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For a special case where the NRA is applicable to the slowing down of absorber, the first-order
solution can be written in the conventional form
σ p + σ b
ϕ( u)
≅
(7.3.1-3)
σ ( u)
+ σ
t
b
This first-order solution is usually adopted to construct a cross-section set of the Bondarenko
type 51) with the resonance shielding factors for use in fast reactor analysis. For the higher energy
region, say E > 130 eV, the NRA is considered to be a reasonable approximation for heavy nuclides.
That is, the flux of Eq.(7.3.1-3) does not so much deviate from the exact one of Eq.(7.3.1-1) in the
meaning of the weighting function for cross-section averaging. On the other hand, for the light and
intermediate mass nuclides with resonance structure, the SRAC library has been generated assuming
the spectrum of Eq.(7.3.1-3). In fact, no simple and convenient spectrum has been proposed to treat
these nuclides. Since the resonance structure of light and intermediate mass nuclide is of minor
importance in thermal and intermediate reactors, the present treatment will, in practice, be sufficient.
Hence, we can think of Eq.(7.3.1-3) as representing a standard form of weighting spectrum for the
higher energy regions.
For a homogeneous system including many moderator nuclides, the slowing down equation can
be written as
1
u m
s ∑ j j j
(7.3.1-4)
n
{ σ ( ) + σ } ϕ(
u)
= K(
σ ϕ)
+ n σ K ( ϕ)
t
f
j
where
σ
m
1
=
n
f
∑
j
n σ
j
j
(7.3.1-5)
and K j is the slowing down kernel for moderator j; n f and n j are the atomic number density of absorber
and moderator nuclides, respectively.
When the NRA is applicable to the slowing down of moderators (referred to as NRA moderator),
we have
{ σ t u)
+ σ m} ϕ(
u)
= K ( σ sϕ)
+ σ m
( (7.3.1-6)
Consequently, a homogeneous system with the NRA moderators has the same effective
cross-section as the homogeneous system described by Eq.(7.3.1-1). That is, the effective
cross-sections can be calculated by calculating σ m as to be used for the table-look-up of the resonance
shielding tables. Here, it should be noted that the slowing down of absorber is still accurately
estimated in the present treatment.
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