We present a method for measuring branching fractions for the decay of J=1/2 atomic energy levels to lower-lying states based on time-resolved recording of the atom's fluorescence during a series of population transfers. We apply this method to measure the branching fractions for the decay of the 4²P(1/2) state of 40Ca+ to the 4²S(1/2) and 3²D(3/2) states to be 0.935 65(7) and 0.
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