Beta radiation

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β - radiation (protons red, neutrons blue)
β + radiation

Beta radiation or β radiation is ionizing radiation that occurs during radioactive decay , beta decay or beta transition . The atomic nucleus of a beta emitter is transformed into an atomic nucleus of another chemical element . In the case of a β - decay (pronounced: beta minus) this is the element with the next higher atomic number , in a β + decay (pronounced: beta plus) the element with the next lower. The radiating atomic nucleus is called the mother nuclide, the resulting daughter nuclide .

Beta radiation is particle radiation and consists of so-called beta particles . In the case of β - radiation, these are negatively charged electrons , and in the case of β + radiation, positively charged positrons . In addition to the beta particle, an electron antineutrino is released in the event of a β - decay and an electron neutrino in the event of a β + decay . As a rule, these particles cannot be detected and are not counted as beta radiation. In addition, low-energy electromagnetic radiation is released with each beta decay. In contrast to alpha radiation, the kinetic energy of the beta particles emitted can assume any value from almost zero to a maximum energy. The typical maximum energy of beta radiation is in the range of hundreds of kiloelectronvolts to a few megaelectronvolts and depends on the specific decay.

The name comes from the first division of ionizing rays from radioactive decay into alpha rays , beta rays and gamma rays , which in this order show increasing permeability of matter.


Feynman diagram for the decay of a neutron  n into proton  p , electron  e - and electron antineutrino  mediated via a
W boson W - . 

Beta decay of atomic nuclei

Beta decay is a radioactive type of decay of atomic nuclei . In the event of a β - decay, a neutral neutron in the atomic nucleus is transformed into a positively charged proton . Corresponding to the conservation of charge , a negatively charged electron is created in this process, and an additional electron antineutrino , corresponding to the conservation of lepton numbers. During the β + decay, a proton is transformed into a neutron, the positive charge is carried away by a positron and the lepton number is maintained by an electron neutrino. In both decay processes the core converts to an atomic nucleus having the same mass number , but modified by one atomic number in order. This means that the resulting atomic nucleus has (almost) the same weight - protons and neutrons have a slightly different mass and there is also a mass defect due to the release of energy - but it belongs to a different chemical element. Such atomic nuclei are called isobars .

Such a decay is possible if the atomic mass of the parent nuclide is greater than the sum of the atomic mass of the daughter nuclide and that of the beta particle, since the difference in masses according to Einstein's equivalence of mass and energy can then be released as kinetic energy of the particles. If the isobars are lighter in both directions of the periodic table, then a particle can decay both β - and β + . This occurs, for example, with potassium -40, which can break down to calcium -40 as well as argon -40. Because of the conservation of energy and momentum (see kinematics (particle processes) ), the light beta particle and the almost massless (anti-) neutrino receive the vast majority of the energy. In the case of the heavy daughter core, only a very small proportion of a few eV remains.

In the early days of nuclear physics, the observation of beta electrons temporarily led to the false conclusion that electrons were part of the atomic nucleus. According to current knowledge, however, the two emitted particles are only generated at the time of the nuclear transformation.

Modern theory describes beta decay as a process of weak interaction . During the β - decay at the level of the elementary particles, one of the two d-quarks of the neutron ( ) is converted into a u-quark through interaction with a W - boson . The neutron becomes a proton ( ), while the W boson decays into an electron and an antineutrino. In the case of β + decay, conversely, one of the u quarks of a proton is converted into a d quark by means of a W + boson.

The fact that beta-minus rays are actually the same type of particle as the electrons in the atomic shell is shown by their interaction with matter. The Pauli principle , which only applies to identical particles, prevents the electron from being trapped in already occupied states of a neutral atom after it has been decelerated. This capture has never actually been observed with beta-minus rays, while for other negatively charged particles, for example muons , this capture is not prohibited and is also observed.

Beta-minus decay (β - )

Nuclides with an excess of neutrons decay via the β - process. A neutron in the nucleus transforms into a proton and sends out an electron ( ) and an electron antineutrino ( ). Electron and antineutrino leave the atomic nucleus because they are leptons and are not subject to the strong interaction . Since there is one neutron less but one more proton in the nucleus after the decay process, the mass number remains unchanged while the atomic number increases by 1. So the element goes into its successor in the periodic table .

