Nuclear cross section

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The nuclear cross section of a nucleus is used to characterize the probability that a nuclear reaction will occur. The concept of a nuclear cross section is somewhat difficult to conceptualize but can be quantified physically in terms of "characteristic area" where a larger area means a larger probability of interaction. The standard unit for measuring a nuclear cross section (denoted as σ) is the barn, which is equal to 10^-24 [cm²]. Most nuclear cross sections deal with neutron interactions and are known as neutron cross sections, and within these interactions there are a subset of nuclear cross sections such as total cross section, absorption cross section, scattering cross section, n,2n cross section and others specific to individual types of neutron reactions.

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 σ_T.

The typical nuclear radius is of the order of 10⁻¹² cm. We might therefore expect the cross sections for nuclear reactions to be of the order of $π r 2$ 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.

Nuclear cross sections are used in determining the nuclear reaction rate, and are governed by the reaction rate equation for a particular set of particles (usually viewed as a "beam and target" thought experiment where one particle or nucleus is the "target" [typically at rest] and the other is treated as a "beam" [projectile with a given energy]). For neutron interactions incident upon a nucleus target, the nuclear reaction rate equation is:

$R = \Phi \ \sigma \ N_A$

where:

R = number of reactions/second
$Φ$ = neutron beam flux in units of n/area/second
σ = proportionality constant in unit of area (usually barns or cm²). In this equation, σ is also known as the microscopic cross section, which is typically used when dealing with fission reaction rates.
N_A = density of atoms in the target

[edit] References

Nuclear Reactor Analysis by James J. Duderstadt and Louis J. Hamilton - Published by John Wilet & Sons, Inc.
Perkins, Donald H. (1999). Introduction to High Energy Physics. Cambridge University Press. ISBN 0-521-62196-8.