Civil Engineering Reference
In-Depth Information
!
and to N
n
!
v
;
v
; Ω
dV
σ
(v) is a measure for the probability of the nuclear
reactions and is called microscopic cross section of the nucleus for a specific type of
reaction. The microscopic cross section
The proportionality factor
(v) is measured in 10
24
cm
2
1 barn. It
is a function of the velocity, v, or kinetic energy, E, of the neutron and of the type of
reaction and differs for every type of atomic nucleus. As for an absorption reaction
the neutron can either remain captured or lead to fission of a heavy nucleus the
relation
σ
≙
σ
a
v
ðÞ¼σ
c
v
ðÞþσ
f
v
ðÞ
Is valid with
σ
a
(v) microscopic absorption cross section
σ
c
(v) microscopic capture cross section
σ
f
(v) microscopic fission cross section
The reaction rate can be written
v
N
!
v
v
v
R
!
n
!
!
!
;
¼ σ
ðÞ
v
v
;
¼ Σ
;
ϕ
;
v
!
The quantity
Σ
;
¼
N
σ
ðÞ
v
is called macroscopic cross section.
v
is called the neutron flux.
Figure
2.3
shows the microscopic fission cross section as a function of the
neutron kinetic energy for the heavy nuclei U-235, U-238 and Pu-239. The fission
cross sections for U-235 and Pu-239 increase with decreasing kinetic energies. In
the energy region of about 0.1-10
3
eV this behavior is superposed by resonance
cross sections [
12
-
14
].
The capture cross section for U-238 is shown in Fig.
2.4
.
Neutron capture in U-238 leads to U-239 and after
v
!
n
!
The quantity
ϕ
;
¼
v
;
β
-decay to Np-239 which
again decays to Pu-239.
n
,
γ
β
β
238
239
239
239
92
U
!
92
U
!
93
Np
!
94
Pu
23
:
5min
2
:
35 d
Such microscopic cross sections (measured in barn) are steadily compiled,
evaluated, supplemented and revised in nuclear data libraries [
15
-
17
].
The capture cross section of U-238 (Fig.
2.4
) shows distinct narrow resonance
peaks above about 5 eV. At medium neutron energies (keV range) the resonance
peaks become smaller and above about 10 keV—in the so-called unresolved
resonance energy range—they cannot be resolved any more by experiments
because of resonance overlapping. These resolved and unresolved resonance
peaks broaden if the temperature of the U-238 fuel increases. This phenomenon
