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5.2
Establishing a "transport formula"
(3) The number of particles j that are born in the scattering
interactions with medium atoms in
∆
V :
Introducing as the probability per unit path length
that a particle j' with energy E' and direction
Ω
' will produce
a secondary particle j with energy E and direction
Ω
, we
'
j
j
→
σ
have:
3
j,secondaries
'
'
' 1
d
d
d d ' d '
j
j
j
j
V E
N
L
E
→
= Ω
=
⋅
Ω
∑ ∫ ∫ ∫
σ
3
'
'
' 1
d
d ' d ' d d d
j
j
j
j
V E
E E V
→
= Ω
=
⋅ Φ Ω Ω
∑ ∫ ∫ ∫
σ
35