particle physics Particle physics or high-energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the s ...

and

nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies th ...

, the branching fraction (or branching ratio) for a decay is the fraction of particles which decay by an individual decay mode or with respect to the total number of particles which decay. It applies to either the

radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is conside ...

atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...

s or the decay of

elementary particles In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a con ...

. It is equal to the ratio of the partial decay constant of the decay mode to the overall

decay constant A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda) is a positive rate ...

. Sometimes a partial half-life is given, but this term is misleading; due to competing modes, it is not true that half of the particles will decay through a particular decay mode after its partial

half-life Half-life is a mathematical and scientific description of exponential or gradual decay. Half-life, half life or halflife may also refer to: Film * Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang * ''Half Life: ...

. The partial half-life is merely an alternate way to specify the partial decay constant , the two being related through: :

t_ = \frac.

For example, for decays of Cs, 98.13% are ε (

electron capture Electron capture (K-electron capture, also K-capture, or L-electron capture, L-capture) is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shells. Th ...

) or β (

positron The positron or antielectron is the particle with an electric charge of +1''elementary charge, e'', a Spin (physics), spin of 1/2 (the same as the electron), and the same Electron rest mass, mass as an electron. It is the antiparticle (antimatt ...

) decays, and 1.87% are β (

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

) decays. The half-life of this isotope is 6.480 days, which corresponds to a total decay constant of 0.1070 d. Then the partial decay constants, as computed from the branching fractions, are 0.1050 d for ε/β decays, and 2.14×10 d for β decays. Their respective partial half-lives are 6.603 d and 347 d. Isotopes with significant branching of decay modes include copper-64, arsenic-74, rhodium-102, indium-112, iodine-126 and holmium-164.

Branching fractions of atomic states

$Branching fraction$ In the field of

atomic, molecular, and optical physics Atomic, molecular, and optical physics (AMO) is the study of matter–matter and light–matter interactions, at the scale of one or a few atoms and energy scales around several electron volts. The three areas are closely interrelated. AMO th ...

, a branching fraction refers to the probability of decay to a specific lower-lying energy states from some excited state. Suppose we drive a transition in an atomic system to an excited state , which can decay into either the ground state or a long-lived state . If the probability to decay (the branching fraction) into the state is , then the probability to decay into the other state would be . Further possible decays would split appropriately, with their probabilities summing to 1. In some instances, instead of a branching fraction, a branching ratio is used. In this case, the branching ratio is just the ratio of the branching fractions between two states. To use our example from before, if the branching fraction to state is , then the branching ratio comparing the transition rates to and would be . Branching fractions can be measured in a variety of ways, including time-resolved recording of the atom's fluorescence during a series of population transfers in the relevant states.

References

External links

LBNL Isotopes Project

Particle Data Group
(listings for particle physics) * '
Nuclear Structure and Decay Data - IAEA
'' for nuclear decays {{Authority control Particle physics Nuclear physics Radioactivity Ratios