N
DOE-HDBK-1019/1-93
NUCLEAR CROSS SECTIONS AND NEUTRON FLUX
Reactor Theory (Neutron Characteristics)
NP-02
Page 8
Rev. 0
Whether a neutron will interact with a certain volume of material depends not only on the
microscopic cross section of the individual nuclei but also on the number of nuclei within that
volume. Therefore, it is necessary to define another kind of cross section known as the
macroscopic cross section ( ). The macroscopic cross section is the probability of a given
reaction occurring per unit travel of the neutron. is related to the microscopic cross section
( ) by the relationship shown below.
(2-2)
where:
=
macroscopic cross section (cm )
-1
N =
atom density of material (atoms/cm )3
=
microscopic cross-section (cm )2
The difference between the microscopic and macroscopic cross sections is extremely important
and is restated for clarity. The microscopic cross section ( ) represents the effective target area
that a single nucleus presents to a bombarding particle. The units are given in barns or cm .2
The macroscopic cross section ( ) represents the effective target area that is presented by all of
the nuclei contained in 1 cm of the material. The units are given as 1/cm or cm .
3
-1
A neutron interacts with an atom of the material it enters in two basic ways. It will either
interact through a scattering interaction or through an absorption reaction. The probability of
a neutron being absorbed by a particular atom is the microscopic cross section for absorption,
. The probability of a neutron scattering off of a particular nucleus is the microscopic cross
a
section for scattering,
. The sum of the microscopic cross section for absorption and the
s
microscopic cross section for scattering is the total microscopic cross section,
.
T
=
+
T
a
s
Both the absorption and the scattering microscopic cross sections can be further divided. For
instance, the scattering cross section is the sum of the elastic scattering cross section (
) and
se
the inelastic scattering cross section (
).
si
=
+
s
se
si
The microscopic absorption cross section (
) includes all reactions except scattering. However,
a
for most purposes it is sufficient to merely separate it into two categories, fission (
) and
f
capture (
). Radiative capture of neutrons was described in the Neutron Interactions chapter
c
of Module 1.
=
+
a
f
c
