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.^[1] 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 λ, the two being related through:

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

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,^[2] 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.