Vacuum ultraviolet oscillator strengths of Hg measured by sum-frequency mixing

We have measured oscillator strengths for the transitions 6 ${}_{}{}^1{}_{}{}^{}S$ to (5$d^{10}$6s np) n ${}_{}{}^1{}_{}{}^{}$,3${\mathrm{P}}_1$ for n=6 to 13 and to (5$d^9$6$s^2$6p) 6p’ ${}_{}{}^1{}_{}{}^{}P$ for atomic Hg. Two new techniques for measuring dispersion based on nonlinear-optical sum-frequency mixing are used to achieve 10% accuracy for the stronger transitions. One method uses crossed beams in a Hg heat-pipe cell to map dispersion curves in regions of anomalous dispersion. The second method uses input beams of three separate frequencies and maps regions of normal and anomalous dispersion by tuning one of the input frequencies to the red and blue of the 6 ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ level. Because the dispersion of the refractive index near a resonance is determined over a large wavelength range, the oscillator strength of that resonance is determined independent of the strengths of other transitions.