56
2 Critical Mass, Efficiency, and Yield
0
100
200
300
400
500
600
700
800
1
2
3
4
5
6
7
8
9
10
fission cross-section (bn)
Energy (eV)
Fig. 2.3 Cross-section for the 235 U(n, f) reaction over the energy range 1-10 eV. At 0.01 eV (off
the left end of the graph), the cross-section for this reaction is about 930 bn. Data from National
Nuclear Data Center. See also Figs. 1.11 and 3.1
x
No
incident
neutrons
Ne
escaping
neutrons
dx
x = 0
x = L
Fig. 2.4 Neutrons penetrating a target of thickness L
x = L will be P react = 1 − e
−σ nL . It follows that if N o neutrons are incident at the
x = 0 face, then the number that will be consumed in reactions within the slab will
be N react = N o
1 − e
−σ nL
. We will use this result in a moment.
Also from (2.7), the number of neutrons that penetrate to distances x and x + dx
are given by
N x = N o e
−σ n x
(2.9)
and
N x+dx = N o e
−σ n(x+dx)
.
(2.10)
2 Critical Mass, Efficiency, and Yield
0
100
200
300
400
500
600
700
800
1
2
3
4
5
6
7
8
9
10
fission cross-section (bn)
Energy (eV)
Fig. 2.3 Cross-section for the 235 U(n, f) reaction over the energy range 1-10 eV. At 0.01 eV (off
the left end of the graph), the cross-section for this reaction is about 930 bn. Data from National
Nuclear Data Center. See also Figs. 1.11 and 3.1
x
No
incident
neutrons
Ne
escaping
neutrons
dx
x = 0
x = L
Fig. 2.4 Neutrons penetrating a target of thickness L
x = L will be P react = 1 − e
−σ nL . It follows that if N o neutrons are incident at the
x = 0 face, then the number that will be consumed in reactions within the slab will
be N react = N o
1 − e
−σ nL
. We will use this result in a moment.
Also from (2.7), the number of neutrons that penetrate to distances x and x + dx
are given by
N x = N o e
−σ n x
(2.9)
and
N x+dx = N o e
−σ n(x+dx)
.
(2.10)