In physics, the radiation length is a characteristic of a material, related to the energy loss of high energy

particles In the physical sciences, a particle (or corpuscule in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from s ...

electromagnetically interacting with it.

Definition

In materials of high atomic number (e.g. W, U, Pu) the

electrons The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...

of energies >~10 MeV predominantly lose energy by

bremsstrahlung ''Bremsstrahlung'' (), from "to brake" and "radiation"; i.e., "braking radiation" or "deceleration radiation", is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typicall ...

, and high-energy

photons A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alway ...

by pair production. The characteristic amount of matter traversed for these related interactions is called the radiation length , usually measured in g·cm⁻². It is both the mean distance over which a high-energy electron loses all but of its energy by bremsstrahlung, and of the mean free path for

pair production Pair production is the creation of a subatomic particle and its antiparticle from a neutral boson. Examples include creating an electron and a positron, a muon and an antimuon, or a proton and an antiproton. Pair production often refers specific ...

by a high-energy photon. It is also the appropriate length scale for describing high-energy electromagnetic cascades. The radiation length for a given material consisting of a single type of nucleus can be approximated by the following expression: (http://pdg.lbl.gov/)

X_0 = 716.4\;\mathrm g\, \mathrm^ \frac = 1433 \;\mathrm g\, \mathrm^ \frac

, where is the

atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...

and is

mass number The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic weight, also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approxima ...

of the nucleus. For

Z > 4

, a good approximation is

\frac = 4 \left( \frac \right)^2 Z(Z+1) \alpha^3 n_ \log\left(\frac\right)

, where

n_

is the number density of the nucleus,

\hbar

denotes the reduced

Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...

m_

the

electron rest mass The electron mass (symbol: ''m''e) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about or about , which has an energy-equivalent of a ...

c

the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...

, and

\alpha

the

fine-structure constant In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between ele ...

. For electrons at lower energies (below few tens of

MeV In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacu ...

), the energy loss by

ionization Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule i ...

is predominant. While this definition may also be used for other electromagnetic interacting particles beyond

lepton In particle physics, a lepton is an elementary particle of half-integer spin ( spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...

s and photons, the presence of the stronger hadronic and nuclear interaction makes it a far less interesting characterisation of the material; the

nuclear collision length Nuclear collision length is the mean free path of a particle before undergoing a nuclear reaction, for a given particle in a given medium. The collision length is smaller than the nuclear interaction length because the latter excludes the elastic an ...

and

nuclear interaction length Nuclear interaction length is the mean distance travelled by a hadronic particle before undergoing an inelastic nuclear interaction. See also * Nuclear collision length * Radiation length External linksParticle Data Group site Experimental parti ...

are more relevant. Comprehensive tables for radiation lengths and other properties of materials are available from the

Particle Data Group The Particle Data Group (or PDG) is an international collaboration of particle physicists that compiles and reanalyzes published results related to the properties of particles and fundamental interactions. It also publishes reviews of theoretical r ...

References

Experimental particle physics {{particle-stub