THE EGS5 CODE SYSTEM

PEGS functions BHABDM, BHABRM, and BHABTM evaluate Equations 2.208, 2.209, and 2.211, respectively.In sampling the differential cross section to obtain the electron energy, we take E = ˘T − / ˘T 0 asthe variable to be sampled and obtaind˘Σ Bhabha (Ĕ0)dE= X 0n2πr 2 0 m˘T 0 E 0f(E)g(E) (2.212)whereE 0 1f(E) =1 − E 0 E 2 , E ∈ (E 0, 1) , (2.213)[ ]1g(E) = (1 − E 0 )β 2 − E (B 1 − E (B 2 − E(B 3 − EB 4 ))) , (2.214)E 0 = T E / ˘T 0 , (2.215)y = 1/(γ + 1) , (2.216)B 4 = (1 − 2y) 3 , (2.217)B 3 = B 4 + (1 − 2y) 2 , (2.218)B 2 = (1 − 2y)(3 + y 2 ), (2.219)B 1 = 2 − y 2 . (2.220)(Note that EGS uses variable YY to avoid conflict with the variable name of the y-coordinate ofparticle.)The sampling method is as follows:1. Compute parameters depending on Ĕ0 but not E: E 0 , β, γ, B 1 , B 2 , B 3 , and B 4 .2. Sample E from f(E) usingE = E 0 /[1 − (1 − E 0 )ζ 1 ]. (2.221)3. Compute the rejection function g(E). If ζ 2 > g(E), reject and return to Step 2.The rest of the procedure is similar that used in sampling from the Møller cross section exceptthat now the delta ray may have the most energy, in which case the contents of the two top locationsof the EGS particle stack must be interchanged to ensure that the particle with the lower energywill be tracked first.2.12 Two Photon Positron-Electron AnnihilationThe two photon positron-electron annihilation cross sections in EGS are taken from Heitler[71] (seep. 268-270 therein). Using Heitler’s formula 6 (on p. 269), translating to the laboratory frame,69