)
200
100
Flux= 618.75e-0.009(thickness)
*expected a 1% decrease but instead
found 15% decrease
0
-5
0
5
10
15
Lead Thickness (cm)
20
25
30
9
15%
Decrease?
The concrete of the
building (4th floor
and roof concrete).
155/170 = less than
10% of muons are
blocked.
10
Justification for
the Exponential
Fit
The range for the
correlation
coefficient (R2) is
from -1 to 1.
How good of a
correlation
between two data
sets.
R2
=0.7907
Natural Log of Flux
6.4
6.2
6
5.8
Ln (Flux)
(Counts/min)
LN
Linear (LN)
5.6
5.4
5.2
5
0
5
10
15
20
Lead Thickness (cm)
25
30
11
Energy
Loss Graph
This graph shows the
loss of energy per
distance traveled, for
different elements.
Experiment: Analysis
12
 Energy Loss:
Lead Density=11.3 g/cm3
Minimum Ionization energy
-dE/dρx=(1.12MeVcm2/g)(11.3g/cm3)
-dE/dx=(12.7MeV/cm)
Find deltaE by multiplying the –dE/dx by the thickness of the brick (5
cm).
DeltaEBrick =60.35MeV
13
Muon
Counts
This shows the
cumulative counts per
second for energies of
muons (at sea level).
Energy loss and count
rate connection.
Less than
1% of
muons
have less
than
60MeV of
kinetic
energy.
Recreating the Energy Distribution
14
 50cm of concrete blocks less than 10% muons
~10% of muons in
20MeV -> 400MeV range
-> Flux vs. Energy graph would be moved
to lower energies by 400MeV
The larger population of higher
energy muons are slowed down
-> more lower energy muons
after concrete.
Recreating the Energy Distribution
15
Total Population = 100%
10% are lost -> Total = 90% of
original population.
After shift to lower energies,
20/90 = 22% of muons are less
than 500MeV.
500MeV/8.3 = 60MeV, so
22%/8.3 = 2.66% > percent
of muons with less than
60MeV of kinetic energy.
2.66% is much less than 15%
Theoretical
5 cm Lead
50 cm Concrete
Energy Before Concrete
16
Next Step…
17
We could increase data run time to get a more
accurate percentage loss while doing further
research into energy distribution.
One layer of lead repeat: 8% decrease (?)
Thank You for Your Time
18
AND TO ALL THOSE WHO HELPED:
STUART BRIBER
VICKI JOHNSON
JASON NIELSEN
TANMAYI SAI
BRENDAN WELLS
THE SPEAKERS
AND THE OTHER INTERNS