Bremsstrahlung (German pronunciation: [ˈbʁɛmsˌʃtʁaːlʊŋ] (listen)), from bremsen "to brake" and Strahlung "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, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation (i.e., a photon), thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases.

Broadly speaking, bremsstrahlung or braking radiation is any radiation produced due to the deceleration (negative acceleration) of a charged particle, which includes synchrotron radiation (i.e. photon emission by a relativistic particle), cyclotron radiation (i.e. photon emission by a non-relativistic particle), and the emission of electrons and positrons during beta decay. However, the term is frequently used in the more narrow sense of radiation from electrons (from whatever source) slowing in matter.

Bremsstrahlung emitted from plasma is sometimes referred to as free/free radiation. This refers to the fact that the radiation in this case is created by charged particles that are free; i.e., not part of an ion, atom or molecule, both before and after the deflection (acceleration) that caused the emission.

Bremsstrahlung produced by a high-energy electron deflected in the electric field of an atomic nucleus.

Particle in vacuum

A charged particle accelerating in a vacuum radiates power, as described by the Larmor formula and its relativistic generalizations. Although the term, bremsstrahlung, is usually reserved for charged particles accelerating in matter, not vacuum, the formulas are similar. (In this respect, bremsstrahlung differs from Cherenkov radiation, another kind of braking radiation which occurs only in matter, and not in a vacuum.)

Total radiated power

The most established relativistic formula for total radiated power is given by[1]

where (the velocity of the particle divided by the speed of light), is the Lorentz factor, signifies a time derivative of , and q is the charge of the particle. This is commonly written in the mathematically equivalent form [2] using :

In the case where velocity is parallel to acceleration (for example, linear motion), the formula simplifies to[3]

where is the acceleration. For the case of acceleration perpendicular to the velocity (a case that arises in circular particle accelerators known as synchrotrons), the total power radiated reduces to

radiated in the two limiting cases is proportional to or . Since , we see that the total radiated power goes as or , which accounts for why electrons lose energy to bremsstrahlung radiation much more rapidly than heavier charged particles (e.g., muons, protons, alpha particles). This is the reason a TeV energy electron-positron collider (such as the proposed International Linear Collider) cannot use a circular tunnel (requiring constant acceleration), while a proton-proton collider (such as the Large Hadron Collider) can utilize a circular tunnel. The electrons lose energy due to bremsstrahlung at a rate times higher than protons do.

Angular distribution

The most general formula for radiated power as a function of angle is:[2]

where is a unit vector pointing from the particle towards the observer, and is an infinitesimal bit of solid angle.

In the case where velocity is parallel to acceleration (for example, linear motion), this simplifies to[2]

where is the angle between and the direction of observation.

Thermal bremsstrahlung

Bremsstrahlung power2
The bremsstrahlung power spectrum rapidly decreases for large , and is also suppressed near . This plot is for the quantum case , and .

NOTE: this article currently gives formulas that apply in the Rayleigh-Jeans limit , and does not use a quantized (Planck) treatment of radiation. Thus a usual factor like does not appear. The appearance of in y below is due to the quantum-mechanical treatment of collisions.

In a plasma, the free electrons continually collide with the ions, producing bremsstrahlung. A complete analysis requires accounting for both binary Coulomb collisions as well as collective (dielectric) behavior. A detailed treatment is given by Bekefi,[4] while a simplified one is given by Ichimaru.[5] In this section we follow Bekefi's dielectric treatment, with collisions included approximately via the cutoff wavenumber, .

Consider a uniform plasma, with thermal electrons distributed according to the Maxwell–Boltzmann distribution with the temperature . Following Bekefi, the power spectral density (power per angular frequency interval per volume, integrated over the whole sr of solid angle, and in both polarizations) of the bremsstrahlung radiated, is calculated to be

where is the electron plasma frequency, is the photon frequency, is the number density of electrons and ions, and other symbols are physical constants. The second bracketed factor is the index of refraction of a light wave in a plasma, and shows that emission is greatly suppressed for (this is the cutoff condition for a light wave in a plasma; in this case the light wave is evanescent). This formula thus only applies for . This formula should be summed over ion species in a multi-species plasma.

The special function is defined in the exponential integral article, and the unitless quantity is

is a maximum or cutoff wavenumber, arising due to binary collisions, and can vary with ion species. Roughly, when (typical in plasmas that are not too cold), where eV is the Hartree energy, and is the electron thermal de Broglie wavelength. Otherwise, where is the classical Coulomb distance of closest approach.

