1. Update on Muon Flux Underground Using Geant4 Simulation
Martina Hurwitz
University of Chicago
Braidwood meeting, 5/14/05

2. Reminder of goals of exercise
Neutrons from cosmic ray muons may contribute significantly to backgrounds at Braidwood
First step in being able to simulate neutrons is knowing spectrum of muons underground
Not much information on spectrum of muons at Braidwood’s depth available
Use best knowledge of muon flux at sea level and Geant4 simulation of muon interactions in rock to find flux underground
Exercise has provided some useful results to the collaboration

3. Reminder: Sea level muon flux
Standard Gaisser parameterization doesn’t fit data very well for ~100 GeV muons, particularly at high zenith angles.
We use fits to measurements for muons at cosθ = 1.0 and at cosθ = 0.26 with linear interpolation in cosθ in between.
Note:
At low energies flux of vertical muons roughly equal to flux of muons at high zenith angles.
At high energies flux of vertical muons lower than flux of muons at high zenith angles

4. Reminder: Comparison of G4 flux to MUSIC, data
Vertical muons
Red points: Geant4 sim
Green points: MUSIC sim
Used Gaisser spectrum for purpose of comparison
Unfilled markers: data
Verification that Geant4 giving reasonable results

5. Limitations of Geant4 program implemented last year
Overburden
Simplified material description: Z = 11, A = 22
Uniform density (2.5 g/cm3) throughout overburden
Generator
Muons at sea level were generated up to a 2.5 TeV cutoff energy
While fixing this, found bigger problem in setting energy of muons: generator was sampling from vertical muon energy distribution instead of distribution integrated over all zenith angles
Depth of detector
At time we were still thinking anywhere between 300 and 500 mwe; files of underground muons at 500 mwe

6. Overburden
Read out energies, angles, and position of muons
Detailed table of layers of rock, their chemical compositions and densities at end of talk
Composition of rock: mostly CaCO3 and SiO2 with some MgCO3; Z/A roughly the same as before.
Density effect: stopping power decreased for high-energy muons; average density of overburden has increased roughly 2%

7. Generator
Flux distribution depends on both energy and zenith angle, so program first chooses energy, then angle.
Energy sampling:
Uses probability distribution function to choose energy (fill array with energies, associated probabilities)
Before: filled this array with probabilities based on vertical muon flux at each energy
Now: fill this array with probabilities based on muon flux at each energy integrated over all zenith angles
This will tend to increase the flux of high-energy muons relative to flux of low-energy muons because flux of high-energy muons is higher at high zenith angles.
Increase maximum energy of muons at sea level:
No significant effect on flux, since these muons very rare
Significantly changes average energy of muons underground

8. Depth of detector Was 500 m.w.e. Now: 600 ft = 182.9 m
Middle of deepest layer of limestone, above layer of sandstone
Using densities of layers in overburden, m = m.w.e.

9. Effect of changes in MC simulation on fluxes, Eave
Depth (mwe)
Changes
Flux (/m2/sec)
( ± statistical errors)
Eave underground (GeV)
500.0
Last year’s estimate
0.145
91.2
463.8
Detector placed at design depth
0.181 ± 0.004
85.9
Modified generator: fixed problem with energy spectrum sampling; high-energy cutoff for generation increased from 2.5 TeV to 100 TeV
0.200 ± 0.004
107.6
Incorporated data from boreholes about density and material composition of overburden
0.213 ± 0.004
110.1

10. Flux as function of Vertex Energy

11. Flux as function of energy at detector

12. Radial distance from vertex to detector
Sea level
detector
Muon R

13. Angular distribution of muons at detector

14. Conclusions
Have updated G4 simulation of muon flux with details of Braidwood geometry
Uncovered major mistake in generator, fixed it
Improved generator to simulate high-energy muons
Produced new file (same structure) with ~100,000 events

15. Exact overburden Material Chemical composition Density (g/cm3)
Depth of top of layer (m)
Soil
SiO2
1.60
0.0
Mudstone
2.46
11.3
2.52
27.1
Limestone
CaCO3
2.61
42.7
2.63
61.0
2.60
63.1
Dolomitic Limestone
0.63* CaCO *MgCO3
2.58
82.6
2.62
98.8
2.71
116.4
135.0
142.3
157.6
2.66
168.9