VanWasshenova Thesis: Difference between revisions

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===[[Isotropic Spread in CM for 5 to 40 degrees in Lab Frame]]===
===[[Isotropic Spread in CM for 5 to 40 degrees in Lab Frame]]===


===[[Determining Momentum Components After Collision in CM Frame]]===
====[[Theta Dependent Components]]====
====[[Phi Dependent Components]]====
====[[Electron Center of Mass Frame]]====
===[[Weight]]===
===[[Weight]]===


Revision as of 23:07, 27 July 2017

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

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

LH2 Target

Simulation Setup

NH2 Target

LH2 Vs. NH3

Effects Due to Target Material

Target Density

Atomic Mass and Electron Number Effects

Differential Cross-Section Offset

Modeling the EG12 Drift Chamber

Drift Chamber

Determining wire-theta correspondence

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

Weighted Isotropic Distribution in Lab Frame

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

Weight

Detector Occupancy

Whitney Rates

GEANT Moller Simulations

Comparison of GEANT Simulation to Whitney Data

Isotropic Weighted Moller Distribution in GEMC

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