If you write mass numbers at the top and atomic charge numbers at the bottom of the symbols as usual , the decay of the neutron can be described by the following formula:

If X denotes the mother nuclide and Y the daughter nuclide , the following generally applies to the β - decay:

A typical β - radiator is 198 Au . Here is the conversion into formula notation:

The usually high energy of the generated electron prevents an immediate capture in one of the high-lying free states of the same atom. However, especially with highly charged heavy ions, a transition to such a bound state can take place directly; this process is called bound beta decay.

The transformation or decay energy is:

In the literature on beta decay spectroscopy, this decay was formerly also called negatron decay (“negatron” for electron).

Beta plus decay (β + )

The β + decay occurs in proton-rich nuclides. A proton in the nucleus is converted into a neutron. An electron neutrino is emitted together with a positron (positron radiation). As with β - decay, the mass number remains unchanged, but the atomic number is reduced by 1, so the element is transferred to its predecessor in the periodic table.

The formula for converting the proton into a neutron is:

With the same notations as above, the general β + -decay can be described as:

Beta-plus decay can only occur if the transition energy of the transition is at least 1022 keV. This is twice the rest energy of an electron or positron, because the positron has to be generated, and the conversion energy is also defined as the mass difference between the starting atom (atomic number Z) and the end atom (atomic number Z-1), which are each assumed to be neutral; the end atom has one less electron than the starting atom. The transformation or decay energy is:

with the electron mass.

The most frequently occurring primordial nuclide in which (among other things) β + decay occurs is potassium-40 ( 40 K ), but the decay is very rare. Here is the formula:

Electron capture (ε)

A process that competes with β + decay is electron capture (also called ε (epsilon) decay or K capture). It is counted among the beta decays, although no beta radiation occurs. Here, too, a proton in the nucleus is converted into a neutron, while an electron from a shell near the nucleus of the atomic shell is destroyed and a neutrino is generated and emitted:

This process occurs as a further decay channel for every β + emitter . It is the only decay channel when the transformation energy of the transition is less than 1022 keV. Electron capture also requires a conversion energy of at least one electron rest energy, which is 511 keV.

Electron capture also proves that shell electrons and beta electrons are the same type of particle.

The name K capture comes from the fact that an electron is usually captured from the K shell. The “gap” created there leads to the emission of a characteristic X-ray photon or the emission of Auger electrons .

Decay of the free neutron

A free neutron is also subject to beta-minus decay . It is converted into a proton, an electron antineutrino and an electron that can be detected as beta radiation:

The lifespan for this decay is 880.3 ± 1.1 seconds, that is just under 15 minutes. This corresponds to a half-life of around 10 minutes. In normal surroundings on earth (e.g. in air) every neutron released is captured by an atomic nucleus in a much shorter time; therefore this decay does not play a practical role here.

Inverse beta decay

In inverse beta decay (IBD), a proton is converted into a neutron by reacting with a neutrino:

With this process, the first neutrino detection was achieved in 1959 ( Cowan-Reines-Neutrinoexperiment ) and in later neutrino detectors (especially in experiments with low-energy neutrinos such as experiments with reactor and geoneutrinos, on neutrino oscillations and for the search for sterile neutrinos ). A minimum energy of the antineutrino of 1.806 MeV is necessary for this process. In typical neutrino experiments, the positron leads to annihilation with an electron, which leads to a photon with energy keV; generated the neutron, after moderation in z. B. water, when captured by a suitable atomic nucleus (such as cadmium -113) delays a gamma radiation of characteristic energy for electron-positron annihilation.

The reaction process corresponding to electron capture is also referred to as inverse beta decay :

It plays a role in astrophysics with high density matter (neutron stars, white dwarfs).

Energy spectrum

In contrast to alpha radiation, the energy distribution of beta radiation ( beta spectrum ) is continuous, since the energy released during decay is not distributed over two, but three particles - atomic nucleus, electron / positron and antineutrino / neutrino. While maintaining the total momentum, the energies of the individual particles are not fixed (see kinematics (particle processes) ).

