1. BY DEREK H. AND YAZMEEN T. Lead Shielding and Muons 1

2. TO DETERMINE HOW LEAD THICKNESS AFFECTS THE MUON COUNT RATE 2 Purpose

3. 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.

4. 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. 4

5. 5 Calibration/Plateauing This is done to achieve the maximum signal to noise ratio

6. Experiment Set-Up Detector A Detector B Detector C Detector D Lead Bricks 6 40cm

7. 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 With an increase of thickness=decrease in flux Flux= 618.75e -0.009(thickness) *expected a 1% decrease but instead found 15% decrease 8

9. 15% Decrease? The concrete of the building (4 th floor and roof concrete). 155/170 = less than 10% of muons are blocked. 9

10. Justification for the Exponential Fit The range for the correlation coefficient (R 2 ) is from -1 to 1. How good of a correlation between two data sets. R 2 =0.7907 10

11. Energy Loss Graph This graph shows the loss of energy per distance traveled, for different elements. 11

12. Experiment: Analysis Energy Loss: Lead Density=11.3 g/cm 3 -dE/dρx=(1.12MeVcm 2 /g)(11.3g/cm 3 ) -dE/dx=(12.7MeV/cm) Find deltaE by multiplying the –dE/dx by the thickness of the brick (5 cm). DeltaE Brick =60.35MeV 12 Minimum Ionization energy

13. Muon Counts This shows the cumulative counts per second for energies of muons (at sea level). Energy loss and count rate connection. 13 Less than 1% of muons have less than 60MeV of kinetic energy.

14. 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.

15. 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%

16. 16 5 cm Lead 50 cm Concrete Energy Before Concrete Theoretical

17. 17 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 (?)

18. AND TO ALL THOSE WHO HELPED: STUART BRIBER VICKI JOHNSON JASON NIELSEN TANMAYI SAI BRENDAN WELLS THE SPEAKERS AND THE OTHER INTERNS 18 Thank You for Your Time