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Fluence, probability, cross-section, and the barn
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Fluence is the number of particles traversing a sphere of unit area and
therefore has dimension m^-2 (per square meter, also expressible as per
barn or per acre; ICRU Report 33, 1980). In atomic, nuclear, and
particle physics, cross sections can be viewed as "interaction
probability per unit fluence" (ICRU Report 33, 1980).
Thinking of an interaction cross section as a probability per unit
fluence avoids the conceptual difficulty of imagining a "target" much
larger than an interaction diameter for billiard ball-like collisions.