# 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 with respect to the total number of particles which decay.[1] It is equal to the ratio of the partial decay constant 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 λ, the two being related through:

${\displaystyle t_{1/2}={\frac {\ln 2}{\lambda }}.}$

For example, for spontaneous decays of 132Cs, 98.1% are ε or β+ decays, and 1.9% are β decays. The partial decay constants can be calculated from the branching fraction and the half-life of 132Cs (6.479 d), they are: 0.10 d−1 (ε + β+) and .0020 d−1). The partial half-lives are 6.60 d (ε + β+) and 341 d (β). Here the problem with the term partial half-life is evident: after (341+6.60) days almost all the nuclei will have decayed, not only half as one may initially think.

Isotopes with significant branching of decay modes include copper-64, arsenic-74, rhodium-102, indium-112, iodine-126 and holmium-164.

## ReferencesEdit

1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "branching fraction".