We consider some simple theories regarding nuclear reactions here.
##
Reaction Cross Sections

In a nuclear reaction, the area of the target nucleus *seen* by
the incidant particle is proportional to the rate of reaction, and
hence the term **cross section** is used to mean a constant related
to the rate of a reaction.
The unit for the cross section is a barn (b, or 10^{-28}).
However, the cross section is really an experimental value obtained
from experiment. The *rate of reaction* (number per unit time)
in an experiment is equal to the product of the cross section,
s,
the number of target atoms per unit area *N*, and the intensity
of the flux (number of particles per unit area per unit time s^{-1}
cm^{-2}) *I*. That is,

*rate* = s *N I*.

A sample irradiated in the core of a nuclear reactor differs from
irradiated by a unidirectional beam. Neutrons in reactor bombard
the sample from all directions. For neutron irradiation in reactor
core, the cross section is calculated by dividing the rate of
reaction by the total number of nuclei, and the intensity of the flux,
Note that the unit of the cross section so calculated is cm^{-2}
or m^{-2}, depending on the unit used for *I*.
The unit barn (=10^{-28} m^{2} or 10^{-24}
cm^{2}) has been used for the tabulation of cross sections
of nuclides. Cross sections have a very large range, 10^{6}
to 10^{-6}. The range indicates a very complicated
particle-nucleus interaction.
Thus, the cross section is really a measure of the probability of a
given reaction, and the total cross section of absorption of a particular
accelerated particle is the sum of all partial cross sections.

**
Example 1**