JAEA-Data/Code 2007-004 - Welcome to Research Group for ...

If a group-dependent form of Fick’s law is postulated, i.e.,
J
( r)
= − ( r)
∇Φ
( r)
g D g
g
(7.2-5)
then from Eq.(7.2-4) the diffusion coefficient can be formally expressed by
with
D g
Σ
1
( r)
= (7.2-6)
3Σ
( )
( r)
≡ Σ
tr, g r
−
Σ
tr, g t,
g ∑ s1,
g ' →g
J g ' g r
g '
( r) / J ( )
(7.2-7)
If the group width is wider compared with the maximum energy degradation of neutron by
elastic collision and the quantity EJ(r, E) can be assumed to be energy-independent in the width, we
can show 52)
∑
g '
Σ
in this case, we have
∑
( r ) / J ( r)
≅ Σ = ( μ Σ
(7.2-8)
s1 , g ' →g
J g ' g
s1,
g→g'
) g
g'
s,
g
Σ
tr, g ( r)
= Σ
t,
g
−
∑
g '
Σ
s1,
g→g'
(7.2-9)
Four methods are prepared to define the transport cross-section to be used as total cross-sections
in the isotropic transport calculation or diffusion calculation.
(1) Optional Process IC16 = 0
The first one treats simply the anisotropic scattering effect in the isotropic transport calculation
by the extended transport approximation 23) . Here, the macroscopic transport cross-section is defined
by
Σ
tr,
g
= Σ
t,
g
−
∑
g'
Σ
s1,
g→g'
(7.2-10)
It should be noted that the total cross-section, instead of the transport cross-section, is used to
calculate the collision probability in the second resonance range, where the ultra-fine spectrum is
calculated by assuming isotropic neutron scattering.
(2) Optional Process IC16 = 1 or 2
The second and third methods are based on the P 1 and B 1 approximation, respectively, for fast
neutron spectrum calculation in homogeneous media 24) . By choice of the option IC16= 1 or 2, the
system under study is, first, homogenized by simple smearing of the atomic number densities in the
cell, if IC2>0 is specified, and the P 1 and B 1 equations are solved by assuming an appropriate buckling.
247