For the usual case , we find

The formula for is approximate, in that it neglects enhanced emission occurring for slightly above .

In the limit , we can approximate E1 as where is the Euler–Mascheroni constant. The leading, logarithmic term is frequently used, and resembles the Coulomb logarithm that occurs in other collisional plasma calculations. For the log term is negative, and the approximation is clearly inadequate. Bekefi gives corrected expressions for the logarithmic term that match detailed binary-collision calculations.

The total emission power density, integrated over all frequencies, is

and decreases with ; it is always positive. For , we find

Note the appearance of due to the quantum nature of . In practical units, a commonly used version of this formula for is [6]

This formula is 1.59 times the one given above, with the difference due to details of binary collisions. Such ambiguity is often expressed by introducing Gaunt factor , e.g. in [7] one finds

where everything is expressed in the CGS units.

Relativistic corrections

Brem cross section
Relativistic corrections to the emission of a 30-keV photon by an electron impacting on a proton.

For very high temperatures there are relativistic corrections to this formula, that is, additional terms of the order of [8]

Bremsstrahlung cooling

If the plasma is optically thin, the bremsstrahlung radiation leaves the plasma, carrying part of the internal plasma energy. This effect is known as the bremsstrahlung cooling. It is a type of radiative cooling. The energy carried away by bremsstrahlung is called bremsstrahlung losses and represents a type of radiative losses. One generally uses the term bremsstrahlung losses in the context when the plasma cooling is undesired, as e.g. in fusion plasmas.

Polarizational bremsstrahlung

Polarizational bremsstrahlung (sometimes referred to as "atomic bremsstrahlung") is the radiation emitted by the target's atomic electrons as the target atom is polarized by the Coulomb field of the incident charged particle.[9][10] Polarizational bremsstrahlung contributions to the total bremsstrahlung spectrum have been observed in experiments involving relatively massive incident particles,[11] resonance processes,[12] and free atoms.[13] However, there is still some debate as to whether or not there are significant polarizational bremsstrahlung contributions in experiments involving fast electrons incident on solid targets.[14][15]

It is worth noting that the term "polarizational" is not meant to imply that the emitted bremsstrahlung is polarized. Also, the angular distribution of polarizational bremsstrahlung is theoretically quite different than ordinary bremsstrahlung.[16]

Sources of bremsstrahlung

X-ray tube

Spectrum of the X-rays emitted by an X-ray tube with a rhodium target, operated at 60 kV. The continuous curve is due to bremsstrahlung, and the spikes are characteristic K lines for rhodium. The curve goes to zero at 21 pm in agreement with the Duane–Hunt law, as described in the text.

In an X-ray tube, electrons are accelerated in a vacuum by an electric field towards a piece of metal called the "target". X-rays are emitted as the electrons slow down (decelerate) in the metal. The output spectrum consists of a continuous spectrum of X-rays, with additional sharp peaks at certain energies. The continuous spectrum is due to bremsstrahlung, while the sharp peaks are characteristic X-rays associated with the atoms in the target. For this reason, bremsstrahlung in this context is also called continuous X-rays.[17]

The shape of this continuum spectrum is approximately described by Kramers' law.

The formula for Kramers' law is usually given as the distribution of intensity (photon count) against the wavelength of the emitted radiation:[18]

The constant K is proportional to the atomic number of the target element, and is the minimum wavelength given by the Duane–Hunt law.

The spectrum has a sharp cutoff at , which is due to the limited energy of the incoming electrons. For example, if an electron in the tube is accelerated through 60 kV, then it will acquire a kinetic energy of 60 keV, and when it strikes the target it can create X-rays with energy of at most 60 keV, by conservation of energy. (This upper limit corresponds to the electron coming to a stop by emitting just one X-ray photon. Usually the electron emits many photons, and each has an energy less than 60 keV.) A photon with energy of at most 60 keV has wavelength of at least 21 pm, so the continuous X-ray spectrum has exactly that cutoff, as seen in the graph. More generally the formula for the low-wavelength cutoff, the Duane-Hunt law, is:[19]

where h is Planck's constant, c is the speed of light, V is the voltage that the electrons are accelerated through, e is the elementary charge, and pm is picometres.

