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Accelerator mass spectrometry uses ion acceleration and particle identification to count rare isotopes relative to abundant ones. For radiocarbon dating, it measures carbon-14 directly rather than waiting to count its beta decays.

Beta decay is a weak interaction process changing the proton-to-neutron composition of an atomic nucleus while preserving its mass number. In beta-minus decay, a neutron converts to a proton with an emitted electron and electron antineutrino; in beta-plus decay, a proton converts to a neutron with an emitted Positron and electron neutrino, when the complete energy balance permits it.^[ref]

The emitted beta particle is created in the transition rather than being an ordinary orbital electron expelled from the atom. Its kinetic energy varies because the available Q value is shared with the neutrino and daughter recoil. A magnetic electron spectrometer can separate different emitted momenta; a detector then records a continuous distribution rather than one universal electron energy.

Conservation of electric charge, energy and angular momentum constrains the final state. Nuclear binding matters: a free proton cannot undergo ordinary beta-plus decay, although an energetically allowed proton-to-neutron transition can occur within an appropriate atomic nucleus.

A beta-decay spectrum gives the distribution of emitted electron or positron energies in beta decay. In ordinary three-body beta decay, the charged lepton shares the available energy with a neutrino and the recoiling daughter nucleus, producing a continuous spectrum.

For a simple allowed decay, its shape includes phase-space factors, an electron Coulomb correction and an endpoint set by the available energy. Schematically, $d\Gamma /dE\propto F(Z,E)pE(E_0-E{)}^2$ when the neutrino mass is neglected and $E$ is total electron energy. Nuclear matrix elements and forbiddenness can modify this expression. The continuum was central to understanding the missing energy carried by the neutrino.

A nuclear beta decay connects initial and final quantum states through vector and axial-vector parts of the weak charged current. At leading order in the lepton wavelength expansion, Fermi transitions carry lepton-pair spin $S=0$, while Gamow-Teller transitions carry $S=1$. If the lepton pair carries orbital angular momentum $l$, its total angular momentum is $J=l$ for $S=0$, or $J=|l-1|,\dots ,l+1$ for $S=1$. The nuclear states must obey $|J_i-J_f|\le J\le J_i+J_f$, and their parities satisfy ${\pi }_f/{\pi }_i=(-1{)}^l$ in this leading orbital classification. The least permitted $l$ labels the degree of forbiddenness. Real forbidden transitions involve several weak multipole operators; the elementary spin classification does not assert that only one operator or nuclear matrix element exists.

A beta particle is an electron or Positron emitted in beta decay. It has the same intrinsic properties as an electron or Positron produced by another process; the name identifies its origin rather than a new particle species.

Unlike a specified two-body alpha transition, ordinary beta emission shares available energy with a neutrino and daughter recoil. The emitted beta particles therefore have a continuous range of kinetic energies. In an applied magnetic field, electrons and positrons curve in opposite senses for the same incident direction. Detector response, energy loss in the sample and collection geometry modify the measured distribution.

Chien-Shiung Wu and collaborators tested parity conservation by measuring the beta decay of oriented cobalt-60 nuclei at very low temperature. Their apparatus placed a beta counter inside a demagnetization cryostat and used the accompanying gamma ray anisotropy to monitor nuclear orientation. The emitted electrons favored one direction relative to the nuclear spin. Because parity reverses momentum while leaving angular momentum unchanged, that directional asymmetry distinguishes a process from its mirror image and demonstrated parity violation in the weak interaction.^[ref]

A physicist.^[ref]

An experimental nuclear physicist who coauthored the Wu experiment. Comparing beta decay from oriented cobalt-60 nuclei with the opposite orientation tested whether a mirror-reflected process would have the same probability. The observed directional asymmetry showed failure of parity conservation in the weak interaction.^[ref]

Double beta decay changes the atomic number of a nucleus by two while preserving its mass number. The ordinary two-neutrino process can connect even-even nuclear isobars when the intermediate odd-odd nucleus is too heavy for a single beta decay. Neutrinoless variants would violate lepton number and require additional physics.

The down quark $d$ is the first-generation down-type quark, with electric charge $-e/3$, spin $1/2$ and baryon number $1/3$. Together with the up quark, it supplies the net valence flavor content of ordinary protons and neutrons.^[ref]

The minimal neutron content $udd$ has total electric charge zero and baryon number one. In beta decay, a down-to-up weak charged current can turn a neutron into a proton, accompanied by the required leptons. This is a flavor change, rather than an electron previously stored inside the neutron escaping. Additional quark pairs and gluons are part of the full hadron state.

An energy deposition in a target's electronic degrees of freedom, as opposed to a nuclear recoil. gamma rays and beta decay can produce backgrounds in this channel. Detector discrimination is statistical because the measured light and charge distributions have finite widths.

Isotope abundance, nuclear separation energies, spin and nuclear magnetic moments supply complementary tests: abundance concerns which atomic nuclei survive and accumulate, removal energy concerns binding, and magnetic properties test the angular momentum assignments. Agreement across these observables is more informative than fitting one list of numbers.

In her 1963 lecture, Maria Goeppert Mayer recalled excess abundances at $N=50$ and $82$. She contrasted the strong binding of the last neutron in oxygen isotope ${}^{16}\mathrm{O}$ with the weaker extra neutron in oxygen isotope ${}^{17}\mathrm{O}$, and displayed beta decay energies near $N=20$ and $50$. These are compiled empirical patterns, rather than readings from an apparatus she built.^[ref]

Her 1949 letter compared observed spins and nuclear magnetic moments with orbital assignments. For example, lead isotope ${}^{207}\mathrm{Pb}$ was assigned a $p_{1/2}$ neutron hole near $N=126$, whereas bismuth's odd proton began the next shell as $h_{9/2}$. The moments tested orbital character as well as spin.^[ref]

A useful comparison holds $Z$ fixed when comparing neighboring isotopes, and examines odd-even staggering separately from a shell discontinuity. Abundance additionally depends on production and decay history. Neither the abundance pattern nor a successful spin assignment directly images orbiting particles; neither fixes a unique nuclear mean field. The experimental techniques themselves include mass spectrometry and nuclear magnetic resonance, whose preparation and readout differ. The Hofstadter nuclear electron scattering experiment separately constrains nuclear size and nuclear charge distributions, rather than measuring these occupancies.

