betaplusdecay

Beta-plus decay, or positron emission, is a mode of radioactive decay in which a proton-rich nucleus converts one proton into a neutron, emitting a positron and an electron neutrino. The process decreases the atomic number by one while leaving the mass number unchanged, producing a daughter nucleus with Z−1 and the same A.

The decay occurs via the weak interaction, described by the transformation p → n + e+ + νe. Because the parent atom initially contains Z electrons, the daughter atom ends up with Z−1 electrons. The emitted positron carries kinetic energy, and the neutrino takes part of the energy as well. The overall energy balance determines whether beta-plus decay is allowed for a given nuclide.

Energetically, beta-plus decay requires a positive Q-value. In practice, the condition is often written as Qβ+ = [M(A,Z) − M(A,Z−1) − 2me]c2 > 0, where M(A,Z) and M(A,Z−1) are atomic masses and me is the electron rest mass. This effectively means the parent must exceed the daughter by more than twice the electron rest mass (about 1.022 MeV). If this energy is insufficient, beta-plus decay is forbidden and other decay modes, such as electron capture, may dominate.

Observables and applications: The emitted positron annihilates with electrons, producing characteristic 511 keV gamma rays. Beta-plus emitters are widely used in medical imaging, notably in positron emission tomography (PET), with common isotopes including 18F, 11C, 13N, and 15O. Regions near the proton drip line exhibit beta-plus decay most prominently, and the process provides insight into nuclear structure and weak interactions.

Production and study: Positron-emitting nuclides are produced in cyclotrons or nuclear reactors and studied in nuclear physics and medical contexts to understand decay schemes, half-lives, and energy spectra.