VanWasshenova Thesis
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Contents
1
Docker
1.1
Set up Docker Container
2
Introduction
3
Moller Scattering
3.1
Moller Scattering Definition
3.2
Relativistic Frames of Reference
3.2.1
Relativistic Units
3.3
4-vectors
3.3.1
4-momenta
3.3.2
Frame of Reference Transformation
3.3.3
4-gradient
3.4
Mandelstam Representation
3.4.1
s-Channel
3.4.2
t-Channel
3.4.3
u-Channel
3.4.4
Limits based on Mandelstam Variables
3.4.4.1
Limit of Energy in Lab Frame
3.4.4.2
Limit of Scattering Angle Theta in Lab Frame
3.5
Initial 4-momentum Components
3.5.1
Initial Lab Frame 4-momentum components
3.5.2
Initial CM Frame 4-momentum components
3.5.3
Special Case of Equal Mass Particles
3.5.3.1
Total Energy in CM Frame
3.5.3.2
Scattered and Moller Electron Energies in CM Frame
3.6
Final 4-momentum components
3.6.1
Final Lab Frame Moller Electron 4-momentum components in XZ Plane
3.6.2
Final Lab Frame Moller Electron 4-momentum components in XY Plane
3.6.2.1
Momentum Components in the XY Plane Based on Angle Phi
3.6.3
Final CM Frame Moller Electron 4-momentum components
3.6.4
Final CM Frame Scattered Electron 4-momentum components
3.6.5
Final Lab Frame Scattered Electron 4-momentum components
3.7
Summary of 4-momentum components
3.8
Verification of 4-momentum components
3.9
Feynman Calculus
3.9.1
Flux of Incoming Particles
3.9.2
Invariant Lorentz Phase Space
3.9.3
Relativistic Differential Cross-section
3.10
Scattering Amplitude
3.11
Differential Cross-Section
3.12
Moller Differential Cross-Section
4
GEANT4 Simulation of Moller Scattering of Target Material
4.1
LH2 Target
4.1.1
6e7 incident electrons on 1cm square LH2 target Simulation Setup
4.1.2
6e7 incident electrons on 5cm cylinder LH2 target Simulation Setup
4.1.3
6e7 incident electrons on 1mm cylinder LH2 target Simulation Setup
4.1.3.1
Converting the number of scattered electrons per scattering angle theta to a differential cross-section in barns.
4.1.4
Effects Due to Target Length
4.2
NH2 Target
4.2.1
Replacing the LH2 target with an NH3 target
4.3
LH2 Vs. NH3
4.4
Effects Due to Target Material
4.4.1
Target Density
4.4.2
Atomic Mass and Electron Number Effects
4.5
Differential Cross-Section Offset
5
GEANT4 Simulation of Lead Conic Moller Shield
5.1
Lead Shield Cone
6
GEANT4 Simulation of Triangular Plane of Liquid Argon Drift Chamber
7
Modeling the EG12 Drift Chamber
7.1
Drift Chamber
7.1.1
Determining wire-theta correspondence
7.1.1.1
GEMC Verification
7.1.1.2
CED Verification of DC Angle Theta and Wire Correspondance
7.1.1.3
DC Super Layer 1:Layer 1
7.1.2
DC Binning Based On Wire Numbers
7.1.3
Detector_Geometry Simulation
7.1.3.1
Conic Sections
7.1.3.1.1
Circular Cross Sections
7.1.3.1.2
Elliptical Cross Sections
7.1.3.2
Determing Elliptical Components
7.1.3.3
Determing Elliptical Equations
7.1.3.3.1
Test for Theta at 20 degrees and Phi at 0
7.1.3.4
In the Detector Plane
7.1.3.4.1
Test in Plane for Theta at 20 degrees and Phi at 0
7.1.3.4.2
Test in Plane for Theta at 20 degrees and Phi at 1 degree
7.1.4
Function for change in x', Lab frame
7.1.5
Wire Number Function
7.1.6
Mathematica Simulation
7.1.6.1
In the Detector Frame
7.1.6.2
In the wire frame
7.1.6.2.1
Points of Intersection
7.1.6.2.2
The Wires
7.1.6.2.3
Right Hand Wall
7.1.6.2.4
Left Hand Wall
7.1.6.2.5
The Ellipse
7.1.6.3
Plotting Different Frames
7.1.6.4
Parameterizing the Ellipse Equation
7.1.6.5
Change in Wire Bin Number
7.1.7
One Hit per Wire Bin
7.1.7.1
One Hit Per Wire Bin at phi=0
7.1.7.2
Wire Bin Number as a function of Theta and Phi for Right Side
7.1.7.3
Wire Bin Number as a function of Theta and Phi for Left Side
8
Preparing Drift Chamber Efficiency Tests
8.1
Uniform distribution in Energy and Theta LUND files
8.1.1
1000 Events per degree in the range 5 to 40 degrees for Lab Frame
8.1.2
Isotropic Spread in CM for 5 to 40 degrees in Lab Frame at Phi=0
8.1.3
Isotropic Spread in Lab Frame for 5 to 40 degrees in Theta and for Phi between -30 and 30 Degrees
8.1.4
Reading_LUND_files
8.1.5
Run GEMC Isotropic Theta and Phi for Sector 1 DC
8.1.6
Analysis of evio files
8.1.6.1
Little Runs
8.1.6.2
Bin Test
8.1.6.3
Field Test
8.1.6.4
Bin Shapes
8.1.6.5
Limit Adjustment on Walls
8.1.7
HITs in DC
8.1.8
