Beta decay

Nuclear physics

Classical decays
Cluster decay

Advanced decays
Isomeric transition

Emission processes
Proton emission

Capturing
S · P · Rp

Fission
Spontaneous fission · Spallation · Cosmic ray spallation · Photodisintegration

Nucleosynthesis
Stellar Nucleosynthesis Big Bang nucleosynthesis Supernova nucleosynthesis

Scientists
Pierre Curie · Hans Bethe · others

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In nuclear physics, beta decay is a type of positron emission as "beta plus" (β⁺).

In β⁻ decay, the weak interaction converts a anti-neutrino ( $\bar{\nu}_e$ ):

$n^0 \rightarrow p^+ + e^- + \bar{\nu}_e$ .

At the W^- boson; the W^- boson subsequently decays into an electron and an anti-neutrino.

In β⁺ decay, energy is used to convert a proton into a neutron, a neutrino ( $ν e$ ):

$\mathrm{energy} + p^+ \rightarrow n^0 + e^+ + {\nu}_e$ .

So, unlike beta minus decay, beta plus decay cannot occur in isolation, because it requires energy, the mass of the neutron being greater than the mass of the proton. Beta plus decay can only happen inside nuclei when the absolute value of the binding energy of the daughter nucleus is higher than that of the mother nucleus. The difference between these energies goes into the reaction of converting a proton into a neutron, a positron and a neutrino and into the kinetic energy of these particles.

In all the cases where β⁺ decay is allowed energetically (and the proton is a part of a nucleus with electron shells), it is accompanied by the electron capture process, when an atomic electron is captured by a nucleus with the emission of a neutrino:

$\mathrm{energy} + p^+ + e^- \rightarrow n^0 + {\nu}_e$ .

But if the energy difference between initial and final states is low (less than 2m_ec²), then β⁺ decay is not energetically possible, and electron capture is the sole decay mode.

If the proton and neutron are part of an transmute one chemical element into another. For example:

$\mathrm{{}^1{}^{37}_{55}Cs}\rightarrow\mathrm{{}^1{}^{37}_{56}Ba}+ e^- + \bar{\nu}_e$ (beta minus),

$\mathrm{~^{22}_{11}Na}\rightarrow\mathrm{~^{22}_{10}Ne} + e^+ + {\nu}_e$ (beta plus),

$\mathrm{~^{22}_{11}Na} + e^- \rightarrow\mathrm{~^{22}_{10}Ne} + {\nu}_e$ (electron capture).

Beta decay does not change the number of ⁴⁰K, which undergoes all three types of beta decay (beta minus, beta plus and electron capture) with half life of 1.277×10⁹ years.

Some nuclei can undergo double beta decay (ββ decay) where the charge of the nucleus changes by two units. In most practically interesting cases, single beta decay is energetically forbidden for such nuclei, because when β and ββ decays are both allowed, the probability of β decay is (usually) much higher, preventing investigations of very rare ββ decays. Thus, ββ decay is usually studied only for beta stable nuclei. Like single beta decay, double beta decay does not change A; thus, at least one of the nuclides with some given A has to be stable with regard to both single and double beta decay.

Beta decay can be considered as a perturbation as described in quantum mechanics, and thus follows Fermi's Golden Rule.

Kurie plot

A Kurie plot (also known as a Fermi-Kurie plot) is a graph used in studying beta decay, in which the square root of the number of beta particles whose momenta (or energy) lie within a certain narrow range, divided by a function worked out by Fermi, is plotted against beta-particle energy; it is a straight line for allowed transitions and some forbidden transitions, in accord with the Fermi beta-decay theory.

References

Franz N. D. Kurie, J. R. Richardson, H. C. Paxton (March 1936). "The Radiations Emitted from Artificially Produced Radioactive Substances. I. The Upper Limits and Shapes of the β-Ray Spectra from Several Elements". Physical Review 49 (5): 368-381. doi:10.1103/PhysRev.49.368.
F. N. D. Kurie (May 1948). "On the Use of the Kurie Plot". Physical Review 73 (10): 1207. doi:10.1103/PhysRev.73.1207.

History

Historically, the study of beta decay provided the first physical evidence of the Rutherford prediction of ½.

In 1920-1927, Charles Drummond Ellis (along with James Chadwick and colleagues) established clearly that the beta decay spectrum is really continuous, ending all controversies.

In a famous letter written in 1930 neutrino, and in 1934 Fermi published a very successful model of beta decay in which neutrinos were produced.

Making it simple to understand the concept of beta decay is generally represented in the following way:

$\mathrm{~^{A}_{Z}X}_{N}\rightarrow\mathrm{~^{A}_{Z+1}Y}_{N-1} + e^- + \bar{\nu}_e$ (beta minus)

$\mathrm{~^{A}_{Z}X}_N\rightarrow\mathrm{~^{A}_{Z-1}Y}_{N+1} + e^+ + {\nu}_e$ (beta plus)

$\mathrm{~^{A}_{Z}X}_N+ e^-\rightarrow\mathrm{~^{A}_{Z-1}Y}_{N+1} + {\nu}_e$ (electron capture)

Where X and Y represent the parent and daughter nuclei respectively, (A= mass number, Z= atomic number, N= number of neutrons).

Beta decay

Kurie plot

References

History

See also