Beta decay

Beta particle-emitting substances sometimes exhibit a weak radiation with continuous spectrum that is due to bremsstrahlung (see the "outer bremsstrahlung" below). In this context, bremsstrahlung is a type of "secondary radiation", in that it is produced as a result of stopping (or slowing) the primary radiation (beta particles). It is very similar to X-rays produced by bombarding metal targets with electrons in X-ray generators (as above) except that it is produced by high-speed electrons from beta radiation.

Inner and outer bremsstrahlung

The "inner" bremsstrahlung (also known as "internal bremsstrahlung") arises from the creation of the electron and its loss of energy (due to the strong electric field in the region of the nucleus undergoing decay) as it leaves the nucleus. Such radiation is a feature of beta decay in nuclei, but it is occasionally (less commonly) seen in the beta decay of free neutrons to protons, where it is created as the beta electron leaves the proton.

In electron and positron emission by beta decay the photon's energy comes from the electron-nucleon pair, with the spectrum of the bremsstrahlung decreasing continuously with increasing energy of the beta particle. In electron capture, the energy comes at the expense of the neutrino, and the spectrum is greatest at about one third of the normal neutrino energy, decreasing to zero electromagnetic energy at normal neutrino energy. Note that in the case of electron capture, bremsstrahlung is emitted even though no charged particle is emitted. Instead, the bremsstrahlung radiation may be thought of as being created as the captured electron is accelerated toward being absorbed. Such radiation may be at frequencies that are the same as soft gamma radiation, but it exhibits none of the sharp spectral lines of gamma decay, and thus is not technically gamma radiation.

The internal process is to be contrasted with the "outer" bremsstrahlung due to the impingement on the nucleus of electrons coming from the outside (i.e., emitted by another nucleus), as discussed above.[20]

Radiation safety

In some cases, e.g. 32
, the bremsstrahlung produced by shielding the beta radiation with the normally used dense materials (e.g. lead) is itself dangerous; in such cases, shielding must be accomplished with low density materials, e.g. Plexiglas (Lucite), plastic, wood, or water;[21] as the atomic number is lower for these materials, the intensity of bremsstrahlung is significantly reduced, but a larger thickness of shielding is required to stop the electrons (beta radiation).

In astrophysics

The dominant luminous component in a cluster of galaxies is the 107 to 108 kelvin intracluster medium. The emission from the intracluster medium is characterized by thermal bremsstrahlung. This radiation is in the energy range of X-rays and can be easily observed with space-based telescopes such as Chandra X-ray Observatory, XMM-Newton, ROSAT, ASCA, EXOSAT, Suzaku, RHESSI and future missions like IXO [3] and Astro-H [4].

Bremsstrahlung is also the dominant emission mechanism for H II regions at radio wavelengths.

In electric discharges

In electric discharges, for example as laboratory discharges between two electrodes or as lightning discharges between cloud and ground or within clouds, electrons produce Bremsstrahlung photons while scattering off air molecules. These photons become manifest in terrestrial gamma-ray flashes and are the source for beams of electrons, positrons, neutrons and protons.[22] The appearance of Bremsstrahlung photons also influences the propagation and morphology of discharges in nitrogen-oxygen mixtures with low percentages of oxygen.[23]

Quantum mechanical description

The complete quantum mechanical description was first performed by Bethe and Heitler.[24] They assumed plane waves for electrons which scatter at the nucleus of an atom, and derived a cross section which relates the complete geometry of that process to the frequency of the emitted photon. The quadruply differential cross section which shows a quantum mechanical symmetry to pair production, is:

There is the atomic number, the fine structure constant, the reduced Planck's constant and the speed of light. The kinetic energy of the electron in the initial and final state is connected to its total energy or its momenta via

where is the mass of an electron. Conservation of energy gives

where is the photon energy. The directions of the emitted photon and the scattered electron are given by

where is the momentum of the photon.

The differentials are given as

The absolute value of the virtual photon between the nucleus and electron is

The range of validity is given by the Born approximation

where this relation has to be fulfilled for the velocity of the electron in the initial and final state.

For practical applications (e.g. in Monte Carlo codes) it can be interesting to focus on the relation between the frequency of the emitted photon and the angle between this photon and the incident electron. Köhn and Ebert [25] integrated the quadruply differential cross section by Bethe and Heitler over and and obtained:



However, a much simpler expression for the same integral can be found in [26] (Eq. 2BN) and in [27] (Eq. 4.1).