An experimental physicist whose cryogenic expertise contributed to the Wu experiment. The National Bureau of Standards laboratory could align atomic nuclei at extremely low temperature, enabling a directional beta decay test in cobalt-60. The collaboration demonstrated a failure of parity conservation.^[ref]

The electron-nucleus Coulomb-distortion factor multiplying an otherwise plane-wave beta decay spectrum. It depends on daughter charge, lepton charge and lepton energy. Its energy dependence means that a pure fifth-power phase-space rule is not generally exact.

A first-forbidden unique beta decay has $|\Delta J|=2$ with a parity change. Its leading lepton shape factor contains two additional powers of momentum relative to an allowed beta decay. In the massless, no-Coulomb limit, ${\int }_0^Q{E}^2(Q-E{)}^2[E^2+(Q-E{)}^2]dE=2Q^7/105$. Thus its microscopic reduced nuclear matrix element multiplies a seventh-power phase-space factor, rather than the fifth power in the Sargent rule. A fifth-power comparison across different forbiddenness classes instead extracts convention-dependent effective strengths.

Nuclear isobars are different nuclides with the same mass number $A$ and different atomic numbers $Z$. They differ from isotopes, which have fixed $Z$. Beta decay connects neighboring nuclear isobars.

Neptunium is the chemical element with atomic number 93. Its isotope neptunium-239 occurs between uranium-239 and plutonium-239 in a neutron-capture and beta decay production chain.

Nuclear fission splits an atomic nucleus into two major fragments, usually accompanied by emitted neutrons and gamma rays. It can follow neutron absorption or occur spontaneously in some heavy nuclides. When the products have greater total nuclear binding energy, the decrease in rest energy supplies fragment kinetic energy and radiation.

The fragments are often neutron-rich and undergo subsequent beta decay, producing an evolving inventory of fission products. Some emitted neutrons can cause further nuclear fission, enabling a nuclear chain reaction; others are absorbed without fission or escape.

The discovery combined chemical and physical evidence. Otto Hahn and Fritz Strassmann identified barium among products of neutron-irradiated uranium, rather than merely an adjacent heavy element. Lise Meitner and Otto Robert Frisch interpreted this as division of the atomic nucleus and estimated the large released energy from mass differences. Chemical separation identified the unexpected product: the same procedure could separate a radium isotope from barium, whereas the new radioactive activity followed barium. This chemical comparison did not by itself measure every fragment's motion.^[ref]

At fixed mass number $A$, the smooth semi-empirical mass formula makes the atomic mass approximately quadratic and convex in atomic number $Z$. Neighboring nuclear isobars undergo energetically allowed beta decay toward a discrete local minimum, subject to the electron-mass threshold for beta-plus decay. For odd $A$ there is one smooth branch; for even $A$, nuclear pairing splits the even-even and odd-odd branches. A local minimum against a single change of $Z$ need not be stable against double beta decay.

Nuclear physics studies atomic nuclei, their internal structure and the processes that change them. A nucleus contains protons and neutrons, whose short-range nuclear forces bind them while the Coulomb force repels the protons. The resulting nuclear energy levels and nuclear binding energies connect this subject to the low-energy consequences of quantum chromodynamics. Weak interactions additionally permit changes of nuclear composition through beta decay.

The mass defect makes the connection between structure and released energy quantitative. For a nucleus with $Z$ protons, $N$ neutrons and nuclear mass $M_{\mathrm{nuc}}$, its nuclear binding energy isA bound nucleus has less rest energy than its separated nucleons. In a nuclear reaction, the difference between the sums of initial and final rest energies supplies the Q value. The sign of that difference and the Coulomb barrier answer different questions: a reaction can release energy overall while still requiring a way to cross an entrance barrier.

Scattering experiments supplied an early structural clue. Rare large deflections of alpha particles by thin matter could be explained by close encounters with a highly concentrated central charge. Ernest Rutherford's 1911 analysis connected such angular measurements to a compact atomic centre, establishing a route from measured scattering cross-sections to internal structure.^[ref]

Let $M_P$ and $M_D$ denote neutral atomic rest masses for the appropriate parent and daughter, and initially neglect electronic binding energy corrections and daughter excitation. The Q values areFor beta-minus decay, the daughter nucleus has one extra positive charge. Its neutral atom contains one more electron than the neutral parent, cancelling the emitted electron's rest mass in the atomic accounting. For beta-plus decay, the neutral parent contains one more electron than the neutral daughter; together with the emitted Positron, this gives the $2m_e$ subtraction. Thus beta-plus decay requires an atomic mass difference exceeding $2m_e{c}^2$, whereas electron capture need not.

For electron capture, the captured bound electron is already included in $M_P$. Capture from a shell leaving an atomic hole of excitation energy $E_{\mathrm{hole}}$, and a nuclear excited state of energy $E_x$, gives approximatelyThe hole's energy later appears as atomic radiation or Auger electrons. Subtract $E_x$ for either beta decay as well. Exact endpoints also depend on daughter ionization and small atomic binding energy changes; the boxed expressions are the conventional leading atomic-mass formulas.