1182-1183 / 2239
5.2
Making the integrals practical, summary
...d d
E
E
Ω
Ω
′
′
∫ ∫
(
)
(
)
(
)
att
prim ph, ,
scat ph, ,
ph
prim ph, ,
scat ph, ,
ph ph,
prim ph, ,
scat ph, ,
,
att
el, ,
el
el,
ph el,
prim ph, ,
sca
,
,
d d
E
E
E
E
E
E
E E
E
E
E
E
E E
E
S
E
Ω
Ω
Ω
Ω
Ω
Ω
Ω Ω
Ω
Ω
Ω
Ω
Ω Ω
Ω Φ
Φ
σ Φ
Φ
σ
Φ
Φ
Ω
Ω Φ σ
Φ
σ
Φ
Φ
′ ′
′ ′
→
′
′
→ →
′ ′
→
′
′
→ →
′
′
⋅∇
+
+ ⋅
+
=
+
∂
⋅∇ +
−
=
+
∂
∫ ∫
uur
uur
(
)
t ph, ,
el el,
el, ,
,
d d
E
E
E E
E
E
Ω
Ω
Ω Ω
Ω
σ
Φ
Ω
′ ′
′ ′
→
′
′
→ →
′
′
+
∫ ∫
( )
( )
(
)
( )
( )
( )
(
)
( )
att
N l
N l
m
m
m
m
m
m
E
E Y
E
E Y
Ω
φ
φ
Ω σ
φ
φ
Ω
⋅∇
+
+
+
=
∑ ∑
∑ ∑
uur
Setting up equations:
( )
prim ph,
scat ph,
phot
prim ph,
scat ph,
0
0
ph ph,
prim ph,
l
i
l
i
l
l
i
l
i
l
l
m l
l
m l
m
l
i
l
E
σ
φ
= =−
= =−
→
′
=
( )
( )
(
)
( )
scat ph,
0
....and similar for the electron equation
i
N l
m
m
i
l
i
l
i
E l
m l
E
E Y
E
∆
φ
Ω ∆
′ = =−
′
′
′
′
+
∑∑ ∑
9