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Journal of Physics B Atomic Molecular and Optical Physics

Influence of the duration of collision effects on the imprisonment of resonance radiation at higher optical depths

Niels Schoon, Eric Desoppere, Tania Van Bever

Published Apr 28, 1998• 2 citations
Publisher

Abstract

Measurements of the radiative decay of the state in Kr are performed in the 0.006 - 10 Torr pressure range in a cylindrical geometry with a radius of 0.0128 m. Due to the good accuracy of the experimental results a decrease of the fundamental mode radiative decay rate is observed in the 0.6 - 4 Torr interval, where present theories, based on the impact approximation, predict a nearly constant decay rate. This decrease has not been reported previously in the literature. It is shown that the impact approximation is not valid in this optical depth range and that the duration of collision effects has to be taken into account. An analytical formula for the apparent decay rate , in which the pressure broadening is treated regardless of the duration of the collisions, is proposed. This formula yields a precise reproduction of the observed decrease.

DOI
10.1088/0953-4075/31/8/004

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Canadian Journal of Physics•Mar 1, 1969•45 citations
Measurements of the radiative decay of the state in Kr are performed in the 0.006 - 10 Torr pressure range in a cylindrical geometry with a radius of 0.0128 m. Due to the good accuracy of the experimental results a decrease of the fundamental mode radiative decay rate is observed in the 0.6 - 4 Torr interval, where present theories, based on the impact approximation, predict a nearly constant decay rate. This decrease has not been reported previously in the literature. It is shown that the impact approximation is not valid in this optical depth range and that the duration of collision effects has to be taken into account. An analytical formula for the apparent decay rate , in which the pressure broadening is treated regardless of the duration of the collisions, is proposed. This formula yields a precise reproduction of the observed decrease.
We have extended our previous studies of the trapping of alkali-atom resonance radiation to conditions where the unity optical depth points are in the quasistatic wings of the foreign-gas pressure-broadened line shape. Under these conditions, and based on the relatively simple Holstein theory, we expected to see a qualitatively different dependence of the effective radiative decay rate on pressure than is observed when the unity optical depth points are in the impact core. However, we found experimentally that the observed dependence is the same as was observed in the lower pressure limit, at least over the range of conditions we were able to access. On the other hand, these observations are found to be consistent with more accurate calculations based upon the Post theory using a recently available experimental line-shape function.
Measurements are reported of the radiative decay rate of the Hg 6 1{\mathrm{}}^{1}1P1{P}_{1}P1​ population under conditions of strong radiation trapping at the 184.9-nm resonance line. The experiments were made in the afterglow of a low-pressure Hg discharge with a dye-laser absorption method. The radiative decay rate as a function of the Hg pressure shows a pronounced minimum. The value at minimum is lower than the limiting value at higher Hg densities by a factor of 2. Furthermore, the experimental rates are up to a factor of 8 lower than those calculated from theory with the usual assumption of complete redistribution. Indeed, complete redistribution is not expected in the present case, where the optical thickness is large and elastic collision rates are smaller than the single atom spontaneous emission rate. We derived an analytical expression for the fundamental-mode radiative decay rate in a homogeneous medium from a theory based on partial redistribution in frequency. A condition for the existence of a fundamental mode is discussed and is shown to be largely satisfied in our experiments. The expression for the decay rate was obtained for a resonance line with a hyperfine structure, and was elaborated for a cylindrical geometry. The resulting calculated decay rates agree with the experimental ones within 25%.
We have studied trapping of resonance radiation under conditions of moderate to low line-center optical depths in sodium-argon mixtures. We report measured effective radiative decay rates, which are compared with predictions of the Post [Phys. Rev. A 33, 2003 (1986)] and the Milne [J. Lond. Math. Soc. 1, 40 (1926)] theories of radiation trapping. These theories are expected to be valid for spectral lines with low to moderate line-center optical depths, where the commonly used Holstein [Phys. Rev. 72, 1212 (1947); 83, 1159 (1951)] theory of radiation trapping is expected to break down. The experiment was performed under conditions in which the trapping was dominated by either the Doppler-broadened Gaussian or by the impact-broadened Lorentzian line-shape function. The measured effective radiative decay rates agree well with those predicted by the Milne and Post theories over the range of low to moderate optical depth.
This study carries out an experimental investigation of the radiative decay kinetics of the resonance states of sodium atoms excited by dye laser radiation. The effective radiative decay rates of the resonance states as a function of vapor temperature, primary and impurity gas presssure, and the radius of the cylindrical volume containing the vapor were obtained by computer processing ofthe experimental curves using a kinetic decay model.-The radiative decay rate calculated in the Holstein approximation is compared to the measured values. The mechanisms of optical excitation of metallic vapors in resonance radiation trapping conditions have been investigated theoretically to a sufficient degree.lr At the same time there have been few experimental studies devoted to this problem. The decay kinetics of the atomic resonance states in the vapors of alkali metals have largely been studied for a planar radiating layer,2-6 where the nonideal geometry of the radiating volume made it necessary to introduce a fitting parameter to compare the experimental results to theory. The radiative decay kinetics of the populations of the resonance 3P states of atomic Na under conditions of axial laser excitation of a cylindrical shell are investigated in the present paper for the first time; this made it possible to carry out a comparison to theory without introducing variable parameters, since in this case exact analytic expressions are known for the effective lifetimes. It should also be emphasized that cylindrically configured cells are most commonly used in experimental research and hence these results have a certain interest in such studies. For our analysis we selected a concentration range of normal sodium atoms of 3 X 1013 <;no<;4 X 1015 cm - where selective optical excitation of the fine structure components (FSC) 32Pl/2 and 32P3/2 are accompanied by collisional mixing, which has a substantial effect on the persistence kinetics of the NaD lines. Under these conditions the decay of the directly excited fine structure component is biexponential, while the time dependence of the population of the corresponding level takes the form
We have studied sodium resonance radiation under conditions of severe radiation trapping in sodium-argon mixtures, and we report measured values of the effective radiative decay rates. The measured values are compared with values calculated from the Holstein theory of radiation trapping in the impact-regime, foreign-gas pressure-broadening limit. The experiment was designed to satisfy all of the validity criteria imposed by the approximations of the Holstein theory, and the experiment and theory are in good agreement. Since the effective radiative decay rate depends upon the collisional line-broadening rate, confirmation of the theory allows such measurements to be used to determine unknown line-broadening constants using only broadband lasers and low resolution monochromaters. We demonstrate this technique for the sodium D lines broadened by xenon and neon perturbers. The values for the broadening constants obtained in this manner are in reasonable agreement with values from several previous studies utilizing more traditional techniques.
The effects of imprisonment of resonance radiation in potassium vapor and of collisions between excited potassium atoms and N2, H2, HD, and D2 molecules, on the measured lifetimes of the 42P states, have been investigated by the method of delayed coincidences. The potassium atoms were excited with short pulses of resonance radiation, and the delays between the exciting and fluorescent pulses were measured with a time-to-amplitude converter. At pure potassium densities below 1010 atoms/cm3, the measured lifetimes approach the constant values 27.8 ± 0.8 and 27.6 ± 0.8 ns, corresponding to the natural lifetimes of the 42P1/2 and 42P3/2 states, respectively. At higher densities the effective lifetimes are in satisfactory agreement with the predictions of Holstein's theory. The decrease in the measured decay rates observed upon addition of the diatomic gases yielded cross sections for quenching collisions with N2, H2, HD, and D2 which equal 34.0 ± 2.0 Å2, 9.4 ± 1.3 Å2, 11.9 ± 1.5 Å2, and 8.0 ± 2.0 Å2, respectively.