Difference between revisions of "DV RunGroupC Moller"
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Using unit analysis on the term outside the parantheses, we find that the differential cross section for an electron at this momentum should be around | Using unit analysis on the term outside the parantheses, we find that the differential cross section for an electron at this momentum should be around | ||
− | <center><math>\frac{ \alpha^2}{2mE}=\frac{.98\times 10^{-7}}{ MeV^{2}}=\frac{9.8\times 10^{-7}}{(1\times 10^6eV)^2}=\frac{9.8\times 10^{-7}}{1\times 10^{12}eV^2}=\frac{9.8\times 10^{-19}}{eV^2}=\frac{9.8\times 10^{- | + | <center><math>\frac{ \alpha^2}{2mE}=\frac{.98\times 10^{-7}}{ MeV^{2}}=\frac{9.8\times 10^{-7}}{(1\times 10^6eV)^2}=\frac{9.8\times 10^{-7}}{1\times 10^{12}eV^2}=\frac{9.8\times 10^{-19}}{eV^2}=\frac{9.8\times 10^{-19}\times(1\times 10^{18})}{1\times 10^{12}eV^2\times(1\times 10^{18})}=\frac{.98}{(1\times 10^{9}eV)^2}</math></center> |
Using the conversion of | Using the conversion of |
Revision as of 15:45, 30 April 2015
Simulating the Moller scattering background for EG1
Step 1
Determine the Moller background using an LH2 target to check the physics in GEANT4
Incident electron energy varies from 1-11 GeV.
LH2 target is a cylinder with a 1.5 cm diameter and 1 cm thickness.
(Following dimensions listed on page 8 of File:PHY02-33.pdf)
Numbers Moller electrons per incident electron.
While 2nd and 3rd generations are created, only 2 2nd generation daughter particles are created for 1E6 incident particles. All knock on electrons are not counted.
Momentum distributions in the Lab Frame.
Momentum distributions in the Center of Mass Frame.
Estimated Momentum Distribution
In the collision of two particles of mass m_1 and m_2, the total energy in the center of mass frame can be written
In the frame where one particle (m2) is at rest
where
in MeV
The velocity of the center of mass in the lab frame is
This gives the momenta of the particles in the center of mass to have equal magnitude, but opposite directions
For an incoming electron with momentum of 11GeV, we should find the momentum in the center of mass to be around 53 MeV which is confirmed in the the data/plots.
KEi | Pxi | Pyi | Pzi | xi | yi | z1 | KEf | Pxf | Pyf | Pzf | xf | yf | zf | KEm | Pxm | Pym | Pzm | xm | ym | zm |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
11000 | 0 | 0 | 11000.5 | 0 | 0 | -510 | 10999.1 | 0.433025 | -0.858867 | 10999.6 | 0 | 0 | -509.276 | 0.905324 | -0.433025 | 0.858867 | 0.905366 | 0 | 0 | -509.276 |
Changing the code for the total Energy to
in the lab frame givesAngular Distribution in the Lab Frame
Angular Distribution in the Center of Mass Frame
Comparing experimental vs. theoretical for Møller differential cross section 11GeV
Using the equation from JLab to approximate Moller scattering (in the Center of Mass Frame)[1]
Plugging in the values expected for a scattering electron:
Using unit analysis on the term outside the parantheses, we find that the differential cross section for an electron at this momentum should be around
Using the conversion of
We find that the differential cross section scale is
Converting the number of electrons to barns,
where ρtarget is the density of the target material, ltarget is the length of the target, and iscattered is the number of incident particles scattered.
Combining these plots, and rescaling the Final Theta in the Center of Mass for milli-barns, we find
![XSect.png](/./images/7/7a/XSect.png)
Step 2
Replace the LH2 target with an NH3 target and compare with LH2 target.
Step 3
Determine impact of Solenoid magnet on Moller events
Papers used
A polarized target for the CLAS detectorFile: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