Beta electron spectrum
of 210 Bi: Plotted (in arbitrary units) is the number of electrons per energy interval as a function of the kinetic energy with which the electron left the atom. As a result of the electrical attraction, this is somewhat smaller than the energy that the electron would have if the nucleus were uncharged ( Coulomb shift ).

The figure shows a simple measured electron spectrum. More complex spectra occur when beta transitions to different energy levels of the daughter nucleus overlap.

Examples of beta highest energies
isotope Energy
( keV )
Decay Remarks
0782.33 β -
003 H
0018.59 β - Second lowest known β - energy, is used in the KATRIN experiment .
011 C 0960.4
β +
014 C 0156.475 β -
020 F 5390.86 β -
037 K 5125.48
β +
163 Ho 0002.555 ε+
187 Re 0002,467 β - Lowest known β - -Energy should, in the experiment MARE be used
210 bi 1162.2 β -

In tables, the total transition energy in the ground state of the daughter nuclide is often given. This may contain subsequent gamma radiation and / or the rest energy of an electron-positron pair.

Conversion electrons

Measurements of the energy distribution of the electrons of beta radiation often result in spectra that contain sharp lines ( peaks ) in addition to the broad continuum . These are electrons that were emitted from the shell by internal conversion of an excited nuclear state. This part of the spectrum used to be called the discrete beta spectrum, although it has nothing to do with the actual beta decay .

Neutrino mass

The shape of the spectrum in the vicinity of the maximum electron or positron energy gives information about the still unknown mass of the electron neutrino or antineutrino. To do this, the high-energy end (the last 1 to 2 eV) of a beta spectrum must be measured with very high accuracy. An abrupt end as opposed to a continuous decrease in the maximum energy would show a neutrino mass other than zero - as expected based on the neutrino oscillations - and its value could be determined. The measurement is preferably carried out during beta decay of nuclides with low decay energy such as tritium (experiment KATRIN ) or rhenium-187 (experiment MARE).

Inner bremsstrahlung

When the beta decays, electrically charged particles are accelerated, which is why electromagnetic radiation occurs in the form of bremsstrahlung . To distinguish it from bremsstrahlung, which arises when the beta particles are braked in matter, this form is called internal bremsstrahlung. It was first described by Aston in 1927. A theoretical treatment was given in 1949 by Wang Chang and Falkoff. The intensity of the internal bremsstrahlung is frequency-independent up to a maximum frequency that follows from the law of conservation of energy. Their polarization lies in the plane of the direction of flight of the beta particle and the direction of observation, their energy is in the classical approximation

with the fine structure constant , the speed of light , the electron mass and the speed of the beta particle . The size is also called rapidity . For slow beta particles,, this energy loss is negligible. For high-energy beta particles, the formula can go through

can be approximated with the energy of the beta particle . Even for high-energy particles with an energy of 5 MeV, the loss due to radiation is only of the order of one percent.

The angular distribution of this inner bremsstrahlung is through

given and is identical to the angular distribution of external bremsstrahlung.

When electrons are captured, radiation is released due to the disappearance of the electric charge and the magnetic moment of the electron. This cannot be described in a classical theory. Martin and Glauber provided an explanation in 1957. The semiclassical treatment of the problem results in the differential intensity distribution

with the reduced Planck quantum of action , the atomic number , the characteristic frequency of the transition with the Rydberg energy and the total energy released by electron capture . The first term comes from the electrical charge, the second from the magnetic moment.

In this approximation, a pole (which cannot be integrated) occurs at. This can be explained by the semi-classical approach that the electron is on a circular orbit around the atomic nucleus: Classically, the electron would continuously emit synchrotron radiation on this circular orbit .


Beta radiation is longitudinally spin-polarized in its direction of emission , that is, fast β - particles have a polarization opposite to the direction of flight (clearly: move like a left-hand screw), fast β + particles have a polarization in the direction of flight. This is a fundamentally interesting property of the weak interaction, since it proves the non-maintenance of parity . However, it plays practically no role in the effects and applications of radiation.

Interaction with matter

When beta particles penetrate a material, energy transfer to the material and ionization take place in a near-surface layer that corresponds to the penetration depth of the particles.

