THE EGS5 CODE SYSTEM

ZθkYOφe0Xk0Figure 2.23: Photon scattering system. An incident photon toward the Z-direction is scattered atpoint O. The propagation vector k ⃗ 0 and polarization vector ⃗e 0 of an incident photon are parallel to⃗e z and ⃗e x , respectively. Here, ⃗e z and ⃗e x are unit vectors along the z- and x-axis. The scattering polarangle is θ and the scattering azimuth angle from the plane of ⃗e 0 is φ. The scattered propagationvector is ⃗ k.method for modeling the scattering of linearly polarized photons in EGS4, and that treatment hasbeen included in EGS5.Consider a photon scattering system of Figure 2.23, in which a completely linearly polarizedphoton, whose propagation vector and polarization vector are ⃗ k 0 and ⃗e 0 , is scattered at pointO, The propagation vector of the scattered photon is ⃗ k, and the polar and azimuth scatteringangles are θ and φ. Using the methodology of Heitler [71], we consider two components of thedirection vector ⃗e, one in the same plane as ⃗e 0 (which we denote as ⃗e ‖ ) and the other componentperpendicular to the plane of ⃗e 0 , (called e⃗⊥ ). Figure 2.24 shows ⃗e ‖ in the plane S defined by ⃗ k and⃗e 0 , and e⃗⊥ perpendicular to the plane S. Under the condition that k ⃗ 0 ‖ ⃗e z and ⃗e 0 ‖ ⃗e x (as shownin Figures 2.23 and 2.24), these two polarization vectors, ⃗e ‖ and e⃗⊥ , can be determined to be thefollowing functions of θ and φ :( ) ( )1 1⃗e ‖ = N ⃗e x −N sin2 θ cos φ sin φ ⃗e y −N cos θ sin θ cos φ ⃗e z (2.428)and( ) ( )1 1e⃗⊥ =N cos θ ⃗e y −N sin θ sin φ ⃗e z . (2.429)√Here, N = cos 2 θ cos 2 φ + sin 2 φ , ⃗e x , ⃗e y , ⃗e z are unit vectors along the x-, y- and z-axis, respectively,and ⃗e ‖ and e⃗⊥ are treated as normalized vectors.The Compton scattering cross section for linearly polarized photons Ribberfors deriveda doubly differential Compton scattering cross section for an unpolarized photon using the relativis-133