THE EGS5 CODE SYSTEM

ρ = material mass density (g/cm 3 ) , (2.295)
M = molecular weight =
χ cc = ‘22.9′
(180/π)
χ c = χ √
cc t
N e ∑
i=1
p i A i , (2.296)
Ĕ MS β , (2.297)
2
√
ρZ S
M (cm−1/2 MeV ) (2.298)
(
Note, PEGS computes χ cc = χ cc
√
X0 (r.l. −1/2 MeV )
‘22.9 ′ = (180/π) √ 4πN a r 0 m = 22.696 (cm MeV ) . (2.299)
Ĕ MS is the energy (in MeV) of the electron that is scattering and may be set equal to the energy at
the beginning or end of the step (or something in between) to try to account for ionization loss over
the step. Equations 2.297 through 2.299 are based on formula 7.4 of Scott[147] which is equivalent
to
χ 2 c = N [
aρ ∑ Ne
M 4πr2 0
i=1
p i Z i (Z i + ξ MS )
] ∫ t
From this we see that, to be proper, we should replace √ t/ĔMSβ 2 using
√ ( ∫ t
t
Ĕ MS β = 2 0
0
)
,
m 2 dt ′
Ĕ(t ′ ) 2 β(t ′ ) 4 . (2.300)
dt ′
Ĕ(t ′ ) 2 β(t ′ ) 4 ) 1/2
, (2.301)
where Ĕ(t′ √
) is the particle’s energy (in MeV) after going a distance t ′ along its path. Likewise,
β(t ′ ) = 1 − m 2 /Ĕ(t′ ) 2 is the particle’s velocity, at the same point, divided by the speed of light.
We assume that our steps are short enough and the energy high enough that Equations 2.297
through 2.299 are sufficiently accurate.
For completeness, we give a derivation of Equations 2.292. We start with the definition of Ω 0 ,
(which differs somewhat from Scott’s definition),
According to Bethe’s formula (22)
Ω 0 ≡ e b . (2.302)
e b = χ2 c
χ 2 α ′ =
χ 2 c
‘1.167 ′ χ 2 α
. (2.303)
From the derivation in Bethe it is seen that
‘1.167 ′ = e 2C−1 (2.304)
where
C = 0.577216 is Euler ′ s constant. (2.305)
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