VanWasshenova Thesis
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
Plotting the 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.
Benchmark GEANT4's Moller scattering prediction with the theoretical cross section using LH2
Comparison of simulation vs. the theoretical Møller differential cross section using 11 GeV electrons impinging LH2
Figure 5c: The experimental and theoretical Moller electron differential cross-section for an incident 11 GeV(Lab) electron in the Center of Mass frame of reference.
Effects Due to Target Length
NH2 Target
Replacing the LH2 target with an NH3 target
Benchmark GEANT4's Moller scattering prediction with the theoretical cross section using NH3
Comparison of simulation vs. the theoretical Møller differential cross section using 11 GeV electrons impinging NH3
Figure 5c: The theoretical and simulated Moller electron differential cross-section for an incident 11 GeV(Lab) electron in the Center of Mass frame of reference for NH3 target.
LH2 Vs. NH3
Benchmark GEANT4's Moller scattering prediction for NH3 and LH2
Effects Due to Target Material
Target Density
Atomic Mass and Electron Number Effects
Differential Cross-Section Offset
Figure 5c: The theoretical and simulated Moller electron differential cross-section for an incident 11 GeV(Lab) electron in the Center of Mass frame of reference for NH3 target. The theoretical differential cross-section has been adjusted to account for the 10 electrons within NH3.