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has been introduced for the corrections 56,57,58) . Since the quantity, a, usually referred to as the Bell or
Levine factor, somewhat fluctuates among resonance levels, there might be some minor problems with
the choice. The exact choice of this quantity is not thought to be important, considering from the
results of many studies done in this field 58) . The values adopted in the SRAC system for the geometric
quantities are shown in the following table.
Table 7.3.2-1
Levine or Bell Factors
l f
Geometry
a
Remarks
Sphere of radius r 4r/3 1.4 cf. 27), 59)
Slab of thickness r 2r 1.2 cf. 27), 19)
Infinite cylinder of radius r 2r 1.2 cf. 56), 57)
Infinite hollow cylinder of
inner radius a and outer
radius b, sinθ=a/b
2rcos 2 θ 1.2 cf. 59), 60)
The Dancoff correction factor and associated quantities will be in more general form discussed
for multi-region problems in the next subsection.
Substituting Eq.(7.3.2-6) into Eq.(7.3.2-4) and subtracting Eq.(7.3.2-5) from the resulting
equation, we obtain the following set of equations for neutron balance:
∑{ Rk
K
k
(
m
}
( σ + s ) ϕ = σ K ( ϕ ) + K ( σ ϕ ) + s ϕ )
(7.3.2-11)
f
f
am
am
f
∑{ Rk
K
k
(
m
}
f
s
f
s ϕ = σ ϕ + ( s − σ ) ϕ )
(7.3.2-12)
f
m
m
m
k
Then, from the two extreme cases representing the limits of NR and WR, respectively, for the
slowing down kernels, the first-order solution for ϕ f and ϕ m can be written as 21)
ϕ
*
(1)
f *
a s am
k
λσ p + κσ am + μ s
( u)
= (7.3.2-13)
σ + λσ + κσ + μ s
with
(1)
(1)
{ 1 − ϕ ( u)
} { μσ + (1 − μ s
ϕ m ( u)
= 1 − s f
m ) } (7.3.2-14)
*
μ = μσ /
m
{ μσ m + (1 − μ)
s} and μ = ∑
k
R μ
k
k
(7.3.2-15)
where μ k is the IR parameter for the outside moderator k. Here, a set of the IR parameters can be
determined by the same procedure as those in a homogeneous system 21) .
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