Precision measurement method for branching fractions of excited P _1/2 states applied to Ca+40

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 4P1/22 state of Ca+40 to the 4S1/22 and 3D3/22 states to be 0.935 65(7) and 0.064 35(7), respectively. The measurement scheme requires that at least one of the lower-lying states be long lived. The method is insensitive to fluctuations in laser light intensity and magnetic field and is readily applicable to various atomic species due to its simplicity. Our result distinguishes well among existing state-of-the-art theoretical models of Ca⁺.