N
NA
M
2.699
g
cm3
6.022 x 1023atoms
mole
26.9815
g
mole
6.024 x 1022atoms
cm3
DOE-HDBK-1019/1-93
Reactor Theory (Neutron Characteristics)
NUCLEAR CROSS SECTIONS AND NEUTRON FLUX
Rev. 0
Page 7
NP-02
Example:
A block of aluminum has a density of 2.699 g/cm . If the gram atomic weight of
3
aluminum is 26.9815 g, calculate the atom density of the aluminum.
Solution:
Cross Sections
The probability of a neutron interacting with a nucleus for a particular reaction is dependent
upon not only the kind of nucleus involved, but also the energy of the neutron. Accordingly,
the absorption of a thermal neutron in most materials is much more probable than the absorption
of a fast neutron. Also, the probability of interaction will vary depending upon the type of
reaction involved.
The probability of a particular reaction occurring between a neutron and a nucleus is called the
microscopic cross section ( ) of the nucleus for the particular reaction. This cross section will
vary with the energy of the neutron. The microscopic cross section may also be regarded as the
effective area the nucleus presents to the neutron for the particular reaction. The larger the
effective area, the greater the probability for reaction.
Because the microscopic cross section is an area, it is expressed in units of area, or square
centimeters. A square centimeter is tremendously large in comparison to the effective area of
a nucleus, and it has been suggested that a physicist once referred to the measure of a square
centimeter as being "as big as a barn" when applied to nuclear processes. The name has
persisted and microscopic cross sections are expressed in terms of barns. The relationship
between barns and cm is shown below.
2
1 barn = 10
cm
-24
2
