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and V = V + V ,
F
f
m
where Σ m , is the macroscopic cross-section of the graphite diluent, and V f and V m are the volumes of
the grain and the associated diluent, respectively. Since we treat only one kind of medium with grain
structure, we drop the subscript I for simplicity.
Insertion of Eqs.(7.3.5-5) and (7.3.5-6) into Eq.(7.3.5-7) gives the equivalent cross-sections of
the fuel compact, Σ F as
( V f Σ + V Σ ) .
1
Σ F = f f m m
(7.3.5-8)
V
When one of four variables;
F
f , Σ , , or α is given, then the rest is determined by the relations
F
α f
m
expressed by Eqs.(7.3.5-5), (7.3.5-6), and (7.3.5-7).
Using the newly defined variables, Eqs.(7.3.5-3) and (7.3.5-4) can be rewritten, respectively, as
P
IJ ( lI
kJ
IJ
l,
k)
= f α P ,
(7.3.5-9)
P
II ( I
lI
kl II
l,
k)
= Q ( l,
k)
− f α (1 − P ) ,
(7.3.5-10)
where f f for the fuel grain, and f = 1 for the diluent.
lI
= lI
When the collision probability is given, Eqs.(7.3.5-1) and (7.3.5-2) can be solved recurrently on
hyper-fine groups in the dominant resonance energy range, E