where N₂₄ is the number of sodium-24 atoms created during each second in
a cubic centimeter of the target; N₂₃ is the number of atoms of
sodium-23 in a cubic centimeter of the target; φ is the number of
neutrons crossing a square centimeter per second (called the neutron
flux); t is the time in seconds that the target is in the reactor; and σ
is a number that represents the probability that the conversion of
sodium-23 to sodium-24 will occur. This last number is called a “cross
section” and it is expressed in “barns”. One barn is equal to 10^{-24}
square centimeter, which is approximately the cross-sectional area of a
typical atomic nucleus.
In an activation analysis experiment, the analyst wants to determine the
number of target atoms (N₂₃ in the above example). He can measure how
long the target was in the nuclear reactor; there are ways of measuring
the neutron flux, φ; and the cross section is fixed and generally known
for each target nucleus. So, by measuring the number of radioactive
atoms created (N₂₄), he can calculate the number of target atoms. See
the figure on the next two pages.
Actually, to get the most accurate results, there are certain practical
tricks he can use that increase the accuracy. Some of these will become
apparent in later sections of this booklet.
The most important of these “tricks” is the use of a “standard” or
“comparator”. This comparator is similar in form and composition to the
sample to be measured but contains a _known_ quantity of the element to
be determined. The steps used for the analysis are simple.
1. Put the sample and comparator together into a reactor and bombard
them with neutrons.