An analysis of the doubly differential cross section above shows that electrons whose kinetic energy is larger than the rest energy (511 keV) emit photons in forward direction while electrons with a small energy emit photons isotropically.

Electron–electron bremsstrahlung

One mechanism, considered important for small atomic numbers , is the scattering of a free electron at the shell electrons of an atom or molecule.[28] Since electron–electron bremsstrahlung is a function of and the usual electron-nucleus bremsstrahlung is a function of , electron–electron bremsstrahlung is negligible for metals. For air, however, it plays an important role in the production of terrestrial gamma-ray flashes.[29]

See also


  1. ^ A Plasma Formulary for Physics, Technology, and Astrophysics, D. Diver, pp. 46–48.
  2. ^ a b c Jackson, Classical Electrodynamics, Sections 14.2–3
  3. ^ Introduction to Electrodynamics, D. J. Griffiths, pp. 463–465
  4. ^ Radiation Processes in Plasmas, G. Bekefi, Wiley, 1st edition (1966)
  5. ^ Basic Principles of Plasmas Physics: A Statistical Approach, S. Ichimaru, p. 228.
  6. ^ NRL Plasma Formulary, 2006 Revision, p. 58.
  7. ^ Radiative Processes in Astrophysics, G.B. Rybicki & A.P. Lightman, p. 162.
  8. ^ Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium, by T.H. Rider, 1995, page 25 MIT PhD thesis
  9. ^ Polarization Bremsstrahlung on Atoms, Plasmas, Nanostructures and Solids, by V. Astapenko
  10. ^ New Developments in Photon and Materials Research, Chapter 3: "Polarizational Bremsstrahlung: A Review", by S. Williams
  11. ^ Ishii, K. Radiat. Phys. Chem. 2006, 75, 1135–1163.
  12. ^ Wendin, G.; Nuroh, K. Phys. Rev. Lett. 1977, 39, 48–51.
  13. ^ Portillo, S.; Quarles, C.A. Phys. Rev. Lett. 2003, 91, 173201.
  14. ^ Astapenko, V.A.; Kubankin, K.S.; Nasonov, N.N.; Polyanskiĭ, V.V.; Pokhil, G.P.; Sergienko, V.I.; Khablo, V.A. JETP Lett. 2006, 84, 281–284.
  15. ^ Williams, S.; Quarles, C.A. Phys. Rev. A 2008, 78, 062704.
  16. ^ Gonzales, D.; Cavness, B.; Williams, S. Phys. Rev. A 2011, 84, 052726.
  17. ^ Electron microprobe analysis and scanning electron microscopy in geology, by S. J. B. Reed, 2005, page 12 Google books link
  18. ^ Laguitton, Daniel; William Parrish (1977). "Experimental Spectral Distribution versus Kramers' Law for Quantitative X-ray Fluorescence by the Fundamental Parameters Method". X-Ray Spectrometry. 6 (4): 201. Bibcode:1977XRS.....6..201L. doi:10.1002/xrs.1300060409.
  19. ^ Handbook of X-ray spectrometry by René Grieken, Andrzej Markowicz, page 3, Google books link
  20. ^ Knipp, J.K.; G.E. Uhlenbeck (June 1936). "Emission of gamma radiation during the beta decay of nuclei". Physica. 3 (6): 425–439. Bibcode:1936Phy.....3..425K. doi:10.1016/S0031-8914(36)80008-1. ISSN 0031-8914. Retrieved 12 May 2010.
  21. ^ "Environment, Health & Safety" (PDF).
  22. ^ Köhn, C., Ebert, U. Calculation of beams of positrons, neutrons, and protons associated with terrestrial gamma ray flashes Journal Geophys. Res. (2015), vol. 120, pp. 1620--1635 ([1])
  23. ^ Köhn, C., Chanrion, O., Neubert, T. The influence of bremsstrahlung on electric discharge streamers in N2, O2 gas mixtures Plasma Sources Sci. Technol. (2017), vol. 26, 015006 ([2])
  24. ^ Bethe, H.A., Heitler, W., 1934. On the stopping of fast particles and on the creation of positive electrons. Proc. Phys. Soc. Lond. 146, 83–112
  25. ^ Köhn, C., Ebert, U., Angular distribution of bremsstrahlung photons and of positrons for calculations of terrestrial gamma-ray flashes and positron beams, Atmos. Res. (2014), vol. 135–136, pp. 432–465
  26. ^ H. W. Koch, J. W. Motz, Bremsstrahlung Cross-Section Formulas and Related Data; Rev. Mod. Phys. 31, 920
  27. ^ R. L. Gluckstern and M. H. Hull, Jr., Polarization Dependence of the Integrated Bremsstrahlung Cross Section; Phys. Rev. 90, 1030
  28. ^ Tessier F and Kawrakow I (2007) Calculation of the electron-electron bremsstrahlung crosssection in the field of atomic electrons, NIM. Phys. Res. B 266 625–634
  29. ^ Köhn, C., Ebert, U. The importance of electron-electron bremsstrahlung for terrestrial gamma-ray flashes, electron beams and electron-positron beams J. Phys. D.: Appl. Phys. as Fast Track Communication (2014), vol. 47, 252001

