Neutron Capture and Cross
Name: Martin S.
Whilst reading a textbook as part of my physics course, I
discovered a reference to the fact that the neutron capture cross-section
of the nucleus can be smaller than the actual geometric
cross-section. How is this possible?
An interaction cross section is more a measure of probability than of size.
If touching the nucleus always means capture and not touching the nucleus
always means freedom, then the capture cross section will be the same as the
geometric cross section. When the capture cross section is less than the
geometric cross section, the neutron is less likely to be captured than to
make contact. Sometimes it will make contact without being captured. The
cross section for neutrino capture (which is even less likely) would be
smaller. Some think of the cross section as "how big the nucleus looks to
Dr. Ken Mellendorf
Illinois Central College
It simply means that a neutron is not necessarily captured every time it
crosses the particular nucleus.
Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
You can think of this as a neutron hitting a nucleus and not
sticking to it but scattering off of it.
The concept of a "cross section" is somewhat of a mis-nomer. It is a measure
of the ability of a target to interact with some incident energy or
particle. It is defined as the RATIO of the total energy per second [Energy
/ sec] scattered by a target (which is measured by some array of appropriate
detectors) to the total incident energy per second per square meter [Energy/
(m)^2 * sec]. This ratio is then:
[Energy / sec] / [Energy / (m)^2 * sec]. This ratio then has the units of
(m)^2, meters squared. It is in this sense that the process is said to have
a "cross section". It is a convenient way to compare the strengths of
interactions, rather than a measure of geometric area. See: "Lectures on
Physics" by R. Feynman, Vol. 1, Ch. 32 for a lucid detailed treatment.
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Update: June 2012