Branching ratio

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In particle physics and nuclear physics, a branching ratio for a decay is the ratio between the decay rates of individual decay modes for a decay and the total decay rate. These decay constants are called partial decay constants, and their sum is the decay constant for the reaction. 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. Thus the branching ratio for ¹³²Cs is 98.1 ε+β⁺ :: 1.9 β⁻. The partial decay constants can be calculated from the branching ratio 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 346 d (β⁻). Here the problem with the term partial half-life is evident: after 346 days almost all the nuclei will have decayed.