DOE-HDBK-1019/1-93
Reactor Theory (Neutron Characteristics)
NUCLEAR CROSS SECTIONS AND NEUTRON FLUX
Rev. 0
Page 17
NP-02
Nuclear Cross Section and Neutron Flux Summary
Atom density (N) is the number of atoms of a given type per unit volume of
material.
Microscopic cross section () ) is the probability of a given reaction occurring
between a neutron and a nucleus.
Microscopic cross sections are measured in units of barns, where 1 barn = 10-24
cm .2
Macroscopic cross section (* ) is the probability of a given reaction occurring per
unit length of travel of the neutron. The units for macroscopic cross section are
cm .
-1
The mean free path ( ) is the average distance that a neutron travels in a material
between interactions.
Neutron flux (1 ) is the total path length traveled by all neutrons in one cubic
centimeter of material during one second.
The macroscopic cross section for a material can be calculated using the equation
below.
*
= N )
The absorption cross section for a material usually has three distinct regions. At
low neutron energies (<1 eV) the cross section is inversely proportional to the
neutron velocity.
Resonance absorption occurs when the sum of the kinetic energy of the neutron
and its binding energy is equal to an allowed nuclear energy level of the nucleus.
Resonance peaks exist at intermediate energy levels. For higher neutron energies,
the absorption cross section steadily decreases as the neutron energy increases.
The mean free path equals 1/* .
The macroscopic cross section for a mixture of materials can be calculated using
the equation below.
*
= N ) + N ) + N ) + ....... N )
1
1
2
2
3
3
n
n
Self-shielding is where the local neutron flux is depressed within a material due to
neutron absorption near the surface of the material.
