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where λ and
i
n m≠n
*
i
n
i
n
i
n
i 1
i i μ g(
C )(1 − C )
σ 0, n
= ∑ ( λm
N
mσ
t,
m
) +
(1.6-5)
i
N
N L
*
μ
are the IR parameters which are obtained by solving the transcendental
equations. 21) In the current version, as the energy range where the resonance parameters are prepared
for the calculation of the IR parameters is limited from 0.419eV to 130.07eV, the NR approximation is
inevitably applied above the upper range even if the IR approximation is selected. The IR
approximation is applied to the restricted major fertile nuclides such as Th-232, U-238 and Pu-240.
1.6.3 Direct Calculation on Hyper-fine Energy Group Structure (PEACO)
A direct cell calculation on hyper-fine energy group structure to the heterogeneous lattice cell is
available by the collision probability method. The following slowing-down equations on the ultra-fine
lethargy mesh (Δu) of about 10 -3 -10 -4 are solved by the PEACO routine 7) to obtain the hyper-fine
spectra as shown in Fig.1.6-1.
V Σ ( u)
ϕ ( u)
=
i
i
i
J
∑
P ( u)
V
N
∑
ji j
j= 1 n=
1
S
jn
( u)
(1.6-6)
S
jn
u
1
( u)
= ∫ exp{ − ( u − u'
)}
Σ sjn ( u'
) ϕ j ( u'
) du'
(1.6-7)
1 − α
n u−ε
n
α
n
⎧ A
− 1 ⎫
2 , ε = − lnα
⎭
n
= ⎨ ⎬
n
n
(1.6-8)
An
+ 1
⎩
where the subscripts i, j denote the region
numbers, n the nuclide, P ji (u) the probability that
a neutron scattered isotropically in the region j
has the first collision in region i, S jn (u) the
slowing-down source. The neutron spectrum
ϕ i (u) is numerically calculated by the
recurrence method developed by Kier. 22)
The effective fine-group cross-sections are
directly calculated with ϕ (u)
and hyper-fine
cross-sections. The use of the PEACO routine is,
in principle, limited to the system which
i
includes one or two different resonance Fig.1.6-1 Neutron spectra by PEACO
14