# Beta decay

In nuclear physics, beta decay is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted. In the case of electron emission, it is referred to as "beta minus" (β), while in the case of a positron emission as "beta plus" (β+).

In β decay, the weak nuclear force converts a neutron into a proton while emitting an electron and an anti-neutrino:

${\displaystyle \mathrm {n} \rightarrow \mathrm {p} +\mathrm {e} ^{-}+{\bar {\nu }}_{e}}$

At the fundamental level (as depicted in the Feynman diagram below), this is due to the conversion of a down quark to an up quark by emission of a W boson.

In β+ decay, a proton is converted into a neutron, a positron and a neutrino:

${\displaystyle \mathrm {energy} +\mathrm {p} \rightarrow \mathrm {n} +\mathrm {e} ^{+}+{\nu }_{e}}$

So, unlike beta minus decay, beta plus decay cannot occur in isolation, because the mass of the neutron alone is greater than the mass of the proton. Beta plus decay can only happen inside nuclei with high binding energy and this energy goes into the reaction of converting a proton into a neutron.

If the proton and neutron are part of an atomic nucleus, these decay processes transmute one chemical element into another. For example:

${\displaystyle \mathrm {{}^{1}{}_{55}^{37}Cs} \rightarrow \mathrm {{}^{1}{}_{56}^{37}Ba} +\mathrm {e} ^{-}+{\bar {\nu }}_{e}}$ (beta minus)
${\displaystyle \mathrm {~_{11}^{22}Na} \rightarrow \mathrm {~_{10}^{22}Ne} +\mathrm {e} ^{+}+{\nu }_{e}}$ (beta plus)

Historically, the study of beta decay provided the first physical evidence of the neutrino. In 1911 Lise Meitner and Otto Hahn performed an experiment that showed that the energies of electrons emitted by beta decay had a continuous rather than discrete spectrum. This was in apparent contradiction to the law of conservation of energy, as it appeared that energy was lost in the beta decay process. A second problem was that the spin of the Nitrogen 14 atom was 1, in contradiction to the Rutherford prediction of 1/2. In a famous letter written in 1930 Wolfgang Pauli suggested that in addition to electrons and protons atoms also contained an extremely light neutral particle which he called the neutron. He suggested that this neutron was also emitted during beta decay and had simply not yet been observed. In 1931 Enrico Fermi renamed Pauli's neutron the neutrino, and in 1934 Fermi published a very successful model of beta decay in which neutrinos were produced.

In some nuclei, beta decay is energetically prevented, and in some of these cases the nuclei may undergo double beta decay.

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