Further reading

External links

Aneutronic fusion

Aneutronic fusion is any form of fusion power in which neutrons carry no more than 1% of the total released energy. The most-studied fusion reactions release up to 80% of their energy in neutrons. Successful aneutronic fusion would greatly reduce problems associated with neutron radiation such as ionizing damage, neutron activation and requirements for biological shielding, remote handling and safety.

Some proponents see a potential for dramatic cost reductions by converting energy directly to electricity. However, the conditions required to harness aneutronic fusion are much more extreme than those required for the conventional deuterium–tritium (D-T) nuclear fuel cycle.

Arkady Migdal

Arkady Beynusovich (Benediktovich) Migdal (Russian: Арка́дий Бе́йнусович (Бенеди́ктович) Мигда́л; Lida, Russian Empire, 11 March 1911 – Princeton, United States, 9 February 1991) was a Soviet physicist and member of the USSR Academy of Sciences. He developed the formula that accounts for the Landau–Pomeranchuk–Migdal effect, a reduction of the bremsstrahlung and pair production cross sections at high energies or high matter densities.His son, Alexander Arkadyevich Migdal, is also a renowned physicist.


Beamstrahlung (from beam + bremsstrahlung ) is the radiation from one beam of charged particles in storage rings or linear colliders caused by its interaction with the electromagnetic field of the other beam. Coined by J. Rees in 1978.It is a source of radiation loss in colliders, more specifically a type of synchrotron radiation.

Continuous spectrum

In physics, a continuous spectrum usually means a set of attainable values for some physical quantity (such as energy or wavelength) that is best described as an interval of real numbers, as opposed to a discrete spectrum, a set of attainable values that is discrete in the mathematical sense, where there is a positive gap between each value and the next one.

The classical example of a continuous spectrum, from which the name is derived, is the part of the spectrum of the light emitted by excited atoms of hydrogen that is due to free electrons becoming bound to a hydrogen ion and emitting photons, which are smoothly spread over a wide range of wavelengths, in contrast to the discrete lines due to electrons falling from some bound quantum state to a state of lower energy.

As in that classical example, the term is most often used when the range of values of a physical quantity may have both a continuous and a discrete part, whether at the same time or in different situations. In quantum systems, continuous spectra (as in bremsstrahlung and thermal radiation) are usually associated with free particles, such as atoms in a gas, electrons in an electron beam, or conduction band electrons in a metal. In particular, the position and momentum of a free particle has a continuous spectrum, but when the particle is confined to a limited space its spectrum becomes discrete.

Often a continuous spectrum may be just a convenient model for a discrete spectrum whose values are too close to be distinguished, as in the phonons in a crystal.

The continuous and discrete spectra of physical systems can be modeled in functional analysis as different parts in the decomposition of the spectrum of a linear operator acting on a function space, such as the Hamiltonian operator.

Crystal Ball (detector)

The Crystal Ball was a hermetic particle detector used initially with the SPEAR particle accelerator at the Stanford Linear Accelerator Center beginning in 1979. It was designed to detect neutral particles and was used to discover the ηc meson. Its central section was a spark chamber surrounded by a nearly-complete sphere of scintillating crystals (NaI(Tl)), for which it was named. With the addition of endcaps of similar construction, the detector covered 98% of the solid angle around the interaction point.

After its decommissioning at SLAC, the detector was carried to DESY, where it was used for b-physics experiments.

In 1996, it was moved to the Alternating Gradient Synchrotron (AGS) at Brookhaven National Laboratory, where it was used in a series of pion- and kaon-induced experiments on the proton. Currently it is located at Mainz Microtron facility, where it is being used by the A2 Collaboration for a diverse program of measurements using energy tagged Bremsstrahlung photons.

