Beta decay is a form of radioactivity governed by the weak interaction, in which a neutron changes into a proton or a proton changes into a neutron. In its two principal emission modes, an atomic nucleus releases an electron and an antineutrino, or a positron and a neutrino. The emitted charged particles are called beta particles. A closely related process, electron capture, produces the same kind of nuclear transformation without emitting a beta particle. Beta decay changes the identity of a chemical element while preserving the total number of protons and neutrons in the nucleus. (energy.gov)
Principal decay modes
In beta-minus decay (β⁻), a neutron becomes a proton, producing an electron and an electron antineutrino:
[ n\rightarrow p+e^-+\bar{\nu}_e. ]
For a nucleus with atomic number (Z) and mass number (A), the transformation is
[ {}^{A}{Z}X\rightarrow{}^{A}{Z+1}Y+e^-+\bar{\nu}_e. ]
The daughter nucleus therefore has one more proton and one fewer neutron than the parent. Carbon-14, for example, decays into nitrogen-14 through this process. The electron is created in the decay; it is not an electron previously stored inside the nucleus. (www2.lbl.gov)
In beta-plus decay (β⁺), a proton within a nucleus becomes a neutron, producing a positron and an electron neutrino:
[ p\rightarrow n+e^++\nu_e. ]
Here (Z) decreases by one, while (A) remains unchanged. Unlike a free neutron, an isolated proton cannot undergo this transformation spontaneously: positron emission requires an energetically favorable change in the entire nuclear system. Neutron-rich nuclei commonly undergo beta-minus decay, whereas proton-rich nuclei may undergo beta-plus decay. (www2.lbl.gov)
In electron capture, the nucleus absorbs an electron from its surrounding atomic electron cloud:
[ p+e^-\rightarrow n+\nu_e. ]
Like beta-plus decay, this decreases the atomic number by one without changing the mass number. Its inclusion under “beta decay” reflects the shared weak-interaction mechanism rather than the emission of a beta particle. (www2.lbl.gov)
Microscopic mechanism and conservation laws
Within the Standard Model, beta decay is a charged-current weak process mediated by a W boson. At the quark level, neutron beta decay converts a down quark into an up quark, changing the neutron’s quark composition into that of a proton. A virtual (W^-) connects this transformation to the production of the electron and antineutrino. The corresponding nuclear proton-to-neutron transformation reverses the quark-flavor change. (s3.cern.ch)
The reactions conserve electric charge, energy, momentum, and angular momentum. Ordinary beta decay also preserves lepton number: the electron and antineutrino carry opposite lepton numbers, as do the positron and neutrino. These emitted leptons are products of the interaction, not pre-existing nuclear constituents. (www2.lbl.gov)
Energy spectrum and decay rates
Beta particles from a particular nuclear transition have a continuous range of kinetic energies. The available energy is shared among the charged particle, the neutrino or antineutrino, and the recoiling daughter nucleus. Consequently, the beta particle does not generally receive a fixed energy, unlike particles emitted in a simple two-body decay. The upper end of its spectrum is called the endpoint. (www2.lbl.gov)
The transformation is possible only when the complete final state is energetically accessible. Differences in nuclear binding and particle rest energies determine the available decay energy. A free neutron is unstable, but a neutron bound in a stable nucleus need not decay because the corresponding daughter system may not be energetically accessible. Beta-decay lifetimes therefore depend on the particular isotope and nuclear transition. (www2.lbl.gov)
For a population with a constant decay rate (\lambda), the expected number of surviving parent nuclei follows
[ N(t)=N_0e^{-\lambda t}, \qquad t_{1/2}=\frac{\ln 2}{\lambda}. ]
The half-life (t_{1/2}) is the time required for half the parent nuclei to decay. It describes the behavior of a population, not a scheduled lifetime for an individual nucleus. (www2.lbl.gov)
Historical significance
The continuous beta spectrum initially posed a difficulty for interpreting radioactive decay as an energy-conserving process. In 1930, Wolfgang Pauli proposed an additional neutral particle that could carry away the unobserved energy and momentum. Enrico Fermi subsequently developed a theory of beta decay, published in 1934, incorporating the particle that became known as the neutrino. (katrin.kit.edu)
Beta decay also provided decisive evidence that parity, or mirror-inversion symmetry, is not conserved by the weak interaction. Experiments conducted in late 1956 by Chien-Shiung Wu and collaborators at the US National Bureau of Standards measured asymmetric electron emission from aligned cobalt-60 nuclei. Their results were published in 1957 and demonstrated that weak processes can distinguish between mirror-related configurations. (nist.gov)
Double beta decay and research
In double beta decay, a nucleus undergoes a transformation involving two beta conversions. The observed two-neutrino beta-minus mode produces two electrons and two electron antineutrinos. Its hypothetical counterpart, neutrinoless double beta decay, would emit two electrons without accompanying antineutrinos. Searches for this process investigate whether neutrinos are their own antiparticles and whether lepton number can be violated. (energy.gov)
Ordinary beta spectra also provide a direct way to investigate neutrino mass. The KATRIN experiment measures the electron spectrum near the endpoint of tritium beta decay, where neutrino mass affects the spectrum’s shape. Such measurements use decay kinematics rather than inferring mass solely from neutrino oscillations. (katrin.kit.edu)