THE EGS5 CODE SYSTEM

and use this as the variable to be sampled instead of ˘k. The expressions for ∆ and δ then become∆ =mE2Ĕ0(1 − E)(2.70)andδ i =136 Z−1/3 iĔ 0 (1 − E)mELet us also define a variable (corresponding to DEL in EGS). (2.71)∆ E =E(1 − E)Ĕ0, (2.72)so thatδ i = 136 mZ −1/3i ∆ E . (2.73)Since overall factors do not matter let us factorize X 0 dΣ Brem /d˘k. From Equations 2.60 and 2.43with A ′ = 1, and the definition of X 0 in Table 2.1, we obtaind˘Σ BremdEdΣ Brem= X 0dE(∑ Ne=i=1∑N e= 〈×××i=1[p idσ uncorrecteddEp iZ i (Z i + ξ(Z i ))E)/ [ ]4αr0(Z 2 AB − Z F ){(1 + (1 − E) 2 )(4f c (Z i ) if Ĕ 0 > 50, 0) ] − 2 (1 − E)3φ ′ 1 (Z i, Ĕ0, δ i ) − 4 3 ln Z i −[φ ′ 2(Z i , Ĕ0, δ i ) − 4 (3 ln Z i − 4f c (Z i ) if Ĕ 0 > 50, 0) ]} 〉14(Z AB − Z F ) . (2.74)For some brevity let us useφ ′ ji for φ′ j (Z iĔ0, δ i ), f ′ ci for (f c(Z i ) if Ĕ 0 > 50, 0), and ξ i for ξ(Z i ) .Then after some rearrangement Equation 2.74 becomesNow defined˘Σ BremdE=14(Z AB − Z F )+ 8(ln Z −1/3iN e ∑i=1{ ( ) 2 [3φ′p i Z i (Z i + ξ i )3 1i − φ ′ 2i (2.75)− f ′ ci ) ] ( 1 − EE) [] }+ φ ′ 1i + 4(ln Z−1/3 i − f ci ′ ) Eˆφ j (∆ E ) =N e ∑i=1p i Z i (Z i + ξ i )φ ′ j (Z i, Ĕ0, 136 Z −1/3i m∆ E ) for j = 1, 2 . (2.76)45