Duane–Hunt law

The Duane–Hunt law, named after the American physicists William Duane and Franklin Hunt, gives the maximum frequency of X-rays that can be emitted by Bremsstrahlung in an X-ray tube by accelerating electrons through an excitation voltage V into a metal target.

The maximum frequency νmax is given by

which corresponds to a minimum wavelength

where h is Planck's constant, e is the charge of the electron, and c is the speed of light. This can also be written as:

The process of X-ray emission by incoming electrons is also known as the inverse photoelectric effect.

Eddington luminosity

The Eddington luminosity, also referred to as the Eddington limit, is the maximum luminosity a body (such as a star) can achieve when there is balance between the force of radiation acting outward and the gravitational force acting inward. The state of balance is called hydrostatic equilibrium. When a star exceeds the Eddington luminosity, it will initiate a very intense radiation-driven stellar wind from its outer layers. Since most massive stars have luminosities far below the Eddington luminosity, their winds are mostly driven by the less intense line absorption. The Eddington limit is invoked to explain the observed luminosity of accreting black holes such as quasars.

Originally, Sir Arthur Stanley Eddington took only the electron scattering into account when calculating this limit, something that now is called the classical Eddington limit. Nowadays, the modified Eddington limit also counts on other radiation processes such as bound-free and free-free radiation (see Bremsstrahlung) interaction.

Gamma ray

A gamma ray or gamma radiation (symbol γ or ), is a penetrating electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves and so imparts the highest photon energy. Paul Villard, a French chemist and physicist, discovered gamma radiation in 1900 while studying radiation emitted by radium. In 1903, Ernest Rutherford named this radiation gamma rays based on their relatively strong penetration of matter; he had previously discovered two less penetrating types of decay radiation, which he named alpha rays and beta rays in ascending order of penetrating power.

Gamma rays from radioactive decay are in the energy range from a few keV to ~8 MeV, corresponding to the typical energy levels in nuclei with reasonably long lifetimes. The energy spectrum of gamma rays can be used to identify the decaying radionuclides using gamma spectroscopy. Very-high-energy gamma rays in the 100–1000 TeV range have been observed from sources such as the Cygnus X-3 microquasar.

Natural sources of gamma rays originating on Earth are mostly as a result of radioactive decay and secondary radiation from atmospheric interactions with cosmic ray particles. However there are other rare natural sources, such as terrestrial gamma-ray flashes, that produce gamma rays from electron action upon the nucleus. Notable artificial sources of gamma rays include fission, such as occurs in nuclear reactors, as well as high energy physics experiments, such as neutral pion decay and nuclear fusion.

Gamma rays and X-rays are both electromagnetic radiation and they overlap in the electromagnetic spectrum, the terminology varies between scientific disciplines. In some fields of physics, they are distinguished by their origin: Gamma rays are created by nuclear decay, while in the case of X-rays, the origin is outside the nucleus. In astrophysics, gamma rays are conventionally defined as having photon energies above 100 keV and are the subject of gamma ray astronomy, while radiation below 100 keV is classified as X-rays and is the subject of X-ray astronomy. This convention stems from the early man-made X-rays, which had energies only up to 100 keV, whereas many gamma rays could go to higher energies. A large fraction of astronomical gamma rays are screened by Earth's atmosphere.

Gamma rays are ionizing radiation and are thus biologically hazardous. Due to their high penetration power, they can damage bone marrow and internal organs. Unlike alpha and beta rays, they pass easily through the body and thus pose a formidable radiation protection challenge, requiring shielding made from dense materials such as lead or concrete.

Infrared divergence

In physics, an infrared divergence (also IR divergence or infrared catastrophe) is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with very small energy approaching zero, or, equivalently, because of physical phenomena at very long distances.

Kramers' opacity law

Kramers' opacity law describes the opacity of a medium in terms of the ambient density and temperature, assuming that the opacity is dominated by bound-free absorption (the absorption of light during ionization of a bound electron) or free-free absorption (the absorption of light when scattering a free ion, also called bremsstrahlung). It is often used to model radiative transfer, particularly in stellar atmospheres. The relation is named after the Dutch physicist Hendrik Kramers, who first derived the form in 1923.

The general functional form of the opacity law is

where is the resulting average opacity, is the density and the temperature of the medium. Often the overall opacity is inferred from observations, and this form of the relation describes how changes in the density or temperature will affect the opacity.

