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BY DEREK H. AND YAZMEEN T.

Lead Shielding and Muons

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TO DETERMINE HOW LEAD

THICKNESS AFFECTS THE

MUON COUNT RATE

Purpose

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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

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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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Experiment Set-Up

Detector A

Detector BDetector CDetector D

Lead Bricks40cm

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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

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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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5 cm Lead

50 cm Concrete

Energy Before Concrete

Theoretical

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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 (?)

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AND TO ALL THOSE WHO HELPED :STUART BRIBERVICKI JOHNSONJASON NIELSEN

TANMAYI SAIBRENDAN WELLS

THE SPEAKERSAND THE OTHER INTERNS

Thank You for Your Time