Precision Measurement Method for Branching Fractions of Excited P1/2 States Applied to 40Ca+

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 4$^{2}$P$_{1/2}$ state of $^{40}$\Ca to the 4$^{2}$S$_{1/2}$ and 3$^{2}$D$_{3/2}$ states to be \branching\ and \branchingsm, 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.