Decay channel

In physics, the decay channel or mode of decay refers to the possibility of an unstable particle or system - for example an elementary particle , a radioactive atomic nucleus or a compound nucleus  - decaying into certain other particles , i.e. i.e. to transform spontaneously. Particles include z. B. also photons ; a decay does not have to be connected with a loss of mass . However, decay only takes place if the sum of the masses of the decay products is less than the initial mass. This expresses the conservation of energy . The loss of total mass occurs according to the mass-energy equivalence as the kinetic energy of the decay products.

For example, the atomic nucleus of potassium -40 (in its ground state ) has three decay channels: It can transform itself

• into a calcium 40 nucleus, one electron and one electron antineutrino ( beta-minus decay )
• or in an argon 40 nucleus, a positron and an electron neutrino ( beta plus decay )
• or, after capturing an electron from its atomic shell, without emitting a positron into an argon-40 nucleus and an electron neutrino ( electron capture ).

The first system discovered with more than one decay channel was a radionuclide that emits both alpha and beta radiation (see History below ). Many other radionuclides have e.g. B. the two decay channels alpha decay and spontaneous fission . In general, such a case of an atomic nucleus with two decay channels is sometimes referred to as dual nuclear decay .

Decay constant and branching ratio

Each decay channel is characterized by a certain decay constant (Greek letter lambda ), which is the probability per unit of time for the decay in this channel. Its dimension is the reciprocal of time, the usual unit of measurement . ${\displaystyle \lambda }$ ${\displaystyle 1/\mathrm {s} }$

If there are several decay channels, their individual (partial) decay constants add up to a total decay constant . This is the probability per unit of time that the system will break down into any of the channels: ${\displaystyle \lambda _{\mathrm {tot} }}$

${\displaystyle \lambda _{1}+\lambda _{2}+\lambda _{3}+\dotsb =\lambda _{\mathrm {tot} }.}$

The value of - always with the existence of several channels  - determines in the law of decay how quickly or slowly the amount of substance (and thus also its activity ) decreases. ${\displaystyle \lambda }$ ${\displaystyle \lambda _{\mathrm {tot} }}$

The size

${\displaystyle B_{i}={\frac {\lambda _{i}}{\lambda _{\mathrm {tot} }}}}$

is called the branching fraction or branching ratio of the channel . B. specified in percent and describes the proportion of all decay events leading to this channel. ${\displaystyle i.}$

Lifespan, half-life, decay range

The reciprocal of the total decay constant is the mean lifetime (Greek letter tau ): ${\displaystyle \tau }$

${\displaystyle \tau ={\frac {1}{\lambda _{\mathrm {tot} }}}}$

After the time , only the portion of the initial amount of substance remains. ${\displaystyle \tau }$ ${\displaystyle 1/e\approx 1/2{,}72\approx 0{,}368=36{,}8\,\%}$

The half-life is shorter and is a good 69 percent of the service life : ${\displaystyle T_{1/2}}$ ${\displaystyle \tau }$

${\displaystyle T_{1/2}=\tau \cdot \ln 2\approx \tau \cdot 0{,}693=69{,}3\,\%\cdot \tau }$

Extremely short lifetimes in the sub-picosecond range are often measured and specified as the decay width , especially in particle physics, by measuring the mass uncertainty ( rest energy uncertainty ) .

Partial half-life

Formally, a corresponding “partial lifetime” and “partial half-life” can also be calculated for each partial decay constant . This would be the time in which the amount of substance would increase or decrease if the relevant decay channel existed alone. Since in reality the other decay channels cannot be “switched off”, these partial periods of time are fictitious, unobservable quantities. Nevertheless, because of its clarity, the partial half-life is considered in some textbooks and in extremely rare decay processes (see e.g. double beta decay ). It can be calculated from the measured half-life - which is then called the "effective" or "total" half-life - together with the associated measured branching ratio. ${\displaystyle 1/e}$ ${\displaystyle 1/2}$

Decay channels within a type of decay

In the case of radioactive conversions, it is sometimes necessary to differentiate between different cases within the same type of decay of the same nuclide, for example

• Alpha decays to different energy levels of the daughter nucleus,
• Spontaneous fission with generation of a specific fission product or pair of fission fragments
• or multi-stage gamma decays (so-called cascades ), which run over different intermediate levels and therefore result in gamma spectral lines of different energies.

They are generally not referred to as decay channels, but they are subject to the same rules. In the case of gamma lines, the size corresponding to the branching ratio, the number of photons of this energy per decay, is often called "intensity" and is designated by or . ${\displaystyle I}$ ${\displaystyle I_{\gamma }}$

Data collections

For elementary particles you get an overview of the different decay channels and decay probabilities in the Review of Particle Physics published by the Particle Data Group or in its short version, the Particle Physics Booklet .

For radionuclides, half-lives and decay channels are e.g. B. specified in the Karlsruhe nuclide map . Branching ratios and other data can be found in the extensive book Table of Isotopes.

history

Alpha and beta (dual core) decay channels of Bi-212

Two different decay channels of the same radionuclide were first discovered in 1906 by Otto Hahn during his stay in Lord Rutherford's laboratory in Montreal (Canada) on the bismuth isotope Bi-212 (the nuclide was then initially called thorium B, shortly afterwards thorium C. ). The figure opposite shows the decay scheme of Bi-212.

literature

• H. Krieger: Fundamentals of radiation physics and radiation protection. 2007, ISBN 978-3-8351-0199-9 .
• W. Stolz: Radioactivity. 2005, ISBN 3-519-53022-8 .
• J. Magill, J. Galy: Radioactivity, Radionuclides, Radiation. 2005, ISBN 3-540-21116-0 .

Individual evidence

1. ^ ^{A b} Karl Heinrich Lieser: Introduction to nuclear chemistry. (1991), ISBN 3-527-28329-3 .
2. ↑ ^{a b} Richard B. Firestone, Coral M. Baglin (Ed.): Table of Isotopes, 8th Edition, 1999 Update . Wiley, New York 1999. ISBN 0-471-35633-6 -.
3. ↑ Otto Hahn, Physikalische Zeitschrift Vol. 7, pp. 412-419, 456-462 (1906).
4. ↑ Ernest Rutherford: Radioactive substances and their radiations. P. 479 (1913).
5. ↑ Otto Hahn: From Radiothor to Uranium Fission. Pp. 24-27 (1962).