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where
X = 2R
p
( Σ
C = 2R
πρ R
p
F
F(
x)
= 1 − 2 1
f
− Σ m ) ,
2
F{ 2R
( Σ − Σ ) }
f
2
{ − (1 + x) exp( −x)
}/
x ,
f
m
,
R p , the radius of the coated particle, and ρ is the number density of particles. The equivalent
cross-section corresponds to the smaller root of Eq.(7.3.5-24), and is always slightly larger than
Σ
m
+ C / 2R
p .
If account is taken of the fact that F(x) is a monotonously increasing function for x > 0 and
⎧2
2
⎪ x + O(
x ) for x > 1 .
we can show that Eq.(7.3.5-24) has the proper limit values for the black limit (R f Σ f >> 1) and the
homogeneous limit ( ( Σ f − Σ m ) R f 130 eV. We take the table-look-up method for the resonance shielding factors.
73)
We adopted Segev’s expression based on the NR approximation for the background cross-section
presenting the heterogeneous ef fect, i.e. ,
1−
c a
Σe =
,
(7.3.5-26)
l 1+
c ( aβ −1)
f
Vm
/VF
and β =
,
(7.3.5-27)
V / V + (1 − C)
A / L(1
+ C(
A −1))
m
F
where a and A are the Bell or Levine factor for the microscopic and macroscopic cells, respectively,
and C and L are the Dancoff correction and the mean chord length of the macroscopic cell,
respectively.
The above treatment is incorporated into the SRAC code system together with the models
described above for the lower energy range, to yield the resonance absorption in a doubly
heterogeneous cell.
A sequence of study using the present method gives us confidence that the present approach is
straightforwardly applicable to the doubly heterogeneous system with the realistic geometry such as
LWR and LMFBR lattice cells since our treatment on the macroscopic geometry is fairly general.
This method allowing three one-dimensional (sphere, plane and cylinder) cells as optional microscopic
geometry has been incorporated in the SRAC code system.
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