text: In the field of atomic, molecular, and optical physics, a branching fraction refers to the probability of decay to a specific lower-lying energy states from some excited state. Suppose we drive a transition in an atomic system to an excited state , which can decay into either the ground state  or a long-lived state . If the probability to decay (the branching fraction) into the  state is , then the probability to decay into the other state  would be . Further possible decays would split appropriately, with their probabilities summing to 1.
  In some instances, instead of a branching fraction, a branching ratio is used. In this case, the branching ratio is just the ratio of the branching fractions between two states. To use our example from before, if the branching fraction to state  is , then the branching ratio comparing the transition rates to  and  would be .
  Branching fractions can be measured in a variety of ways, including time-resolved recording of the atom's fluorescence during a series of population transfers in the relevant states.