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The lattice cell under study may consist of several materials and each may be subdivided into
several spatial regions. The resonance-absorbing isotopes are contained in some materials
(fuel-materials) and other materials are assumed to have constant cross-sections. Now, for such a
system we select a resonance absorber, say 238 U and define the microscopic resonance cross-section
per the absorber under consideration in the fuel materials by
1
σ I ( E)
= ∑ N Ikσ
k ( E)
( N I ≠ 0)
(7.3.4-13)
N
I
k
where I corresponds to the fuel material, the summation on k is extended over all the resonance
absorbers, σ k (E) is the microscopic total cross-section of the k-th absorber, and N I and N Ik are the
atomic number densities of the absorber under consideration and of the k resonance absorber in the
I-th material, respectively.
Some fuel materials may have the same relative densities N Ik / N I , hence the same value for
σ (E) . In such materials, the value of σ (E)
can be considered as a common variable to express
I
I
the macroscopic total cross-sections. There may be another possibility to find such an independent
variable in other fuel materials. In the present treatment, it is assumed that the macroscopic total
cross-sections can be expressed or be approximated by using at most two such independent variables.
Now, let us denote by Σ 0J the smallest macroscopic total cross-section made by the non-resonant
isotopes in the fuel material J belonging to the independent variable σ (E)
. Let us introduce new
variables defined by
X J = ( N Jσ J + Σ 0 J ) l J
( J = 1, JMAX)
(7.3.4-14)
where JMAX is the number of the independent variables (JMAX ≤ 2) and l J is a parameter with
dimension of length introduced to define the non-dimensional variable X J and assumes the averaged
value of double widths of the regions which belong to the variable σ J (E)
. Then, the collision
probability, P ji (u) in Eqs.(7.3.4-1) or (7.3.4-5) can be considered to be a function of X J (J=1, JMAX).
In the routine ’PEACO’, two kinds of computational methods are adopted for the calculation of
X J (J=1, JMAX). In the first method which is used for the values of X 1 , X 2 ≤ 9, P ji (X 1 , X 2 ) needed for
the interpolation are calculated by calling the routine ‘PIJ2’. The second one uses the asymptotic
expansion of P ji (X 1 , X 2 ) when either X 1 or X 2 ≥ 9.
J
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