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7.5.1 Smearing
Smearing or spatial average of cross-sections is achieved in the MIXX routine by using the
spatial distribution of the flux ϕ i,g obtained by the cell calculation as described in Sect.7.4.
When the second resonance energy range below 130.07eV (or 961.12eV ) is treated by the
direct method described in Sect.7.3 using the PEACO routine, the effective cross-sections in each
region and the fluxes with multi-group structure obtained by Eq.(7.4.1-1) are replaced by those from
the PEACO routine.
∑
Σ z, I , g = Σ V ϕ ( Φ I , gV
)
(7.5-1)
i∈I
∑
i∈I
z,
m,
g
i
i,
g
I
ν Σ f , m,
g = νΣ
V ϕ ( Φ I , gV
)
(7.5-2)
∑
f , m,
g
∑
i
i,
g
I
∑∑
χ (7.5-3)
I , g
= χ m,
g νΣ
f , m,
g ' Viϕi,
g ' νΣ
f , m,
g ' Viϕi,
g '
i∈I
g '
i∈I
g'
Σ
∑
→g
' = Σ V ϕ ( Φ I , gV
)
(7.5-4)
sl, I , g
sl,
m,
g→g
' i i,
g
I
i∈I
Benoist presented a theory of the diffusion coefficient in reactor lattice, leading to expressions
valid in full generality 25) . For the diffusion coefficient of the direction k, omitting the absorption
correction and angular terms, this theory gives
D ϕ ) .
(7.5-5)
= ∑∑Vi
i,
g λ j,
g Pijk
, g 3∑
k , g
( Vi
ϕ i,
g
i j i
where i and j stand for the region number, λ j,g the transport mean free path for region j given by 1/Σ tr,m,g
and P ijk,g is a directional first flight collision probability given by Eq.(7.1-16).
Three options are provided for calculating the diffusion coefficient D k,g .
(1) Optional Process IC17 = 1
The first option is a rather sophisticated one which has been proven by experience to be fairly
accurate, and the diffusion coefficient is given by the inverse of the cell averaged transport
cross-section, i.e.,
D
h
∑ ∑ , g =
Σ
i
V ϕ 3 V ϕ .
(7.5-6)
i
i,
g
( i i,
g tr,
m,
g )
i
When the flux ϕ i,g are flat in the whole system and we can assume
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