VanWasshenova Thesis

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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

Converting the number of scattered electrons per scattering angle theta to a differential cross-section in barns.

Experimental and Theoretical Moller Differential Cross-Section in Center of Mass Frame Frame
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

Theoretical and Simulated Moller Differential Cross-Section in Center of Mass Frame Frame
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

Theoretical and Simulated Moller Differential Cross-Section in Center of Mass Frame Frame
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.

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

Rates for Sector 1

Rates for Different Solenoid Strengths

Rates for all Sectors based on Initial Sector 1 incident Moller electrons

Changing Solenoid Field Rates in Sector 1

Pb Cylinder (AKA "Temp Shield")

Understanding GEMC Component Effects

Forward Chamber

Drift Chamber

Magnets

Solenoid

Torus

CAD Components

BoreShield

CenterTube

DownstreamShieldingPlate

DownstreamVacuumJacket

Hub001

Plates 1-6

Shields 1-7

UpstreamShieldingPlate

UpstreamVacuumJacket

WarmBoreTube

coils 1-6

shell 1-6 a/b

dc supports sectors 1-6 region 1

dc back sectors 1-6 region 1

apex

Isotropic Weighted Moller Distribution in GEMC

Old Stuff

DV_RunGroupC_Moller

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