If the penetrating particle is a positron (β + particle), it will very soon meet an electron, i.e. its antiparticle . This leads to annihilation , from which (mostly) two photons in the gamma range arise .

Biological effect

If the human body is exposed to beta rays from outside, only layers of the skin are damaged. However, there can be intense burns and the resulting long-term effects such as skin cancer . If the eyes are exposed to radiation, the lens can become cloudy .

If beta emitters are absorbed ( incorporated ) into the body, high levels of radiation exposure can result in the vicinity of the emitter. Thyroid cancer is well documented as a result of radioactive iodine -131 ( 131 I) that collects in the thyroid gland . There are also fears in the literature that strontium -90 ( 90 Sr) can lead to bone cancer and leukemia , since strontium, like calcium, accumulates in the bones.

Radiation protection

Beta rays can be shielded well with an absorber a few millimeters thick (e.g. aluminum sheet ) . However, part of the energy of the beta particles is converted into X-ray bremsstrahlung . In order to reduce this proportion, the shielding material should have atoms that are as light as possible, i.e. have a low atomic number . Behind it, a second heavy metal absorber can shield the bremsstrahlung.

Max. Range of β-particles of different energies in different materials
nuclide energy air Plexiglass Glass
187 Re 2.5 keV 1 cm
3 H 19 , 0 keV 8 cm
14 C 156 , 0 keV 65 cm
35 p 167 , 0 keV 70 cm
131 I. 600 , 0 keV 250 cm 2.6 mm
32 P 1710 , 0 keV 710 cm 7.2 mm 4 mm

A material-dependent maximum range can be determined for β-emitters , because β-particles give off their energy (like alpha particles ) in many individual collisions to atomic electrons; the radiation is therefore not attenuated exponentially like gamma radiation . The selection of shielding materials results from this knowledge. For some of the β-emitters widely used in research, the ranges in air, plexiglass and glass are calculated in the adjacent table. A 1 cm thick plexiglass screen can provide reliable screening with the energies specified.

In the case of β + radiation, it should be noted that the β + particles annihilate with electrons (see above), whereby photons are released. These have energies of about 511 keV (corresponding to the mass of the electron) and are therefore in the range of gamma radiation.


In nuclear medicine , beta emitters (e.g. 131 I, 90 Y) are used in radionuclide therapy . In nuclear medicine diagnostics, the β + emitters 18 F, 11 C, 13 N and 15 O are used in positron emission tomography as radioactive marking of the tracers . The radiation generated by pair annihilation is evaluated .

In radiation therapy , beta emitters (e.g. 90 Sr, 106 Ru) are used in brachytherapy .

Beta rays are also used - in addition to X-ray and gamma radiation - for radiation sterilization .

The radiometric measurement of dust , a method for the measurement of gas-borne dusts, uses the absorption of beta-rays. 14 C and 85 Kr , for example, are used as radiation sources .

Beta decay transitions in cores

A distinction is made in beta decays into Fermi decays, in which the spins of the emitted particles (electron and antineutrino or positron and neutrino) are antiparallel and are coupled, and Gamow-Teller transitions, in which the spins are coupled. The total angular momentum of the nuclei does not change with Fermi transitions ( ), with Gamow-Teller transitions it changes . A transition in nuclear spin from to in the Gamow-Teller transition is prohibited. Such transitions (in which only the Fermi transition contributes) are also referred to as super -allowed.

The two transition types correspond to terms in the Hamilton operator of

at the Fermi transition and

at the Gamow-Teller transition

Here are the Pauli matrices the spin operator and the Isospinoperators (he causes the transition of proton to neutron and vice versa) and the unity operator in the spinning space. is the vector coupling constant of the weak interaction (also Fermi coupling constant), the axial vector coupling constant (also Gamow-Teller coupling constant). The Fermi decays were described in the 1930s by an effective theory of the weak interaction by Enrico Fermi , a few years later George Gamow and Edward Teller added an axial vector term.

In the case of beta decays in nuclei, mixtures of the Fermi and Gamow-Teller transition can also occur, if the initial nucleus can decay into the ground state and another time into an excited state.

