Cross Section

A cross section is a physical size corresponding to the probability of interaction of a particle for a given reaction of the Nuclear physics or Physique of the particles. The cross unit of section is a unit of area, and is called the Barn (b): 1 B = 10^-24 cm ².

History

The idea to use a surface to express such a probability of interaction probably goes up with discovered core and of its smallness by Rutherford in 1911: by bombarding a thin sheet of Gold with rays alpha, one notes little deviation of these particles, as if the usable surface of the Atome (does that of its core of it) were very small, like the Sun in the Solar system.

Principle

Statistically, the centers of atoms laid out on a mean surface can be regarded as points distributed uniformly from this point of view. The center of an atomic projectile running up against this plan has a probability geometrically defined to pass at a certain distance R of one of these points. In fact, if there is N atoms in a surface S of this plan, this probability is of (nπ R ²) /S, which is simply the relationship between the entire surface occupied by circles of radius R and S surfaces it plan. If we regard the atoms as impenetrable steel discs and the particle like a negligible ball of diameter, this report/ratio is the probability that the ball runs up against one of the discs, i.e. the projectile is stopped by surface.

In other words, the cross section is the fictitious surface which should have a target particle to reproduce the probability observed of collision or reaction with another particle by supposing that these collisions occur between impenetrable material objects.

This concept can be wide with any interaction between collision of particles such as: nuclear Reaction, diffusion of particles, diffusion of the light. For example, the probability that a particle α running up against a target of Béryllium will produce a neutron can be expressed by the fictitious surface which beryllium in this type of reaction would have to obtain the probability of this reaction according to this scenario.

The cross section is not very dependant on the real size of the particle in question and varies especially according to the true nature of the collision or the reaction, and the interactions existentes between the particles concerned. This explains the use of the cross expression section more simply instead of section .

Unit

The typical ray of the nuclear particles is about 10^-14 Mr. We could thus await us cross sections for nuclear reactions about πr ², that is to say approximately 10^-28 m ², which explains the use of a unit, the Barn, having this value.

The cross sections observed vary in an important way, according to the nature and the speed of the particles. Thus for the reaction (N, γ) of absorption neutrons slow (or “thermics”), the cross section can exceed 1 000 barns, while the cross sections of the transmutations by absorption of rays γ are rather about 0,001 barn.

See too

Internal bonds

Diffusion Thomson
Diffusion Compton
Rayleigh scatter

External bond

Database of cross sections usually used

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