3
The Experiment
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.
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Hypothesis
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.
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Calibration/Plateauing
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.30
10
20
30
40
50
60
70
80
90
100
CPS A:2CPS BCPS CCPS D
• This is done to achieve the maximum signal to noise ratio
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Procedure
• Run a control to find the muon count-rate
• Calculate sky (solid) angle: Angle: 0.455 steradiansPercent 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
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Flux vs. Thickness of Lead
We tried an exponential fit to show the relationship between the flux and lead thickness
With an increase of thickness=decrease in flux
Flux= 618.75e-
0.009(thickness)
*expected a 1% decrease but
instead found 15% decrease
0 5 10 15 20 25 300
100
200
300
400
500
600
700
Counts/min
Exponential (Counts/min)
Lead Thickness (cm)
Flux (Counts/min)
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15% Decrease?
The concrete of the
building (4th floor
and roof concrete).
155/170 = less than
10% of muons are
blocked.
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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
0 5 10 15 20 25 305
5.2
5.4
5.6
5.8
6
6.2
6.4
Natural Log of Flux
LNLinear (LN)Linear (LN)
Lead Thickness (cm)
Ln (Flux) (Counts/min)
11Energy Loss Graph
This graph shows
the loss of energy
per distance
traveled, for
different
elements.
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Experiment: Analysis
Energy Loss:
Lead Density=11.3 g/cm3
-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
Minimum Ionization energy
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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 than60MeV of kinetic energy.
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Recreating the Energy Distribution
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.
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Recreating the Energy Distribution
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%
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Next Step…
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 (?)