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Physical Review A

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

Arlee V. Smith, W. J. Alford

Published May 1, 1986• 18 citations

Abstract

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.

DOI: 10.1103/physreva.33.3172

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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.

We have developed new techniques based on four-wave mixing for the accurate determination of oscillator strengths and applied them to measure 61S - n1,3P and 71S - n1,3P (n = 6 - 13) matrix elements of atomic Hg. For transitions from the 61S ground state, index matching conditions were used to determine refractive indicies and thus f-values, while the frequency dependence of the nonlinear susceptibility was used to deduce matrix elements for transitions involving 71S. For all measurements, two-photon resonance with the 71S state was maintained.

We have measured the null positions in the third-order susceptibility for two-photon resonant (6

^{1}7

^{1}

,3S) sum-frequency mixing in atomic mercury. In addition, we have made measurements of some 7S-nP oscillator strengths using a fluorescence-dip technique. Combined with earlier results we are able to obtain a set of 7S-nP (n=7--13) oscillator strengths which gives a good description of the third-order susceptibility. The uncertainty in the 7S-nP oscillator strengths is typically 35--50%. The absolute third-order susceptibility has been determined for energies less than 83 000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ with an uncertainty of typically 20--30%.

The oscillator strength for the resonance ($1^{1}S\ensuremath{-}2^{1}P$) transition in atomic helium has been determined from a measurement of the lifetime of the

2^{1}P

state. This lifetime was obtained using a modified zero-field level crossing (Hanle) method. The scattering sample was a thermal velocity beam of

2^{1}S

metastable atoms. Resonant 2-\ensuremath{\mu} ($2^{1}S\ensuremath{-}2^{1}P$) radiation is absorbed by the

2^{1}S

atoms, which are excited to the

2^{1}P

state. This state then primarily decays to the ground

1^{1}S

state with the emission of resonance (584 \AA{}) radiation. The lifetime of the

2^{1}P

state was determined from measurements of the magnetic-field dependence of the angular distribution of the 584 \AA{} intensity. This new technique eliminates the problem of constructing a vacuum ultraviolet resonance lamp. The measured lifetime $\ensuremath{\tau} (2^{1}P)$ is (5.63 \ifmmode\pm\else\textpm\fi{} 0.22) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$ sec. The resulting absorption oscillator strength for the resonance transition is 0.273 \ifmmode\pm\else\textpm\fi{} 0.011. This oscillator strength agrees with the theoretical value.

Two tunable dye lasers have been used to generate coherent radiation at a tunable sum frequency in the vacuum-ultraviolet spectral region. Spectral ranges of \ensuremath{\sim}3500 ${\mathrm{cm}}^{\ensuremath{-}1}$ around 1895 \AA{} and \ensuremath{\sim}1200 ${\mathrm{cm}}^{\ensuremath{-}1}$ around 1798 \AA{} have been covered. These ranges may easily be extended. Large (\ensuremath{\sim}\ifmmode\times\else\texttimes\fi{}

{10}^{4}

) enhancements of $2{\ensuremath{\nu}}_{1}+{\ensuremath{\nu}}_{2}$ sum mixing are seen when $2{\ensuremath{\nu}}_{1}$ is tuned to a double-quantum allowed transition from the ground state in Sr vapor.