Landau–Pomeranchuk–Migdal effect

In high-energy physics, the Landau–Pomeranchuk–Migdal effect, also known as the Landau–Pomeranchuk effect and the Pomeranchuk effect, or simply LPM effect, is a reduction of the bremsstrahlung and pair production cross sections at high energies or high matter densities. It is named in honor to Lev Landau, Isaak Pomeranchuk and Arkady Migdal.


The muon (; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 e and a spin of 1/2, but with a much greater mass. It is classified as a lepton. As is the case with other leptons, the muon is not believed to have any sub-structure—that is, it is not thought to be composed of any simpler particles.

The muon is an unstable subatomic particle with a mean lifetime of 2.2 μs, much longer than many other subatomic particles. As with the decay of the non-elementary neutron (with a lifetime around 15 minutes), muon decay is slow (by subatomic standards) because the decay is mediated by the weak interaction exclusively (rather than the more powerful strong interaction or electromagnetic interaction), and because the mass difference between the muon and the set of its decay products is small, providing few kinetic degrees of freedom for decay. Muon decay almost always produces at least three particles, which must include an electron of the same charge as the muon and two neutrinos of different types.

Like all elementary particles, the muon has a corresponding antiparticle of opposite charge (+1 e) but equal mass and spin: the antimuon (also called a positive muon). Muons are denoted by μ− and antimuons by μ+. Muons were previously called mu mesons, but are not classified as mesons by modern particle physicists (see § History), and that name is no longer used by the physics community.

Muons have a mass of 105.7 MeV/c2, which is about 207 times that of the electron. Due to their greater mass, muons are not as sharply accelerated when they encounter electromagnetic fields, and do not emit as much bremsstrahlung (deceleration radiation). This allows muons of a given energy to penetrate far more deeply into matter than electrons since the deceleration of electrons and muons is primarily due to energy loss by the bremsstrahlung mechanism. As an example, so-called "secondary muons", generated by cosmic rays hitting the atmosphere, can penetrate to the Earth's surface, and even into deep mines.

Because muons have a very large mass and energy compared with the decay energy of radioactivity, they are never produced by radioactive decay. They are, however, produced in copious amounts in high-energy interactions in normal matter, in certain particle accelerator experiments with hadrons, or naturally in cosmic ray interactions with matter. These interactions usually produce pi mesons initially, which most often decay to muons.

As with the case of the other charged leptons, the muon has an associated muon neutrino, denoted by νμ, which is not the same particle as the electron neutrino, and does not participate in the same nuclear reactions.

Neutron source

A neutron source is any device that emits neutrons, irrespective of the mechanism used to produce the neutrons. Neutron sources are used in physics, engineering, medicine, nuclear weapons, petroleum exploration, biology, chemistry, and nuclear power.

Neutron source variables include the energy of the neutrons emitted by the source, the rate of neutrons emitted by the source, the size of the source, the cost of owning and maintaining the source, and government regulations related to the source.

Nuclear fusion

In nuclear chemistry, nuclear fusion is a reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles (neutrons or protons). The difference in mass between the reactants and products is manifested as either the release or absorption of energy. This difference in mass arises due to the difference in atomic "binding energy" between the atomic nuclei before and after the reaction. Fusion is the process that powers active or "main sequence" stars, or other high magnitude stars.

A fusion process that produces a nucleus lighter than iron-56 or nickel-62 will generally yield a net energy release. These elements have the smallest mass per nucleon and the largest binding energy per nucleon, respectively. Fusion of light elements toward these releases energy (an exothermic process), while a fusion producing nuclei heavier than these elements will result in energy retained by the resulting nucleons, and the resulting reaction is endothermic. The opposite is true for the reverse process, nuclear fission. This means that the lighter elements, such as hydrogen and helium, are in general more fusible; while the heavier elements, such as uranium, thorium and plutonium, are more fissionable. The extreme astrophysical event of a supernova can produce enough energy to fuse nuclei into elements heavier than iron.