Transitions with orbital angular momentum of the emitted particles other than zero are less likely and are referred to as hindered (with different degrees depending on the orbital angular momentum). Depending on the value of , the parity ( ) or not changes. With simple Fermi and Gamow-Teller transitions with the parity does not change. This distinguishes Gamow-Teller transitions from their analogues in electromagnetic dipole transitions (the operator there is a polar vector and not an axial one, the parity changes).

Research history

In 1903, Ernest Rutherford and Frederick Soddy developed a hypothesis according to which the radioactivity, discovered by Antoine Henri Becquerel in 1896 , is linked to the conversion of elements . The beta decay was identified as the source of the beta radiation. Based on this, Kasimir Fajans and Soddy formulated the so-called radioactive displacement theorems in 1913 , with which the natural decay series are explained by successive alpha and beta decays . The idea that the beta electrons themselves, like the alpha particles, came from the nucleus, solidified in the circle of Ernest Rutherford in 1913.

In the early days, there was long general consensus that beta particles, like alpha particles, have a discrete spectrum that is characteristic of each radioactive element. Experiments by Lise Meitner , Otto Hahn and Otto von Baeyer with photographic plates as detectors, which were published in 1911 and the following years, as well as improved experiments by Jean Danysz in Paris in 1913, however, showed a more complex spectrum with some anomalies (especially with radium E, i.e. 210 Bi ), which indicated a continuous spectrum of beta particles. Like most of her colleagues, Meitner initially considered this to be a secondary effect, i.e. not a characteristic of the electrons originally emitted. It was not until James Chadwick's experiments in Hans Geiger's laboratory in Berlin in 1914 with a magnetic spectrometer and counter tubes as detectors that the continuous spectrum was a characteristic of the beta electrons themselves.

In order to explain this apparent non-conservation of energy (and a violation of the conservation of momentum and angular momentum ), Wolfgang Pauli proposed in a letter in 1930 that a neutral, extremely light elementary particle should be involved in the decay process, which he named “Neutron”. Enrico Fermi changed this name in 1931 to neutrino (Italian for “small neutral”) to distinguish it from the much heavier neutron, which was discovered almost at the same time. The first experimental proof of the neutrino was only achieved in 1956 in one of the first large nuclear reactors (see Cowan-Reines-Neutrinoexperiment ).

The identity of the beta particles with atomic electrons was proven in 1948 by Maurice Goldhaber and Gertrude Scharff-Goldhaber . The β + decay was discovered in 1934 by Irène and Frédéric Joliot-Curie . Electron capture was theoretically predicted by Hideki Yukawa in 1935 and was first demonstrated experimentally in 1937 by Luis Walter Alvarez .

In 1956, an experiment carried out by Chien-Shiung Wu succeeded in demonstrating the parity violation in beta decay postulated shortly before by Tsung-Dao Lee and Chen Ning Yang .

Artificial electron beams

Occasionally, free electrons that are artificially generated (e.g. by a hot cathode ) and brought to high energy in a particle accelerator are also inexactly referred to as beta radiation. The name of the electron accelerator type Betatron also indicates this.

See also


  • Werner Stolz: Radioactivity. Basics - Measurement - Applications. 5th ed. Teubner, 2005, ISBN 3-519-53022-8 .

Nuclear physics

Research history

  • Carsten Jensen: Controversy and Consensus: Nuclear Beta Decay 1911-1934. Birkhäuser 2000.
  • Milorad Mlađenović: The History of Early Nuclear Physics (1896–1931). World Scientific, 1992, ISBN 981-02-0807-3 .

Radiation protection

  • Hanno Krieger: Fundamentals of radiation physics and radiation protection. Vieweg + Teubner, 2007, ISBN 978-3-8351-0199-9 .
  • Claus Grupen: Basic course in radiation protection. Practical knowledge for handling radioactive materials. Springer, 2003, ISBN 3-540-00827-6 .
  • James E. Martin: Physics for Radiation Protection. Wiley, 2006, ISBN 0-471-35373-6 .


