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We define and measure the ratio (R) of the vector ac-Stark effect (or lightshift) in the 6S_1/2 and 5D_3/2 states of a single trapped barium ion to 0.2%accuracy at two different off-resonant wavelengths. We earlier found R =-11.494(13) at 514.531nm and now report the value at 1111.68nm, R = +0.4176(8).These observations together yield a value of the <5D||er||4F> matrix element,previously unknown in the literature. Also, comparison of our results with anab initio calculation of dynamic polarizability would yield a new test ofatomic theory and improve the understanding of atomic structure needed tointerpret a proposed atomic parity violation experiment.

Precision measurement of light shifts at two off-resonant wavelengths in a single trapped Ba+ ion and determination of atomic dipole matrix elements