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Physical Review A

Radiative transport at the 184.9-nm Hg resonance line. I. Experiment and theory

H. A. Post

Published Mar 1, 1986• 71 citations
Publisher

Abstract

Measurements are reported of the radiative decay rate of the Hg 6 ${\mathrm{}}^{1}$${P}_{1}$ 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%.

DOI
10.1103/physreva.33.2003

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Radiative transport at the 184.9-nm Hg resonance line. II. Extensive experiments

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Measurements are reported of the fundamental mode radiative decay rate of the Hg 6 $^{1}P_{1}$ population under conditions of low collision rate and large optical thickness of the 184.9-nm resonance line. The measured data extend over a wide range of experimental conditions. The measurements were made using two different experimental methods, both employing low-pressure mercury--noble-gas discharges. In the first method the decay rate of the 6 $^{1}P_{1}$ population was measured in the afterglow of the discharge using a dye-laser absorption technique. In the second one the decay was measured of the laser-induced fluorescence at the 184.9-nm line created by pulsed optical pumping. Radiative decay rates obtained with the two independent experimental methods for nominally the same conditions agreed within the experimental error of 5%. For zero perturber gas density the radiative decay rate as a function of the Hg density shows a pronounced minimum. This minimum disappears with the addition of an argon density of more than about 3\ifmmode\times\else\texttimes\fi{}${10}^{22}$ ${\mathrm{m}}^{\mathrm{\ensuremath{-}}3}$, which corresponds with an extra collisional broadening of \ensuremath{\sim}15 MHz. The experimental decay rates differ largely from rates calculated with a complete frequency redistribution theory. Comparison with rates calculated from the partial redistribution theory described in paper I (preceding paper) shows agreement within 25%. The behavior of the experimental rates at the lowest mercury densities could be interpreted as due to a deviation from the natural abundance in the 6 $^{1}P_{1}$ excited-state population.

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Radiation trapping of the Hg 185 nm resonance line

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The decay rate of the Hg 61P1 level was measured as a function of cold spot temperature (Hg density) and buffer gas pressure in cylindrical, sealed fused silica cells. The decay rates were obtained using a time-resolved laser-induced 185 nm fluorescence experiment with multi-step excitation. Cold spot temperatures from 25 to 100 °C were studied. The Hg densities for this temperature range and with no buffer gas yield the lowest possible decay rates due to radiation trapping with partial frequency redistribution. Decay rates with argon buffer gas pressures of 3 and 30 Torr were also studied. The results are in agreement with published data from a discharge afterglow experiment. Monte Carlo simulations of radiation transport in the cells, including the effects of hyperfine and isotope structure, the effects of foreign gas broadening, and partial frequency redistribution are compared to the experimental data. Reasonably good agreement is obtained, however there is evidence of quenching of Hg 61P1 atoms in collisions with ground state Hg and Ar atoms. An analytic formula for the fundamental mode trapped decay rate of the 61P1 level, which is applicable over a substantial region of parameter space, was devised from the Monte Carlo results.

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Decay kinetics of optically excited resonance states of atomic sodium in cylindrical cells

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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

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[Radiation trapping effect and measurement of the Cs (6P3/2) level effective radiation rate in the vapor mixed with He].

Xiaoyan Shen, Kang Dai, Yifan Shen

The effective radiation rate for Cs (6P3/2) resonance level in the presence of helium was determined. A cell filled with Cs metal and He at pressure P(He) (0-500 Pa) was established at T = 300 K. The cell was heated in the temperature range between 330 and 370 K, which produced Cs number densities approximately in the range between 10(12) and 10(13) cm(-3). Cs atoms were excited to the 6P3/2 state using a single-mode diode laser(pump laser). The transmission of the medium at the center of the Doppler envelope of the strong h. f. component of the CsD2 line due to hyperfine pumping alone amounts to approximately 5%. The assumption that has been made is that the lower-state hyperfine levels are populated in a statistical ratio. The excited-atom density and spatial distribution were mapped by monitoring the absorption of a counterpropagating single-mode diode laser beam (probe laser) tuned to the 6P3/2 --> 8S1/2 transition which could be translated parallel to the pump beam. In the presence of radiation trapping, the spontaneous radiation rate is multiplied by the transmission factor T6P3/2 -->1/2, which describes the average probability that photons emitted within the fluorescence detection region can pass through the optically thick vapor without being absorbed. The T6P3/2 --> 6S1/2 is related to the frequency dependent absorption cross section and the density and spatial distribution of atoms at the level of the transition. Position dependent 6P3/2 state densities were combined with the collisional broadening rate of 6P3/2 <-- 6S1/2 line due to the perturbation of both helium and cesium to yield T6P3/2 --> 6S1/2. The effective radiation rates of the Cs D2 line as a function of the He pressure P(He) were obtained. The helium caused line broadening and therefore increased the effective radiation rate. The fluorescence intensity I852 of the 6P3/2 --> 6S1/2 emission was measured simultaneously. The measured fluorescence ratios determined the ratios of the effective radiation rates at different He density. These ratios are in agreement with theoretical evaluation.

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Redistribution of radiation in the absence of collisions

Gabriel G. Lombardi, Daniel E. Kelleher, J. Cooper

Redistribution and depolarization of near-resonant radiation is studied for the He 2(1P)-3(1D) line (668 nm) and some data for H-alpha (656 nm) are also presented. A Nd:YAG pumped dye laser, with a bandwidth of 0.1/cm and a power density of 100 kW/sq cm, is used in the experiment. The transitions have lower levels with natural line widths that are large compared with their upper-level natural widths, and, under experimental conditions, their collisional widths are also small. The ratio of fluorescence to Rayleigh intensity is measured and the results indicate that while the Rayleigh emission has the same temporal development as the laser pulse (5 ns FWHM), the fluorescent intensity has a decay time determined by the radiative decay lifetime and by collisional quenching. The prediction that redistribution of radiation occurs in the absence of collisions for transitions having significant lower-level radiative widths is confirmed. Depolarization rates by collisions with helium are also inferred from the measurements.

