138
C. H. Pyeon
neutrons in the specified Pb–Bi-zoned fuel region from (14-13, L; y 1 ) to (14-13, O;
y 2 ) shown in Figs. A2.16a–d, with an interpretation similar to the Cd ratio mentioned
in Sect. 5.3.1 as follows:
235 U fission ratio =
y 2
y 1
R
thermal
U −fission (x 0 , y, z 0 )dy
y 2
y 1
R
fast
U −fission (x 0 , y, z 0 )dy
,
(5.10)
where R
thermal
U −fission and R
fast
U −fission indicate
235 U(n, f ) reaction rates in the thermal (less
than 0.1 eV) and fast (more than 0.1 MeV) neutron regions, respectively.
The numerator in Eq. (5.10) is expressed as follows, with the assumption as
discussed in Sect. 5.1.1:
y 2
y 1
R R
thermal
U −fission (x 0 , y, z 0 )dy = C
thermal
fission
y 2
y 1
R
thermal
I n (n,γ ) (x 0 , y, z 0 )dy,
(5.11)
where C
thermal
fission indicates the proportionality coefficient of cross sections between
115 In(n, γ)
116m In and
235 U(n, f ) reactions in the thermal neutron region. Similarly,
the denominator in Eq. (5.10), by a new assumption of the proportionality of the
In inelastic scattering (threshold energy 0.4 MeV) and
235 U fast fission reactions, is
written as follows:
y 2
y 1
R
fast
U −fission (x 0 , y, z 0 )dy = C
fast
fission
y 2
y 1
R
fast
I n(n,n ) (x 0 , y, z 0 )dy,
(5.12)
where C
fast
fission indicates the proportionality coefficient of cross sections between
115 In(n, n
)
115m In and
235 U(n, f ) reactions in the fast neutron region, although the
assumption of proportionality in the fast neutron region is somewhat complicated
from the viewpoint of the characteristics of cross sections. On the basis of Eqs. (5.11)
and (5.12), the results of C
thermal
fission and C
fast
fission were found to be nearly constant around
1.11 and 6.25, respectively, with the MCNP fixed-source calculations.
Generally, in the experiments, while it is apparently difficult to measure
235 U(n, f )
reaction rates directly, a convenient alternative is to introduce the proportionality of
cross sections discussed in Sect. 5.1.2. Subsequently, special attention was directed to
the property of In wire reaction rates to experimentally obtain neutron flux information on both thermal and fast energy regions simultaneously. Assuming that the
235 U
fission ratio in Eq. (5.9) corresponds approximately to the ratio of
115 In(n, γ)
116m In
and
115 In(n, n
)
115m In reaction rate distributions, a new spectrum index of the In ratio
is, by introducing the coefficients of C
thermal
fission and C
fast
fission , defined as follows:
In ratio =
C
thermal
fission
y 2
y 1
R
thermal
In(n,γ ) (x 0 , y, z 0 )dy
C
fast
fission
y 2
y 1
R
fast
In(n,n ) (x 0 , y, z 0 )dy
.
(5.13)
C. H. Pyeon
neutrons in the specified Pb–Bi-zoned fuel region from (14-13, L; y 1 ) to (14-13, O;
y 2 ) shown in Figs. A2.16a–d, with an interpretation similar to the Cd ratio mentioned
in Sect. 5.3.1 as follows:
235 U fission ratio =
y 2
y 1
R
thermal
U −fission (x 0 , y, z 0 )dy
y 2
y 1
R
fast
U −fission (x 0 , y, z 0 )dy
,
(5.10)
where R
thermal
U −fission and R
fast
U −fission indicate
235 U(n, f ) reaction rates in the thermal (less
than 0.1 eV) and fast (more than 0.1 MeV) neutron regions, respectively.
The numerator in Eq. (5.10) is expressed as follows, with the assumption as
discussed in Sect. 5.1.1:
y 2
y 1
R R
thermal
U −fission (x 0 , y, z 0 )dy = C
thermal
fission
y 2
y 1
R
thermal
I n (n,γ ) (x 0 , y, z 0 )dy,
(5.11)
where C
thermal
fission indicates the proportionality coefficient of cross sections between
115 In(n, γ)
116m In and
235 U(n, f ) reactions in the thermal neutron region. Similarly,
the denominator in Eq. (5.10), by a new assumption of the proportionality of the
In inelastic scattering (threshold energy 0.4 MeV) and
235 U fast fission reactions, is
written as follows:
y 2
y 1
R
fast
U −fission (x 0 , y, z 0 )dy = C
fast
fission
y 2
y 1
R
fast
I n(n,n ) (x 0 , y, z 0 )dy,
(5.12)
where C
fast
fission indicates the proportionality coefficient of cross sections between
115 In(n, n
)
115m In and
235 U(n, f ) reactions in the fast neutron region, although the
assumption of proportionality in the fast neutron region is somewhat complicated
from the viewpoint of the characteristics of cross sections. On the basis of Eqs. (5.11)
and (5.12), the results of C
thermal
fission and C
fast
fission were found to be nearly constant around
1.11 and 6.25, respectively, with the MCNP fixed-source calculations.
Generally, in the experiments, while it is apparently difficult to measure
235 U(n, f )
reaction rates directly, a convenient alternative is to introduce the proportionality of
cross sections discussed in Sect. 5.1.2. Subsequently, special attention was directed to
the property of In wire reaction rates to experimentally obtain neutron flux information on both thermal and fast energy regions simultaneously. Assuming that the
235 U
fission ratio in Eq. (5.9) corresponds approximately to the ratio of
115 In(n, γ)
116m In
and
115 In(n, n
)
115m In reaction rate distributions, a new spectrum index of the In ratio
is, by introducing the coefficients of C
thermal
fission and C
fast
fission , defined as follows:
In ratio =
C
thermal
fission
y 2
y 1
R
thermal
In(n,γ ) (x 0 , y, z 0 )dy
C
fast
fission
y 2
y 1
R
fast
In(n,n ) (x 0 , y, z 0 )dy
.
(5.13)