  Using a single trapped barium ion we have developed an rf spectroscopy
technique to measure the ratio of the off-resonant vector ac Stark effect (or
light shift) in the 6S_{1/2} and 5D_{3/2} states to 0.1% precision. We find R =
Delta_S / Delta_D = -11.494(13) at 514.531 nm where Delta_{S,D} are the light
shifts of the m = +/- 1/2 splittings due to circularly polarized light.
Comparison of this result with an ab initio calculation of R would yield a new
test of atomic theory. By appropriately choosing an off-resonant light shift
wavelength one can emphasize the contribution of one or a few dipole matrix
elements and precisely determine their values.
