THE EGS5 CODE SYSTEM

Also, recall from Table 2.1 the definition of Z B and Z F . We then can rewrite Equation 2.76 as
Now let
and
d˘Σ Brem
d˘k
{ ( ) [
= 2
3
3 ˆφ
(
)]
1 (∆ E ) − φ 2 (∆ E ) + 8 Z B − (Z F if Ĕ 0 > 50, 0)
( ) [ (
)] }
× 1−E
E
+ ˆφ1 (∆ E ) + 4 Z B − (Z F if Ĕ 0 > 50, 0) E
×
1
4(Z AB −Z F ) . (2.77)
Â(∆ E , Ĕ0) = 3 ˆφ 1 (∆ E ) − ˆφ 2 (∆ E ) + 8(Z B − (Z F if Ĕ 0 > 50, 0)) (2.78)
ˆB(∆ E , Ĕ 0 ) = ˆφ 1 (∆ E ) + (Z B − (Z F if Ĕ 0 > 50, 0)). (2.79)
One can show that φ j (δ) have their maximum values at δ = 0, at which they take values[39]
φ 1 (0) = 4 ln 183 (2.80)
φ 2 (0) = φ 1 (0) − 2/3 . (2.81)
The ˆφ j (∆ E ) also are maximum at ∆ E = 0 and, in fact (see Table 2.1),
ˆφ 1 (0) =
ˆφ 2 (0) =
N e ∑
i=1
∑N e
i=1
p i Z i (Z i + ξ i )φ 1 (0) = 4Z A , (2.82)
p i Z i (Z i + ξ i )φ 2 (0) = 4Z A − 2 3 Z T . (2.83)
The maximum values of  and ˆB are now given by
(
 max (Ĕ0) = Â(0, Ĕ0) = 3(4Z A ) − 4Z A − 2 )
3 Z T
(
)
+ 8 Z B − (Z F if Ĕ 0 > 50, 0)
= 2 3 Z T + 8(Z A + Z B − (Z F if Ĕ 0 > 50, 0)) , (2.84)
ˆB max (Ĕ0) = ˆB(0,
(
)
Ĕ0) = 4 Z A + Z B − (Z F if Ĕ 0 > 50, 0) . (2.85)
Now define δ ′ as the weighted geometric mean of the δ i ; that is,
δ ′
≡
( Ne
∏
= exp
i=1
{
) [∑ ] Ne
δ p i=1 p −1
iZ i (Z i +ξ i )
iZ i (Z i +ξ i )
i
Z −1
T
N e ∑
= 136 m∆ E exp
i=1
{
p i Z i (Z i + ξ i )ln δ i
}
Z −1
T
N e ∑
i=1
}
p i Z i (Z i + ξ i )ln Z −1/3
i
= 136 m∆ E exp (Z B /Z T ) = 136 m e Z G
∆ E .
(2.86)
Or if we define
∆ C = 136 m e Z G
, (2.87)
46