Cross Section (physics)

In Nuclear and Particle Physics , the concept of a cross section is used to express the likelihood of interaction between particles. It can therefore characterize the probabilility that a particular Nuclear Reaction will take place, or the statistical nature of scattering events. The cross section is expressed in units of Area , usually in Barn .

SCATTERING

In Scattering , a differential cross section is defined by the Probability to observe a Scattered Particle in a given Quantum State per Solid Angle unit, such as within a given Cone of observation, if the target is irradiated by a Flux of one particle per surface unit:

:

{d \sigma \over d \Omega}={\hbox{Scattered flux / Unit of solid angle} \over \hbox{Incident flux / Unit of surface}}

The integral cross section is the Integral of the differential cross section on the whole sphere of observation (4

\pi

Steradian ):

:

\sigma=\int d\Omega {d \sigma \over d \Omega}

A cross section is therefore a measure of the effective surface area seen by the impinging particles, and as such is expressed in units of area. Usual units are the cm^{2^{, the barn (1 b = 10^{-24^{cm²) and the corresponding submultiples: the millibarn (1 mb = 10^-3 b), the microbarn (1 $\mu$ b = 10^-6 b), the nanobarn ( 1 nb = 10^-9 b), and the picobarn (1 pb = 10^-12 b). The cross section of two Particle s (i.e. observed when the two particles are Colliding with each other) is a measure of the interaction event between the two particles.

Relation to the S Matrix

If the Reduced Mass es and Momenta of the colliding system are ''m_i'', $ec{p}_i$ and ''m_f'', $ec{p}_f$ before and after the collision respectively, the differential cross section is given by}}}}

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Cross Section (physics)