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2.10 Reaction Rate Calculation
The input of this section is optionally required if IC18=1 (Sect.2.2) is specified for the reaction
rate calculation.
A common edit can be executed after any component routine for flux distribution (PIJ, ANISN,
TWOTRAN, TUD or CITATION). The edit routine REACT permits the calculation of reaction
(capture, fission) rate distribution of the detector with or without the filter.
(a) The reaction rate (cm -3 sec -1 ) of the detector without filter is calculated as follows:
r
R(
) =
IGMAX
∑
g=
1
r
Σ x, gΦg(
)
(2.10-1)
where IGMAX is number of energy group, and x means reaction type (e.g. capture, fission, etc.).
(b) The reaction rate (cm -3 s -1 ) of the detector with filter:
r
R(
) =
IGMAX
∑
g=
1
r
f g Σ Φg(
x, g )
, where f g is filter transmission factor (2.10-2)
By adjusting f g , the integration range can be modified. The reaction types edited by (a) and (b)
are Fission, Capture and Absorption (A=F+C).
(c) Spectrum index
As shown in the following equations (2.10-3) through (2.10-8), the fission reaction rate (F),
capture rate (C) of nuclide μ in epi-thermal range (epi), thermal energy range (th) and whole energy
range (all) are calculated as:
F = ∫ ∞
N
μ σ μ ( E)
ϕ(
E)
dE , (2.10-3)
epi
E Cd
f
μ , (2.10-4)
F
th
= ∫
0
E Cd
μ
N σ μ ( E)
ϕ(
E)
dE
f
μ , (2.10-5)
μ
all
μ
th
F = F + F
μ
epi
C = ∫ ∞
N
μ σ μ ( E)
ϕ(
E)
dE , (2.10-6)
epi
E Cd
c
μ , (2.10-7)
C
th
= ∫
0
E Cd
μ
N σ μ ( E)
ϕ(
E)
dE
c
μ 129