Hits with Changing Torus Field and 0T Solenoid
8.1.8.1
Too Large Events
8.1.9
Hits with -5T Torus and Changing Solenoid Field
8.1.10
Weight
8.2
Detector Occupancy
8.2.1
Whitney Rates
8.2.2
GEANT Moller Simulations
8.2.3
Comparison of GEANT Simulation to Whitney Data
8.2.4
Occupancy for Sector 1
8.2.5
Isotropic Weighted Moller Distribution in GEMC
9
Old Stuff
Docker
Set up Docker Container
Introduction
Moller Scattering
Moller Scattering Definition
Relativistic Frames of Reference
Relativistic Units
4-vectors
4-momenta
Frame of Reference Transformation
4-gradient
Mandelstam Representation
s-Channel
t-Channel
u-Channel
Limits based on Mandelstam Variables
Limit of Energy in Lab Frame
Limit of Scattering Angle Theta in Lab Frame
Initial 4-momentum Components
Initial Lab Frame 4-momentum components
Initial CM Frame 4-momentum components
Special Case of Equal Mass Particles
Total Energy in CM Frame
Scattered and Moller Electron Energies in CM Frame
Final 4-momentum components
Final Lab Frame Moller Electron 4-momentum components in XZ Plane
Final Lab Frame Moller Electron 4-momentum components in XY Plane
Momentum Components in the XY Plane Based on Angle Phi
Final CM Frame Moller Electron 4-momentum components
Final CM Frame Scattered Electron 4-momentum components
Final Lab Frame Scattered Electron 4-momentum components
Summary of 4-momentum components
Verification of 4-momentum components
Feynman Calculus
Flux of Incoming Particles
Invariant Lorentz Phase Space
Relativistic Differential Cross-section
Scattering Amplitude
Differential Cross-Section
Moller Differential Cross-Section
GEANT4 Simulation of Moller Scattering of Target Material
LH2 Target
6e7 incident electrons on 1cm square LH2 target Simulation Setup
6e7 incident electrons on 5cm cylinder LH2 target Simulation Setup
6e7 incident electrons on 1mm cylinder LH2 target Simulation Setup
Converting the number of scattered electrons per scattering angle theta to a differential cross-section in barns.
Effects Due to Target Length
NH2 Target
Replacing the LH2 target with an NH3 target
LH2 Vs. NH3
Effects Due to Target Material
Target Density
Atomic Mass and Electron Number Effects
Differential Cross-Section Offset
GEANT4 Simulation of Lead Conic Moller Shield
Lead Shield Cone
GEANT4 Simulation of Triangular Plane of Liquid Argon Drift Chamber
Modeling the EG12 Drift Chamber
Drift Chamber
Determining wire-theta correspondence
GEMC Verification
CED Verification of DC Angle Theta and Wire Correspondance
DC Super Layer 1:Layer 1
DC Binning Based On Wire Numbers
Detector_Geometry Simulation
Conic Sections
Circular Cross Sections
Elliptical Cross Sections
Determing Elliptical Components
Determing Elliptical Equations
Test for Theta at 20 degrees and Phi at 0
In the Detector Plane
Test in Plane for Theta at 20 degrees and Phi at 0
Test in Plane for Theta at 20 degrees and Phi at 1 degree
Function for change in x', Lab frame
Wire Number Function
Mathematica Simulation
In the Detector Frame
In the wire frame
Points of Intersection
The Wires
Right Hand Wall
Left Hand Wall
The Ellipse
Plotting Different Frames
Parameterizing the Ellipse Equation
Change in Wire Bin Number
One Hit per Wire Bin
One Hit Per Wire Bin at phi=0
Wire Bin Number as a function of Theta and Phi for Right Side
Wire Bin Number as a function of Theta and Phi for Left Side
Preparing Drift Chamber Efficiency Tests
Uniform distribution in Energy and Theta LUND files
1000 Events per degree in the range 5 to 40 degrees for Lab Frame
Isotropic Spread in CM for 5 to 40 degrees in Lab Frame at Phi=0
Isotropic Spread in Lab Frame for 5 to 40 degrees in Theta and for Phi between -30 and 30 Degrees
Reading_LUND_files
Run GEMC Isotropic Theta and Phi for Sector 1 DC
Analysis of evio files
Little Runs
Bin Test
Field Test
Bin Shapes
Limit Adjustment on Walls
HITs in DC
Hits with Changing Torus Field and 0T Solenoid
Too Large Events
Hits with -5T Torus and Changing Solenoid Field
Weight
Detector Occupancy
Whitney Rates
GEANT Moller Simulations
Comparison of GEANT Simulation to Whitney Data
Occupancy for Sector 1
Isotropic Weighted Moller Distribution in GEMC
Old Stuff
DV_RunGroupC_Moller
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