THE EGS5 CODE SYSTEM

We proceed now by using Equation 2.91 to eliminate the ˆφ j from Equation 2.78 and Equation
2.79 yielding
Â(∆ 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 obtain
A(δ ′ ) = 3φ 1(δ ′ ) − φ 2 (δ ′ ) + 8(Z V if Ĕ 0 > 50, Z G )
]
2
3
[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 Brem
2 1 − E
=
dE
3 A(δ′ )Âmax(Ĕ0) + B(δ ′ )
E
ˆB max (Ĕ0) E
1
×
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 T
9 [Z A + Z B − (Z F if Ĕ 0 > 50, 0)] + 4 ] ( ) 1 − E
A(δ ′ )
3
E
}
+B(δ ′ )E
(2.97)
[Z A + Z B − (Z F if Ĕ 0 > 50, 0)]
(Z AB − Z F )
{[ ( )]
4
ln 2
3 + 1
9ln 183[1 + (Z U if Ĕ 0 > 50, Z P )]
[ ( )] [ }
1 1 − E
1
×
[A(δ ′ )] + [2E][B(δ
ln 2 E
2]
′ )] . (2.98)
We then see that for Ĕ0 ≤ 50, the case dealt with in Butcher and Messel[39] , we have
{ [ ( )] [ ( )]
d˘Σ Brem
4
= ln 2
dE
3 + 1
1 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