The total decay rate for a given initial state is obtained by summing the partial rates over all final states $$ W = \displaystyle\sum _{f} W_{if}, $$ with the branching fraction to a specific final state given by $$ b_{if} = \frac{W_{if}}{W}. $$ Beta decay lifetime are usually given in terms of the half-life with a total half-life of $$ T_{1/2} = \frac{{\rm ln}(2)}{W}. $$ The partial half-life for a particular final state will be denoted by \( t_{1/2} \) $$ t_{1/2} = \frac{T_{1/2}}{b_{if}}. $$