In nuclear and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles. Nuclear physics is the branch of physics concerned with the nucleus of the atom. ... Thousands of particles explode from the collision point of two relativistic (100 GeV per ion) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ...

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: In particle physics, scattering is a class of phenomena by which particles are deflected by collisions with other particles. ... Probability is the chance that something is likely to happen or be the case. ... Scattering theory is a branch of physics and especially of quantum mechanics whose aim is the study of scattering events. ... A quantum state is any possible state in which a quantum mechanical system can be. ... A solid angle is the three dimensional analog of the ordinary angle. ... This article is about the geometric object, for other uses see Cone. ... flux in science and mathematics. ...

To put it another way, it is the rate of scattering events normalized to the beam intensity, the target density, the length of the beam-target interaction region, the geometrical "size" of detector, and the efficiency of the detector "counting."

If the detector is small and sufficiently far from the target, then the geometrical "size" of the detector is given by:

The integral cross section is the integral of the differential cross section on the whole sphere of observation (4π steradian): In calculus, the integral of a function is an extension of the concept of a sum. ... The steradian (ste from Greek stereos, solid) is the SI derived unit of solid angle, and the 3-dimensional equivalent of the radian. ...

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 cm², the barn (1 b = 10⁻²⁴ cm²) and the corresponding submultiples: the millibarn (1 mb = 10⁻³ b), the microbarn (1 μb = 10⁻⁶ b), the nanobarn ( 1 nb = 10⁻⁹ b), and the picobarn (1 pb = 10⁻¹² b). The cross section of two particles (i.e. observed when the two particles are colliding with each other) is a measure of the interaction event between the two particles. In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not made up of smaller particles. ... For other uses, see Collision (disambiguation). ...

Relation to the S matrix

If the reduced masses and momenta of the colliding system are m_i, and m_f, before and after the collision respectively, the differential cross section is given by Reduced mass is an algebraic term of the form that simplifies an equation of the form The reduced mass is typically used as a relationship between two system elements in parallel, such as resistors; whether these be in the electrical, thermal, hydraulic, or mechanical domains. ... In classical mechanics, momentum (pl. ...

where the on-shell T matrix is defined by

in terms of the S matrix. The δ function is the distribution called the Dirac delta function. The computation of the S matrix is the main aim of the scattering theory. The S-matrix is the matrix in quantum mechanics or quantum field theory that relates the final state in the infinite future and the initial state in the infinite past. ... The Dirac delta function, often referred to as the unit impulse function and introduced by the British theoretical physicist Paul Dirac, can usually be informally thought of as a function δ(x) that has the value of infinity for x = 0, the value zero elsewhere. ... The S-matrix is the matrix in quantum mechanics or quantum field theory that relates the final state in the infinite future and the initial state in the infinite past. ... Scattering theory is a branch of physics and especially of quantum mechanics whose aim is the study of scattering events. ...

Nuclear physics

Main article: nuclear cross section

In nuclear physics, it is found convenient to express probability of a particular event by a cross section. Statistically, the centers of the atoms in a thin foil can be considered as points evenly distributed over a plane. The center of an atomic projectile striking this plane has geometrically a definite probability of passing within a certain distance r of one of these points. In fact, if there are n atomic centers in an area A of the plane, this probability is (nπr²) / A, which is simply the ratio of the aggregate area of circles of radius r drawn around the points to the whole area. If we think of the atoms as impenetrable steel discs and the impinging particle as a bullet of negligible diameter, this ratio is the probability that the bullet will strike a steel disc, i.e., that the atomic projectile will be stopped by the foil. If it is the fraction of impinging atoms getting through the foil which is measured, the result can still be expressed in terms of the equivalent stopping cross section of the atoms. This notion can be extended to any interaction between the impinging particle and the atoms in the target. For example, the probability that an alpha particle striking a beryllium target will produce a neutron can be expressed as the equivalent cross section of beryllium for this type of reaction. The nuclear cross section of a nucleus is used to characterize the probability that a nuclear reaction will occur. ... Nuclear physics is the branch of physics concerned with the nucleus of the atom. ... An alpha particle is deflected by a magnetic field Alpha radiation consists of helium-4 nuclei and is readily stopped by a sheet of paper. ... General Name, Symbol, Number beryllium, Be, 4 Chemical series alkaline earth metals Group, Period, Block 2, 2, s Appearance white-gray metallic Standard atomic weight 9. ...

See also

Radar: The (monostatic) radar cross section is defined as 4 π times the radio differential cross section at 180 degrees. This long range radar antenna, known as ALTAIR, is used to detect and track space objects in conjunction with ABM testing at the Ronald Reagan Test Site on the Kwajalein atoll. ... Radar cross section (RCS) is a description of how an object reflects an incident electromagnetic wave. ...

Bibliography

R.G. Newton, Scattering theory of waves and particles, McGraw Hill, 1966

External links

• [1] and [2]: Scattering Articles at Georgia State University HyperPhysics
• IAEA Nuclear Data Services
• BNL National Nuclear Data Center
• Particle Data Group