THE EGS5 CODE SYSTEM

Scott’s formula (7.25) for χ α is
where
∫ t
χ 2 c ln χ α = 4π
0
dt ′
k 2 (t ′ )
N e ∑
i=1
N i α 2 i
[
ln χ α1 +
]
ln χel i
Z i
. (2.306)
k = p/¯h, (2.307)
p = particle momentum,
N i =
N a ρ
M p i = density of atoms of type i, (2.308)
α i = αZ i /β = Z i e 2 /¯hν , (2.309)
χ αi = the screening angle for atoms of type i,
[
= χ 2 0(1.13 + 3.76α 2 1/2
i )]
, (2.310)
χ 0 =
¯λ 0
,
r TF
(2.311)
¯λ 0 = λ 0 /2π = ¯h/p = wavelength of electron/2π, (2.312)
r TF = Thomas − Fermi radius of atom
= 0.885 a 0 Z −1/3
i , (2.313)
a 0 = Bohr radius = ¯h 2 /m e e 2 (2.314)
χ el
i = screening angle for the atomic
atoms of type i.
The next step is to let β = 1 in the α i that are in the χ αi , to delete the term with χ el
i , and to let
Zi 2 → Z i(Z i + ξ MS ). Recalling that p = Eβ/c, Equation 2.306 now becomes
χ 2 c ln χ α = N [
aρ ∑ Ne
M 4πe4
i=1
p i Z i (Z i + ξ MS ) ln χ αi
] ∫ t
Since e 2 = r 0 m e c 2 , and using Equation 2.301, we obtain
χ 2 c ln χ α = N [ Ne
]
aρ ∑
M 4πr2 0 p i Z i (Z i + ξ MS ) ln χ αi
i=1
Dividing by Equation 2.300 and multiplying by 2, we get
[ Ne
ln χ 2 α = ∑
i=1
But using Equations 2.310 through 2.314,
ln χ 2 0 = ln [
ln χ 2 α i
= ln χ 2 0 + ln
¯h 2 m 2 ee 4
p 2 (0.885) 2¯h 4 Z −2/3
i
p i Z i (Z i + ξ MS ) ln χ 2 α i
]
0
dt ′
E 2 β 4 . (2.315)
m 2 t
. (2.316)
ĔMS 2 β4
Z −1
S
. (2.317)
[
1.13 + 3.76(αZ i ) 2] , (2.318)
] [
]
m 2
= ln
ee 4
p 2¯h 2 − ln Z −2/3
(0.885) 2 i , (2.319)
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