431
where
ϕ
σ
σ
σ
π
s
s s ds
s
s
r
s
0
1
0
2
0
2
∈
( )
=
( )
( ) =
( )
∈
( )
∫
,
.
(21.35)
This result defines the dimensional variable ϕ and dimensionless cross section
σ . The variable ϕ [s 0 ] is calculated based on a detailed graphical frame for
1 < s 0 < 10. I calculated ϕ by a functional asymptotic calculation:
ϕ
β
β
ω β ω
ω
β
β
β
ω
ω
s 0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
1
4
1
2
4
[ ]=
+
−
−
−
− −
+
+
+
ln
ln
ln
ln ln
1 1
0
(
) ( )
–
,
L ω
where s 0 – 1 ≪ 1 or s 0 ≫ 1,
β
ω
β
β
ω
ω
ω
ω
ω
0
2
0
0
0
0
0
1
1
1 1
1
1
1
0
=
−
=
+
(
)
−
(
)
( )=
+
(
)
∫
−
s
L
d
,
,
ln
.
and
(21.36)
The last integral can be written as
ω
ω ω
ω
ω
ω
+
(
)=
+
( )=
+ ( )
′
1
1 1
1
2
0
2
0
0
,
l n
,
L
L
where
′ ( )=
+
=
−
−
( )
∫
∑
−
=
∞
− −
−
L
d
n n
n
n
ω
ω
ω
ω
π
ω
ω
0
1
1
2
1
1
2
0
0
1
1
12
1
ln
(21.37)
This confirmed presentation of the heating photon deliberation readily shall
allow the calculation of ϕ [s 0 ] to determine the accurate value of heating photon
production s 0 . Therefore, the correct functional asymptotic formula is expressed as
follows to confirm the heating photon production:
ϕ
π
s
s
s
s
s
s
s
0
0
0
0
0
2
0
1
0
2
4
2
4
4
2
9
3
4
9
8
[ ]=
−
(
)+
−
(
)−
−
(
) +
+
−
ln
ln
ln
ln
+ +(
)
s 0 1 ,
(21.38)
ϕ s
S
S
S
0
0
3
2
0
5
2
0
2
3
1
5
3
1
1507
420
1
[ ]=
−
(
) +
−
(
)
−
(
–
) ) + +(
)
7
2
0
1 1
s –
. (21.39)
Results and Discussion
where
ϕ
σ
σ
σ
π
s
s s ds
s
s
r
s
0
1
0
2
0
2
∈
( )
=
( )
( ) =
( )
∈
( )
∫
,
.
(21.35)
This result defines the dimensional variable ϕ and dimensionless cross section
σ . The variable ϕ [s 0 ] is calculated based on a detailed graphical frame for
1 < s 0 < 10. I calculated ϕ by a functional asymptotic calculation:
ϕ
β
β
ω β ω
ω
β
β
β
ω
ω
s 0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
1
4
1
2
4
[ ]=
+
−
−
−
− −
+
+
+
ln
ln
ln
ln ln
1 1
0
(
) ( )
–
,
L ω
where s 0 – 1 ≪ 1 or s 0 ≫ 1,
β
ω
β
β
ω
ω
ω
ω
ω
0
2
0
0
0
0
0
1
1
1 1
1
1
1
0
=
−
=
+
(
)
−
(
)
( )=
+
(
)
∫
−
s
L
d
,
,
ln
.
and
(21.36)
The last integral can be written as
ω
ω ω
ω
ω
ω
+
(
)=
+
( )=
+ ( )
′
1
1 1
1
2
0
2
0
0
,
l n
,
L
L
where
′ ( )=
+
=
−
−
( )
∫
∑
−
=
∞
− −
−
L
d
n n
n
n
ω
ω
ω
ω
π
ω
ω
0
1
1
2
1
1
2
0
0
1
1
12
1
ln
(21.37)
This confirmed presentation of the heating photon deliberation readily shall
allow the calculation of ϕ [s 0 ] to determine the accurate value of heating photon
production s 0 . Therefore, the correct functional asymptotic formula is expressed as
follows to confirm the heating photon production:
ϕ
π
s
s
s
s
s
s
s
0
0
0
0
0
2
0
1
0
2
4
2
4
4
2
9
3
4
9
8
[ ]=
−
(
)+
−
(
)−
−
(
) +
+
−
ln
ln
ln
ln
+ +(
)
s 0 1 ,
(21.38)
ϕ s
S
S
S
0
0
3
2
0
5
2
0
2
3
1
5
3
1
1507
420
1
[ ]=
−
(
) +
−
(
)
−
(
–
) ) + +(
)
7
2
0
1 1
s –
. (21.39)
Results and Discussion