DV RunGroupC Moller

need to insert moller shielding into card after moller LUND file is created. (see clas12/beamline)

Simulating the Moller scattering background for EG12

GEANT4 Simulation of Moller Events

Simulation Setup

Determine the Moller background using an LH2 target to check the physics in GEANT4

Distributions For LH2

LH2 Momentum Distribution in the Lab Frame

LH2 Angular Distribution in the Lab Frame

LH2 Momentum distribution in the Center of Mass Frame

LH2 Angular Distribution in the Center of Mass Frame

Comparing experimental vs. theoretical for Møller differential cross section 11GeV

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

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.

Change to a NH3 Target

Replacing the LH2 target with an NH3 target

Figure 6a: The scattered electron momentum distribution for 4E7 incident 11 GeV electrons in the Lab frame of reference.

Figure 6b: The Moller electron momentum distribution for 4E7 incident 11 GeV electrons in the Lab frame of reference.

Increasing the number of incident electrons, Moller Momentum now appears as:

Figure 6c: The Moller electron momentum distribution for 4E8 incident 11 GeV electrons in the Lab frame of reference.

Figure 6d: The scattered electron momentum distribution for 4E7 incident 11 GeV(Lab) electrons in the Center of Mass frame of reference.

Figure 6e: The Moller electron momentum distribution for 4E7 incident 11 GeV(Lab) electrons in the Center of mass frame of reference.

Figure 6f: The Moller electron scattering angle thetea distribution for 4E7 incident 11 GeV electrons in the Lab frame of reference.

Figure 6g: The Moller electron scattering angle theta distribution for 4E7 incident 11 GeV electrons in the Lab frame of reference.

Figure 6h: The Scattered electron scattering angle theta distribution for 4E7 incident 11 GeV(Lab) electrons in the Center of Mass frame of reference.

Figure 6i: The Moller electron scattering angle theta distribution for 4E7 incident 11 GeV(Lab) electrons in the Center of Mass frame of reference.

LH2 Vs. NH3

Plotting the Momentum and Scattering angle Theta in the Lab and Center of Mass frame of reference for LH2 and NH3 targets.

Figure 7a: The scattered electron momentum distribution for 4E7 incident 11 GeV electrons in the Lab frame of reference.

Figure 7b: The Moller electron momentum distribution for 4E7 incident 11 GeV electrons in the Lab frame of reference.

Figure 7c: The Scattered electron scattering angle theta distribution for 4E7 incident 11 GeV electrons in the Lab frame of reference.

Figure 7d: The Moller electron scattering angle theta distribution for 4E7 incident 11 GeV electrons in the Lab frame of reference.

Figure out the offset

Rerunning the GEANT simulation for a target of solo atoms of Carbon 12

Figure 8a: The scattered electron momentum distribution for 4E7 incident 11 GeV electrons in the Lab frame of reference.

Figure 8b: The Moller electron momentum distribution for 4E7 incident 11 GeV electrons in the Lab frame of reference.

These graphs show an offset based upon the density of the target material.

Density of target material

C=2.26 g/cm³

NH3=.86g/cm³

LH2=.07g/cm³

[math]\displaystyle{ \Longrightarrow }[/math]The greater the density, the smaller the solid angle into which the Moller electron will scatter.

Density, atomic mass, and electron number effects

Temporarily changing the density of LH2 to be .86g/cm³, the density of NH3, and altering the atomic mass and electron number, we find

Figure 8c: The Moller electron scattering angle theta distribution for 4E7 incident 11 GeV electrons in the Lab frame of reference.

Differential Cross-Section Offset

Comparing this to the theoretical differential cross section:

As shown above , we find that the differential cross section scale is [math]\displaystyle{ \frac{d\sigma}{d\Omega}\approx 16.2\times 10^{-2}mb=16.2\mu b }[/math]

Converting the number of electrons to barns,

[math]\displaystyle{ L=\frac{i_{scattered}}{\sigma} \approx i_{scattered}\times \rho_{target}\times l_{target} }[/math]

where ρ_target is the density of the target material, l_target is the length of the target, and i_scattered is the number of incident particles scattered.

For LH2:

[math]\displaystyle{ \rho_{target}\times l_{target}=\frac{70.85 kg}{1 m^3}\times \frac{1 mole}{2.02 g} \times \frac{1000g}{1 kg} \times \frac{6\times10^{23} atoms}{1 mole} \times \frac{1m^3}{(100 cm)^3} \times \frac{1 cm}{ } \times \frac{10^{-24} cm^{2}}{barn} =2.10\times 10^{-2} barns }[/math]

[math]\displaystyle{ \frac{1}{\rho_{target}\times l_{target} \times 4\times 10^7}=1.19\times 10^{-6} barns }[/math]

For Carbon:

[math]\displaystyle{ \rho_{target}\times l_{target}=\frac{2.26 g}{1 cm^3}\times \frac{1 mole}{12.0107 g} \times \times \frac{6\times10^{23} atoms}{1 mole} \times \frac{1 cm}{ } \times \frac{10^{-24} cm^{2}}{barn} =1.13\times 10^{-1} barns }[/math]

[math]\displaystyle{ \frac{1}{\rho_{target}\times l_{target} \times 4\times 10^7}=2.21\times 10^{-7} barns }[/math]

For Ammonia:

[math]\displaystyle{ \rho_{target}\times l_{target}=\frac{.8 g}{1 cm^3}\times \frac{1 mole}{17 g} \times \frac{6\times10^{23} atoms}{1 mole} \times \frac{1 cm}{ } \times \frac{10^{-24} cm^2}{barn} =2.82\times 10^{-2} barns }[/math]

[math]\displaystyle{ \frac{1}{\rho_{target}\times l_{target} \times 4\times 10^7}=8.87\times 10^{-7} barns }[/math]

Combing plots in Root:

new TBrowser();
TH1F *LH2=new TH1F("LH2","LH2",360,90,180);
LH2->Add(MollerThetaCM,1.19e-6);
LH2->Draw();

TH1F *C12=new TH1F("C12","C12",360,90,180);
C12->Add(MollerThetaCM,2.21e-7);
C12->Draw();

TH1F *NH3=new TH1F("NH3","NH3",360,90,180);
NH3->Add(MollerThetaCM,8.87e-7);
NH3->Draw();
LH2->Draw("same");
C12->Draw("same");
Theory->Draw("same");

Figure 8c: The Moller electron differential cross-section for 4E7 incident 11 GeV electrons in the Center of Mass frame of reference.

Reconstruction

Moller Track Reconstruction in eg12

Papers used

[1]Farrukh Azfar's Derivation of Moller Scattering

File:FarrukAzfarMollerScatter.pdf

A polarized target for the CLAS detector

File:PHY02-33.pdf

An investigation of the spin structure of the proton in deep inelastic scattering of polarized muons on polarized protons

File:1819.pdf

QED Radiative Corrections to Low-Energy Moller and Bhabha Scattering

http://arxiv.org/abs/1602.07609

EG12