bei48482_FM

Denoting the initial number of incident particles by N 0 , we have



N

N 0

n

x

0

dx

lnNlnN 0 nx (12.20)

Surviving particles NN 0 enx

The number of surviving particles Ndecreases exponentially with increasing slab

thickness x.

The customary unit for nuclear cross sections is the barn,where

1 barn1 b 10 ^28 m^2 100 fm^2

Although not an SI unit, the barn is handy because it is of the same order of magnitude

as the geometrical cross section of a nucleus. The name comes from a more familiar

target cross-sectional area, the side of a barn.

The cross sections for most nuclear reactions depend on the energy of the incident

particle. Figure 12.14 shows how the neutron-capture cross section of^11348 Cd varies

with neutron energy. This reaction, in which the absorption of a neutron is followed

by the emission of a gamma ray, is usually expressed in shorthand form as

(^113) Cd(n,) (^114) Cd
The narrow peak at 0.176 eV is a resonance effect associated with an excited state in
the^114 Cd nucleus. Although the^113 Cd isotope constitutes only 12 percent of natural
cadmium, its capture cross sections for slow neutrons are so great that cadmium is
widely used in control rods for nuclear reactors.
dN

N
Nuclear Transformations 443
0.001 0.01 0.1 11 10
Neutron energy, eV
10
103
102
104
105
Cross section, b
Figure 12.14The cross section for the reaction^113 Cd(n,)^114 Cd varies strongly with neutron energy.
In this reaction a neutron is absorbed and a gamma ray is emitted.
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