G0 - Beam Energy data analysis (10/17/2008)

Questions and progress that I have made on my data analysis:

1.) I have extracted the code for the energy loss calculation from Mceep and tried to understand it.

2.) I have found some defects/erros in my analysis:

- Forgot to consider energy losses of the scattered electrons in the walls of the target chamber, in the air between the HRS and the target chamber and in the entrance window of the HRS. ( This brings the majority of the energy losses of the electrons that scattered from the Ta target. )

- According to Mceep there is 65 cm of air between the target chamber and HRS. Is this true ? Mceep also uses \rho = 0.6 g/cm^3 for the density of the LH2. I believe that in our case (T = 29.27K and p = 29.27psi) the density should be 0.0725 g/cm^3 ?

- Only collisional losses can shift the momentum peak to the lower energies.

- The radiative losses (external and internal bremsstrahlung) only contribute to the radiative tail of the peak.

- In our energy regime the distribution of the collisional energy losses is not Gaussian but Landau function. Therefore the mean value (calculated from the Bethe-Bloch) does not correspond the the *most probable* value of the energy losses. To calculate the most probable energy losses I have used the formula from Mceep (stated in the file eloss_e.f). I am still having some problems understanding where did that formula came from.

3.) I made a stand-alone program for the calculation of the most probable energy loss of the electron.

4.) I have got following results for the most probable energy losses:

dE_Ta = 0.376 MeV

dE_LH2 = 1.358 MeV

These energy losses are a bit different then before. These changes caused my final results to shift a bit to higher values:

Ebeam_HRSL = 361.897 \pm 0.1119 MeV

Ebeam_HRSR = 361.916 \pm 0.08 MeV

I believe that these numbers are very close to the final results! (Hoping that the relation for the Landau distribution is correct!)

TO-DO:

a.) Understand the relation between the mean value and the most probable value of the energy losses in the Landau distribution.

b.) Find a better fit for my data. For now I am using bare Gaussian functions. However, this will not change my results much.

c.) Include the rest of my data (other targets) in my analysis.