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The choice of Eqs.(7.3.4-24), (7.3.4-26) or (7.3.4-27) depends on the values of Z 1 , Z 2 on which the
P ij (X 1 , X 2 ) is to be interpolated.
(3) Conservation and reciprocity of collision probabilities
The first-flight collision probability must satisfy the two important relations, that is, the
conservation law
∑ Pij
=1
j
for all
i
(7.3.4-28)
and the reciprocity relation 61)
V Σ P = V Σ P for all i,
j.
(7.3.4-29)
i
i
ij
j
j
ji
In the routine ‘PEACO’, at first, the values of P ij are calculated only for i ≤ j by Eqs.(7.3.4-15)
and (7.3.4-27). Then, the collision probabilities satisfying Eqs.(7.3.4-28) and (7.3.4-29) are
successively obtained by the following equations starting from i=1:
* 1 − β1
* 1 − β1
Pij = Pij
, Pji
= Pji
( j =
β
β
0
0
i,
J )
,
(7.3.4-30)
J
where β = P and β = ,
(7.3.4-31)
j=
1
j−1
*
ij 1 P ij
i=
1
0 ∑ ∑
with P = V Σ P ( V Σ ) for i j
/ . (7.3.4-32)
ij j j ji i i
<
The collision probabilities P * ij given by Eq.(7.3.4-30) will be readily known to satisfy Eqs.(7.3.4-28)
and (7.3.4-29).
Using the interpolation and the asymptotic expansion, combined with the methods mentioned
above, we can guarantee the accuracy of 0.1% for the calculation of the collision probability, including
the one resonance-absorbing mixture problem. Furthermore it should be emphasized that most of
practical problems can be executed in a computing time of the same order as the convenient method
based on the IRA.
7.3.5 Resonance Absorption in Doubly Heterogeneous System
The HTTR (High Temperature Engineering Test Reactor): an HTGR, constructed at JAEA, uses
fuel in the form of small spherical coated particles. A coated particle consists of a fuel kernel of UO 2
with an ∼600 μm diameter and several layers of pyrolytic carbon and SiC of ∼150 μm thickness. Such
coated particles, together with graphite diluent, are formed into hollow annular fuel compacts that are
packed in a graphite sleeve, and then inserted into a graphite block (See Fig.7.3.5-1).
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