1. Electron Polarization effects in Compton X/γ-ray Sources
Presented by Yingchao Du
Jing Ren, Hongjian He, Chuanxiang Tang
Department of Engineering Physics, Tsinghua University
Beijing, China

2. Content Introduction Simulation results from Cain program
Results from QED theory
Summary

3. Polarization effects in Compton scattering
In Compton scattering X-ray source, the parameters of scattered X-ray are depended on the momenta and polarization vectors of the initial electron, the initial photon, the final electron, the final photon . The polarization of the electron and photon will influent the scattering process. It means that the special polarized X-ray may be obtained with different initial polarizations. It is then to necessary to know the influence of the electron polarization for Compton scattering.
Few formula contain all polarization effect for Compton scattering X-ray source, and all of them are given in the electron’s rest frame.

4. Cain
Monte-Carlo program for the interaction involving high energy electron, positron, and photons.
The electron spin is involved in the case of linear interaction with circular polarized photons.
The differential cross section is given in the electron’s rest frame.

5. Longitudinal polarized electron and circular polarized laser
50MeV electron scattered with 1.5eV photon

6. 500MeV

7. 50GeV

8. Transverse polarized electron and circular polarized laser

9. Outline Introduction Simulation results from Cain program
Results from QED theory
Summary

10. Description of Compton Scattering With QED
Linear interaction, only one photon is absorbed and emitted;
The photon is circular polarized;
The electron is longitudinal polarized;
Electron and photon collide with angle π

11. The amplitude of Compton scattering with the help of Feynman rules:
The Differential Cross Section:
The differential cross section is a function of the particles’ polarization.
There are 16 combinations for all initial and final particle’s polarizations.

12. The results of the amplitude:

13. The value of M/e2 for right-handed circular polarized photon is scattered by ½ spin electron, and the emitted photon polarization is left-handed circular polarized and the finial electron polarization is -½.
Detailed information is given in the paper presented in this workshop.

14. The cross section for experiment:
Not all of the polarization will be observed in the experiment.
Averaging over the unobserved initial polarizations and summing over the unobserved final polarizations can cancel the unobserved terms.
For example, the right-handed circular polarized photon is scattered by unpolarized electron, if we interest in the scattered right-handed circular polarized photon, the cross section is

15. Thomson scattering Set p = 0 and ω-> 0,
Average over initial polarization and sum over final polarization:

16. The amplitude versus scattered angle
The amplitude versus scattered angle. Electron energy 50MeV, Photon energy, 1.5eV

17. The amplitude versus scattered angle
The amplitude versus scattered angle. Electron energy 50GeV, Photon energy, 1.5eV

18. The amplitude versus scattered angle
The amplitude versus scattered angle. Electron energy 50MeV, Photon energy, 1.5keV

19. Final electron polarization is unobserved:

20. Final electron and photon polarization are unobserved:

21. Initial photon and final electron polarization are unobserved:

22. Summary
The influence of electron polarization in linear Compton scattering is studied, and explicit differential cross section in laboratory frame is given.
The electron polarization obviously influent the differential cross section and scattered photon polarization for high energy electron.
For most of the Compton scattering X-ray source, the electron energy is less than 100 MeV, in this case, the electron polarization effect is slight and can be ignored.
The polarization effect in nonlinear Compton scattering will be studied, and a simulated code is being developed.

23. Thanks!