  We perform precision measurements of the branching ratios of the 4P3/2 level
decay of a single 40Ca+ ion suspended in a linear Paul trap. High precision is
achieved by a novel technique based on monitoring the population transfer when
repeatedly pumping the ion between different internal states. The branching
fractions into the 4S1/2, 3D5/2 and 3D3/2 levels are found to be 0.9347(3),
0.0587(2) and 0.00661(4), respectively. For the branching ratio
A(P3/2-S1/2)/\sum_J A(P3/2-D_J)=14.31(5), we find a forty-fold improvement in
accuracy as compared to the best previous measurement.
