THE EGS5 CODE SYSTEM

We proceed now by using Equation 2.91 to eliminate the ˆφ j from Equation 2.78 and Equation2.79 yieldingÂ(∆ E , Ĕ0) = [ 3φ 1 (δ ′ ) − φ 2 (δ ′ ) ] Z T()+8 Z B − (Z F if Ĕ 0 > 50, 0) , (2.94)()ˆB(∆ E , Ĕ0) = φ 1 (δ ′ )Z T + 4 Z B − (Z F if Ĕ 0 > 50, 0) . (2.95)If these are now used in Equations 2.89 and 2.90 we obtainA(δ ′ ) = 3φ 1(δ ′ ) − φ 2 (δ ′ ) + 8(Z V if Ĕ 0 > 50, Z G )]23[ln + 8 (2.96)183 + (Z V if Ĕ 0 > 50, Z G )B(δ ′ ) =φ 1 (δ ′ ) + 4(Z V if Ĕ 0 > 50, Z G )[]4 ln 183 + (Z V if Ĕ 0 > 50, Z G ) .We now return to Equation 2.77 which we were trying to factor. We have{ ( )}d˘Σ Brem2 1 − E=dE3 A(δ′ )Âmax(Ĕ0) + B(δ ′ )EˆB max (Ĕ0) E1×4(Z AB − Z F ){ ( ) [ 2 1 − E 2 () ]=3 A(δ′ )E 3 Z T + 8 Z A + Z B − (Z F if Ĕ 0 > 50, 0)}+ B(δ ′ 1)E [4(Z A + Z B − (Z F if E 0 > 50, 0))]4(Z AB − Z F )==××[Z A + Z B − (Z F if Ĕ 0 > 50, 0)](Z AB − Z F ){[1 Z T9 [Z A + Z B − (Z F if Ĕ 0 > 50, 0)] + 4 ] ( ) 1 − EA(δ ′ )3E}+B(δ ′ )E(2.97)[Z A + Z B − (Z F if Ĕ 0 > 50, 0)](Z AB − Z F ){[ ( )]4ln 23 + 19ln 183[1 + (Z U if Ĕ 0 > 50, Z P )][ ( )] [ }1 1 − E1×[A(δ ′ )] + [2E][B(δln 2 E2]′ )] . (2.98)We then see that for Ĕ0 ≤ 50, the case dealt with in Butcher and Messel[39] , we have{ [ ( )] [ ( )]d˘Σ Brem4= ln 2dE3 + 11 1 − E[A(δ ′ )]9ln 183(1 + Z P ) ln 2 E[ ]} 1+ [2E][B(δ ′ (ZA + Z B ))]. (2.99)2 (Z AB − Z F )48