1000 Events per degree in the range 5 to 40 degrees for Lab Frame

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1000 events per degree of 5 to 40 degrees in the Lab Frame

Examining the CM Frame Theta angles which correspond to Lab frame angles within 5-40 degrees (with bin widths of 0.1 degree), for only on degree in Phi (0 degrees). For each degree in Theta in the Lab frame, the correct kinematic variables for a specific events is written to a LUND file 1000 times. File:LUND Spread LH2 5to40Lab.C

Figure 3a: A plot of the number of Moller scattering angle theta in the lab frame. The width of the bins is 0.5 degrees for the angles 5 to 40 in the lab frame.

Figure 3b: A plot of the number of Moller scattering angle theta in the center of mass frame. The width of the bins is 0.001 degrees for the angles in the center of mass frame corresponding to angles of 5 to 40 degrees in the lab frame.

These events are read from the evio file using File:Evio2root.c

The Moller Scattering angle Theta is read from the LUND file, it's weight applied, and it's weight adjusted by dividing by the number it was multiplied by (1000) to give a differential cross-section for one electron. This is plotted against the theoretical differential cross-section for one Moller electron. File:MollerDiffXSect.c

Figure 4a: A plot of the number of Moller scattering angle theta in the center of mass frame versus the theoretical differential cross section. The width of the bins is 0.001 degrees for the angles in the center of mass frame corresponding to angles of 5 to 40 degrees in the lab frame. A weight has been assigned for each value in theta which will give the theoretical differential cross section when applied.

Figure 4b: A plot of the number of Moller scattering angle theta in the lab frame versus the theoretical differential cross section. The width of the bins is 0.5 degrees for the angles in the lab frame. A weight has been assigned for each value in theta which will give the theoretical differential cross section when applied.

From the evio file, a histogram can be constructed that will only record the Moller events which result in hits in the drift chamber. A hit for this setting is the procID value of 90 which corresponds to a transportation process (i.e. if the particle was a primary particle). Dividing DC hits by the procID variable, we find for the hits which are not transportation process for the primary parent particle:

Figure 5: A plot showing the physical process that is responsible for registered hits in the DC which are not transportation of the primary parent particle.

Process ID

Process Name	ID
1	e ionization
2	compton scattering
3	e bremsstrahlung
4	Photo Electric Effect
5	Gamma Conversion
6	e+ Annihilation
90	na

Plotting the Moller scattering angle Theta in the Center of Mass frame just for on occurance of the CM angle gives the Moller Differential Cross-section.

Figure 6: A plot showing a plot of the Moller scattering angle theta that result in DC hits. Each angle theta is only plotted once, and not repeated for multiple hits using the same angle.

Adjusting the weight by the number of times the specific angle caused hits. We should recover the Moller differential cross-section as found previously.

Figure 7: A plot showing a plot of the Moller scattering angle theta that result in DC hits. Each angle theta is plotted by as many occurances that result in hits, and renormalized to account for only one angle as would be found from one electron.

Once the validity of the Moller differential cross-section is established, we can transform from the center of mass to the lab frame as shown earlier. Since the detector is in the lab frame, the hits collected will have to be used to compose a histogram for the Moller scattering angle in the lab frame. We can show that the Moller events that register as hits in the lab matches the Moller differential cross-section in the lab.

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