  • Günter Goretzki: Medical Radiation Science. Physical and technical basics. Urban & Fischer, 2004, ISBN 3-437-47200-3 .
  • Thomas Herrmann, Michael Baumann and Wolfgang Dörr: Clinical Radiation Biology - in a nutshell. Urban & Fischer, 2006, ISBN 3-437-23960-0 .

Web links

Wiktionary: Beta radiation  - explanations of meanings, word origins, synonyms, translations

Individual evidence

  1. John David Jackson: Classical Electrodynamics . 3. Edition. de Gruyter, Berlin • New York 2002, p. 843-850 .
  2. see e.g. B. Max Planck: The world view of the new physics. Leipzig: Barth, 1929, pp. 17/18.
  3. ^ A b Maurice Goldhaber , Gertrude Scharff-Goldhaber : Identification of beta-rays with atomic electrons . In: Physical Review . Volume 73, No. 12 , 1948, pp. 1472-1473 , doi : 10.1103 / PhysRev.73.1472 .
  4. ^ F Bosch, DR Atanasov, C Brandau, I Dillmann, C Dimopoulou: Beta decay of highly charged ions . In: Physica Scripta . T156, doi : 10.1088 / 0031-8949 / 2013 / t156 / 014025 ( ).
  5. Mayer-Kuckuck, Kernphysik, Teubner, 1979, p. 294
  6. H. Krieger, W. Petzold: radiation physics, dosimetry and radiation protection . Volume 1. 3rd edition, Teubner 1992, ISBN 978-3-519-23052-6 , page 63
  7. Mayer-Kuckuck, Kernphysik, Teubner 1979, p. 294
  8. Mayer-Kuckuck, Kernphysik 1979, p. 295
  9. KA Olive et al. (Particle Data Group), Chin. Phys. C38 , 090001 (2014): N Baryons Summary Table
  10. Spectrum Lexicon Physics, Inverse Beta Decay
  11. Borexino Collaboration: Observation of Geoneutrinos , Phys. Lett. B, Volume 687, 2010, pp. 299-304
  12. Andreas Müller, Betazerfall, Lexicon of Astronomy, Spectrum
  13. Sexl, Sexl, White Dwarf Black Holes, Vieweg 1977, p. 55
  14. z. B. Ch. Gerthsen: Physics. 6th edition, Springer 1960, p. 329.
  15. GH Aston: The Amount of Energy Emitted in the γ-ray form by radium E . In: Mathematical Proceedings of the Cambridge Philosophical Society . tape 23 , no. 8 , 1927, pp. 935-941 .
  16. ^ CS Wang Chang and DL Falkoff: On the Continuous Gamma-Radiation Accompanying the Beta-Decay of Nuclei . In: Physical Review . tape 76 , no. 3 , 1949, pp. 365-371 .
  17. PC Martin and RJ Glauber: Relativistic Theory of Radiative Orbital Electron Capture . In: Physical Reviews . tape 109 , no. 4 , 1958, pp. 1307-1325 .
  18. a b Hanno Krieger: Fundamentals of radiation physics and radiation protection. 2nd Edition. P. 109.
  19. Heinrich Dresia, Franz Spohr: Possible uses and errors of radiometric dust measurement for monitoring emission, immission and workplaces. In: Dust - cleanliness. Air . 38, No. 11, 1978, ISSN  0949-8036 , pp. 431-435.
  20. ^ Franz Joseph Dreyhaupt (ed.): VDI-Lexikon Umwelttechnik. VDI-Verlag Düsseldorf 1994, ISBN 3-18-400891-6 , p. 1119.
  21. ^ Wong, Introductory Nuclear Physics, Wiley-VCH 2004, p. 199
  22. a b For example Enrico Fermi, Nuclear Physics, 1953, pp. 81f
  23. a b Bethge, Walter, Wiedemann, Kernphysik, Springer 2008, p. 252
  24. O. v. Baeyer, L. Meitner, O. Hahn: Magnetic spectra of the beta rays of radium. In: Physikalische Zeitschrift. Volume 12, 1911, pp. 1099-1101 ( [1] PDF).
  25. Chadwick: Intensity distribution in the magnetic spectrum of the beta rays from radium B + C. In: Negotiations of the German Physical Society. Volume 16, 1914, pp. 383-391.
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