A cross section is, mathematically formulated, the set theoretic intersection of a body and a plane, hence the cutting face of an object cut into two with a plane cut. More plainly, when cutting an object into slices one gets many parallel cross sections.
With CAT one gets cross-sectional images without actual cutting.
In, physics a cross section represents the probability of an interaction event between two particles.
Nuclear cross section
In nuclear physics, it is found convenient to express probability of a particular event by a cross section. Statistically, the centers of the atoms in a thin foil can be considered as points evenly distributed over a plane. The center of an atomic projectile striking this plane has geometrically a definite probability of passing within a certain distance (r) of one of these points. In fact, if there are n atomic centers in an area A of the plane, this probability is (nπr2)/A, which is simply the ratio of the aggregate area of circles of radius r drawn around the points to the whole area. If we think of the atoms as impenetrable steel discs and the impinging particle as a bullet of negligible diameter, this ratio is the probability that the bullet will strike a steel disc, i.e., that the atomic projectile will be stopped by the foil. If it is the fraction of impinging atoms getting through the foil which is measured, the result can still be expressed in terms of the equivalent stopping cross section of the atoms. This notion can be extended to any interaction between the impinging particle and the atoms in the target. For example, the probability that an alpha particle striking a beryllium target will produce a neutron can be expressed is the equivalent cross section of beryllium for this type of reaction.
In nuclear physics it is conventional to consider that the impinging particles have negligible diameter. Cross sections can be computed for any sort of process, such as capture scattering, production of neutrons, etc. In many cases, the number of particles emitted or scattered in nuclear processes is not measured directly; one merely measures the attenuation produced in a parallel beam of incident particles by the interposition of a known thickness of a particular material. The cross section obtained in this way is called the total cross section and is usually denoted by a σ or σT.
The typical nuclear diameter is of the order of 10-12 cm. We might therefore expect the cross sections for nuclear reactions to be of the order of πr,2 or roughly 10-24 cm2 and this unit is given its own name, the barn, and is the unit in which cross sections are usually expressed. Actually the observed cross sections vary enormously. Thus for slow neutrons absorbed by the (n, gamma) reaction the cross section in some cases is as much as 1,000 barns, while the cross sections for transmutations by gamma-ray absorption are in the neighborhood of 0.001 barns.