In 1920, Arthur Eddington suggested hydrogen-helium fusion could be the primary source of stellar energy. Quantum tunneling was discovered by Friedrich Hund in 1929, and shortly afterwards Robert Atkinson and Fritz Houtermans used the measured masses of light elements to show that large amounts of energy could be released by fusing small nuclei. Building on the early experiments in nuclear transmutation by Ernest Rutherford, laboratory fusion of hydrogen isotopes was accomplished by Mark Oliphant in 1932. In the remainder of that decade, the theory of the main cycle of nuclear fusion in stars were worked out by Hans Bethe. Research into fusion for military purposes began in the early 1940s as part of the Manhattan Project. Fusion was accomplished in 1951 with the Greenhouse Item nuclear test. Nuclear fusion on a large scale in an explosion was first carried out on November 1, 1952, in the Ivy Mike hydrogen bomb test.

Research into developing controlled thermonuclear fusion for civil purposes began in earnest in the 1940s, and it continues to this day.

Particle shower

In particle physics, a shower is a cascade of secondary particles produced as the result of a high-energy particle interacting with dense matter. The incoming particle interacts, producing multiple new particles with lesser energy; each of these then interacts, in the same way, a process that continues until many thousands, millions, or even billions of low-energy particles are produced. These are then stopped in the matter and absorbed.

Pyroelectric fusion

Pyroelectric fusion refers to the technique of using pyroelectric crystals to generate high strength electrostatic fields to accelerate deuterium ions (tritium might also be used someday) into a metal hydride target also containing deuterium (or tritium) with sufficient kinetic energy to cause these ions to undergo nuclear fusion. It was reported in April 2005 by a team at UCLA. The scientists used a pyroelectric crystal heated from −34 to 7 °C (−29 to 45 °F), combined with a tungsten needle to produce an electric field of about 25 gigavolts per meter to ionize and accelerate deuterium nuclei into an erbium deuteride target. Though the energy of the deuterium ions generated by the crystal has not been directly measured, the authors used 100 keV (a temperature of about 109 K) as an estimate in their modeling. At these energy levels, two deuterium nuclei can fuse together to produce a helium-3 nucleus, a 2.45 MeV neutron and bremsstrahlung. Although it makes a useful neutron generator, the apparatus is not intended for power generation since it requires far more energy than it produces.

Tau (particle)

The tau (τ), also called the tau lepton, tau particle, or tauon, is an elementary particle similar to the electron, with negative electric charge and a spin of 1/2. Together with the electron, the muon, and the three neutrinos, it is a lepton. Like all elementary particles with half-integer spin, the tau has a corresponding antiparticle of opposite charge but equal mass and spin, which in the tau's case is the antitau (also called the positive tau). Tau particles are denoted by τ− and the antitau by τ+.

Tau leptons have a lifetime of 2.9×10−13 s and a mass of 1776.82 MeV/c2 (compared to 105.7 MeV/c2 for muons and 0.511 MeV/c2 for electrons). Since their interactions are very similar to those of the electron, a tau can be thought of as a much heavier version of the electron. Because of their greater mass, tau particles do not emit as much bremsstrahlung radiation as electrons; consequently they are potentially highly penetrating, much more so than electrons.

Because of their short lifetime, the range of the tau is mainly set by their decay length, which is too small for bremsstrahlung to be noticeable. Their penetrating power appears only at ultra-high velocity and energy (above petaelectronvolt energies), when time dilation extends their path-length.As with the case of the other charged leptons, the tau has an associated tau neutrino, denoted by ντ.

X-ray filter

An X-ray filter is a material placed in front of an X-ray source in order to reduce the intensity of particular wavelengths from its spectrum and selectively alter the distribution of X-ray wavelengths within a given beam.

When X-rays hit matter, part of the incoming beam is transmitted through the material and part of it is absorbed by the material. The amount absorbed is dependent on the material's mass absorption coefficient and tends to decrease for incident photons of greater energy. True absorption occurs when X-rays of sufficient energy cause electron energy level transitions in the atoms of the absorbing material. The energy from these X-rays are used to excite the atoms and do not continue past the material (thus being "filtered" out). Because of this, despite the general trend of decreased absorption at higher energy wavelengths, there are periodic spikes in the absorption characteristics of any given material corresponding to each of the atomic energy level transitions. These spikes are called absorption edges. The result is that every material preferentially filters out x-rays corresponding to and slightly above their electron energy levels, while generally allowing X-rays with energies slightly less than these levels to transmit through relatively unscathed.

Therefore, it is possible to selectively fine tune which wavelengths of x-rays are present in a beam by matching materials with particular absorption characteristics to different X-ray source spectra.


Yttrium-90, 90Y, is a medically significant isotope of yttrium. Yttrium-90 has a wide and valuable use in radiation therapy to treat cancer.

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