bei48482_FM

Now we consider the same beam of particles incident on a slab of finite thickness

x. If each particle can interact only once, dNparticles may be thought of as being

removed from the beam in passing through the first dxof the slab. Hence we need a

minus sign in Eq. (12.19), which becomes

 ndx

dN



N

442 Chapter Twelve

N – dN

particles

emerge

from slab

N incident

particles

n atoms /m^3 Area = A

dx dN/N = nσ dx

σ = cross section/atom

Figure 12.13The relationship between cross section and beam intensity.

Geometrical

cross section

Interaction

cross section

Target

nucleus

Only these

particles will

interact

Incident

particles

Figure 12.12A geometrical interpretation of the concept of cross section. The interaction cross section

may be smaller than, equal to, or larger than the geometrical cross section. The cross section of a

nucleus for a particular interaction is a mathematical way to express the probability that the interaction

will occur when a certain particle is incident on the nucleus; the diagram here is nothing more than

a helpful visualization.

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