Rate (particle physics)
When two particles interact, their mutual cross section is the area transverse to their relative motion within which they must meet in order to scatter from each other. If the particles are hard spheres that interact only upon contact, their scattering cross section is related to their geometric size. If the particles interact through some action-at-a-distance force, such as electromagnetism or gravity, their scattering cross section is generally larger than their geometric size. When a cross section is specified as a function of some final-state variable, such as particle angle or energy, it is called a "differential cross section". When a cross section is integrated over all scattering angles (and possibly other variables), it is called a "total cross section". Cross sections are typically denoted σ ("sigma") and measured in units of area.
Scattering cross sections may be defined in nuclear and particle physics for collisions of accelerated beams of one type of particle with targets (either stationary or moving) of a second type of particle. The probability for any given reaction to occur is in proportion to its cross section. Thus, specifying the cross section for a given reaction is a proxy for stating the probability that a given scattering process will occur.
The measured reaction rate of a given process depends strongly on experimental variables such as the density of the target material, the intensity of the beam, the detection efficiency of the apparatus, or the angle setting of the detection apparatus. However, these quantities can be factored away, allowing measurement of the underlying two-particle collisional cross section.
Differential and total scattering cross sections are among the most important measurable quantities in nuclear and particle physics.
In a gas of finite-sized particles there are collisions among particles that depend on their cross-sectional size. The average distance that a particle travels between collisions depends on the density of gas particles. These quantities are related according to
where
If the particles in the gas can be treated as hard spheres of radius that interact by direct contact, as illustrated in the figure, then the effective cross section for the collision of a pair is . If the particles in the gas interact by a force with a larger range that their physical size, then the cross section is a larger effective area that may depend on a variety of variables such as the energy of the particles.
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