The measurement of oscillator strengths in the presence of resonance self-broadening

Collision broadening studies have been made of optical double resonance lines in cadmium. The results indicate that the collision frequency is velocity dependent, contrary to the usual theory of resonance self-broadening. This result supports the suggestion that the broadening results from interactions involving a number of intermediate states rather than only the initial and final states of the optical transition, because of the small oscillator strength ( $f=0.002$ ) for transitions between the ${(5s)}^{2}^{1}S_{0}$ ground state and the excited state in question $(5s5p)^{3}P_{1}$ . The cross section in this case has a $\frac{1}{{{\overline{v}}_{12}}^{\frac{2}{5}}}$ velocity dependence, so the collision frequency varies as ${{\overline{v}}_{12}}^{\frac{3}{5}}$ . Measurements show that under this assumption the self-broadening cross section for cadmium is ${\ensuremath{\sigma}}_{\mathrm{coll}}=(1.9\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}{\mathrm{cm}}^{2}/{{\overline{v}}_{12}}^{\frac{2}{5}},$ where ${\overline{v}}_{12}$ is the average relative velocity in cm/sec. In the course of this work, the lifetime of the $(5s, 5p)^{3}P_{1}$ state was redetermined and found to be (2.39\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ sec.Collision broadening studies have been made of optical double resonance lines in cadmium. The results indicate that the collision frequency is velocity dependent, contrary to the usual theory of resonance self-broadening. This result supports the suggestion that the broadening results from interactions involving a number of intermediate states rather than only the initial and final states of the optical transition, because of the small oscillator strength ($f=0.002$) for transitions between the ${(5s)}^{2}^{1}S_{0}$ ground state and the excited state in question $(5s5p)^{3}P_{1}$. The cross section in this case has a $\frac{1}{{{\overline{v}}_{12}}^{\frac{2}{5}}}$ velocity dependence, so the collision frequency varies as ${{\overline{v}}_{12}}^{\frac{3}{5}}$. Measurements show that under this assumption the self-broadening cross section for cadmium is ${\ensuremath{\sigma}}_{\mathrm{coll}}=(1.9\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}{\mathrm{cm}}^{2}/{{\overline{v}}_{12}}^{\frac{2}{5}},$ where ${\overline{v}}_{12}$ is the average relative velocity in cm/sec. In the course of this work, the lifetime of the $(5s, 5p)^{3}P_{1}$ state was redetermined and found to be (2.39\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ sec.

Physical ReviewMay 4, 196467 citations

Determination of oscillator strengths with the phase-matching condition

H. B. Puell, C. R. Vidal

Optics CommunicationsNov 1, 197619 citations

Theory of Collision Broadening in the Sudden Approximation

F. W. Byron, Henry M. Foley

A method is developed for calculating the cross section for line broadening in the limiting case in which important collisions may be considered to occur very rapidly with respect to the periods corresponding to the transitions in question. This method is essentially an extension of the familiar "sudden" approximation; reference is made throughout to the particular example of optical double resonance only for definiteness and because there are available experimental results for comparison with the theory. Assuming the impact model and considering the case when the energy levels in question are well resolved with respect to their width, an exact expression is found for resonant self-broadening in the usual weak rf field limit of interest in double resonance. For the case of very small oscillator strengths for the optical transition (intercombination lines), the resonant broadening becomes sufficiently small so that second-order, intermediate-state processes dominate, and approximations must be made to effect sums over intermediate states. Here the broadening is of the same sort as foreign gas broadening, and in many cases of interest, the approximations can be made in a sufficiently realistic manner to obtain useful expressions for the broadening. It is shown that the resonant cross section and this "second-order" cross section are not additive, but that the one which is larger dominates the total cross sections very strongly. Finally, we evaluate explicitly the self-broadening and foreign gas broadening (by the noble gases) of double resonance lines in the group II metals and the self-broadening in the optical spectrum of helium. In all cases our theoretical predictions are in good agreement with measurements which have been made.A method is developed for calculating the cross section for line broadening in the limiting case in which important collisions may be considered to occur very rapidly with respect to the periods corresponding to the transitions in question. This method is essentially an extension of the familiar "sudden" approximation; reference is made throughout to the particular example of optical double resonance only for definiteness and because there are available experimental results for comparison with the theory. Assuming the impact model and considering the case when the energy levels in question are well resolved with respect to their width, an exact expression is found for resonant self-broadening in the usual weak rf field limit of interest in double resonance. For the case of very small oscillator strengths for the optical transition (intercombination lines), the resonant broadening becomes sufficiently small so that second-order, intermediate-state processes dominate, and approximations must be made to effect sums over intermediate states. Here the broadening is of the same sort as foreign gas broadening, and in many cases of interest, the approximations can be made in a sufficiently realistic manner to obtain useful expressions for the broadening. It is shown that the resonant cross section and this "second-order" cross section are not additive, but that the one which is larger dominates the total cross sections very strongly. Finally, we evaluate explicitly the self-broadening and foreign gas broadening (by the noble gases) of double resonance lines in the group II metals and the self-broadening in the optical spectrum of helium. In all cases our theoretical predictions are in good agreement with measurements which have been made.

Physical ReviewMay 4, 196497 citations

The Inverse Hook Method for Measuring Oscillator Strengths

William Arie van Wijngaarden, Keith Bonin, W. Happer

Springer series in optical sciences/SPringer series in optical sciencesJan 1, 19870 citations

f=0.002

) for transitions between the ${(5s)}^{2}^{1}S_{0}$ ground state and the excited state in question

(5s5p)^{3}P_{1}

. The cross section in this case has a

\frac{1}{{{\overline{v}}_{12}}^{\frac{2}{5}}}

velocity dependence, so the collision frequency varies as

{{\overline{v}}_{12}}^{\frac{3}{5}}

. Measurements show that under this assumption the self-broadening cross section for cadmium is ${\ensuremath{\sigma}}_{\mathrm{coll}}=(1.9\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}{\mathrm{cm}}^{2}/{{\overline{v}}_{12}}^{\frac{2}{5}},$ where

{\overline{v}}_{12}

is the average relative velocity in cm/sec. In the course of this work, the lifetime of the

(5s, 5p)^{3}P_{1}

state was redetermined and found to be (2.39\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ sec.