Branching fraction
In particle physics and nuclear physics, 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 of atoms or the decay of elementary particles.<ref>Template:GoldBookRef</ref> It is equal to the ratio of the partial decay constant of the decay mode to the overall decay constant. 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. The partial half-life is merely an alternate way to specify the partial decay constant Template:Math, the two being related through:
- <math>t_{1/2} = \frac{\ln 2}{\lambda}.</math>
For example, for decays of 132Cs, 98.13% are ε (electron capture) or β+ (positron) decays, and 1.87% are β− (electron) decays. The half-life of this isotope is 6.480 days,Template:NUBASE2020 which corresponds to a total decay constant of 0.1070 d−1. Then the partial decay constants, as computed from the branching fractions, are 0.1050 d−1 for ε/β+ decays, and 2.14×10−4 d−1 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 statesEdit
In the field of atomic, molecular, and optical physics, 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 Template:Math, which can decay into either the ground state Template:Math or a long-lived state Template:Math. If the probability to decay (the branching fraction) into the Template:Math state is Template:Tmath, then the probability to decay into the other state Template:Math would be Template:Tmath.<ref name=":0">Template:Cite journal</ref> 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 Template:Math is Template:Tmath, then the branching ratio comparing the transition rates to Template:Math and Template:Math would be Template:Tmath.
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.<ref>Template:Cite journal</ref><ref name=":0" />
ReferencesEdit
External linksEdit
- LBNL Isotopes Project
- Particle Data Group (listings for particle physics)
- File:Queryensdf.jpg Nuclear Structure and Decay Data - IAEA for nuclear decays
