Branching fraction

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In particle physics and nuclear physics, the branching fraction 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:

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

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 (β⁻). 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 346 days almost all the nuclei will have decayed.