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Experimental Verification of the "Incoherent Scattering" Theory for the Transport of Resonance Radiation

A. V. Phelps, A. O. McCoubrey

The predictions of the incoherent scattering theory of the transport of resonance radiation developed by Holstein and by Biberman are shown to agree with laboratory measurements of the decay constants for the intensity of the mercury 2537 A resonance radiation following a period of optical excitation. Also, the relative importance of the diffusion of resonance atoms and the escape of resonance radiation as mechanisms for the destruction of mercury atoms in the $^{3}P_{1}$ or resonance state are determined from measurements of decay constants as a function of mercury density and cell radius. The experimental results show that diffusion of the resonance atoms is negligible and that the predictions of imprisonment theory are confirmed to within 15%. The experiment sets an upper limit to the diffusion coefficient at unit gas density for atoms in the $^{3}P_{1}$ state of 5\ifmmode\times\else\texttimes\fi{}${10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ at 340\ifmmode^\circ\else\textdegree\fi{}K, which is consistent with a value of 4\ifmmode\times\else\texttimes\fi{}${10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ predicted using the frequency of excitation transfer collisions calculated by Holstein. The success of the theories based on completely incoherent scattering of resonance radiation points to the desirability of including this feature in the treatment of those astrophysical problems in which the spectral line shape is determined by Doppler broadening or by collision broadening.

Physical Review•Jun 15, 1960•48 citations
Measurements are reported of the radiative decay rate of the Hg 6 {\mathrm{}}^{1}$${P}_{1} 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%.
Measurements are reported of the fundamental mode radiative decay rate of the Hg 6 1P1^{1}P_{1}1P1​ population under conditions of low collision rate and large optical thickness of the 184.9-nm resonance line. The measured data extend over a wide range of experimental conditions. The measurements were made using two different experimental methods, both employing low-pressure mercury--noble-gas discharges. In the first method the decay rate of the 6 1P1^{1}P_{1}1P1​ population was measured in the afterglow of the discharge using a dye-laser absorption technique. In the second one the decay was measured of the laser-induced fluorescence at the 184.9-nm line created by pulsed optical pumping. Radiative decay rates obtained with the two independent experimental methods for nominally the same conditions agreed within the experimental error of 5%. For zero perturber gas density the radiative decay rate as a function of the Hg density shows a pronounced minimum. This minimum disappears with the addition of an argon density of more than about 3\ifmmode\times\else\texttimes\fi{}1022{10}^{22}1022 ${\mathrm{m}}^{\mathrm{\ensuremath{-}}3}$, which corresponds with an extra collisional broadening of \ensuremath{\sim}15 MHz. The experimental decay rates differ largely from rates calculated with a complete frequency redistribution theory. Comparison with rates calculated from the partial redistribution theory described in paper I (preceding paper) shows agreement within 25%. The behavior of the experimental rates at the lowest mercury densities could be interpreted as due to a deviation from the natural abundance in the 6 1P1^{1}P_{1}1P1​ excited-state population.
The decay rate of the Hg 61P1 level was measured as a function of cold spot temperature (Hg density) and buffer gas pressure in cylindrical, sealed fused silica cells. The decay rates were obtained using a time-resolved laser-induced 185 nm fluorescence experiment with multi-step excitation. Cold spot temperatures from 25 to 100 °C were studied. The Hg densities for this temperature range and with no buffer gas yield the lowest possible decay rates due to radiation trapping with partial frequency redistribution. Decay rates with argon buffer gas pressures of 3 and 30 Torr were also studied. The results are in agreement with published data from a discharge afterglow experiment. Monte Carlo simulations of radiation transport in the cells, including the effects of hyperfine and isotope structure, the effects of foreign gas broadening, and partial frequency redistribution are compared to the experimental data. Reasonably good agreement is obtained, however there is evidence of quenching of Hg 61P1 atoms in collisions with ground state Hg and Ar atoms. An analytic formula for the fundamental mode trapped decay rate of the 61P1 level, which is applicable over a substantial region of parameter space, was devised from the Monte Carlo results.
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
The effective radiation rate for Cs (6P3/2) resonance level in the presence of helium was determined. A cell filled with Cs metal and He at pressure P(He) (0-500 Pa) was established at T = 300 K. The cell was heated in the temperature range between 330 and 370 K, which produced Cs number densities approximately in the range between 10(12) and 10(13) cm(-3). Cs atoms were excited to the 6P3/2 state using a single-mode diode laser(pump laser). The transmission of the medium at the center of the Doppler envelope of the strong h. f. component of the CsD2 line due to hyperfine pumping alone amounts to approximately 5%. The assumption that has been made is that the lower-state hyperfine levels are populated in a statistical ratio. The excited-atom density and spatial distribution were mapped by monitoring the absorption of a counterpropagating single-mode diode laser beam (probe laser) tuned to the 6P3/2 --> 8S1/2 transition which could be translated parallel to the pump beam. In the presence of radiation trapping, the spontaneous radiation rate is multiplied by the transmission factor T6P3/2 -->1/2, which describes the average probability that photons emitted within the fluorescence detection region can pass through the optically thick vapor without being absorbed. The T6P3/2 --> 6S1/2 is related to the frequency dependent absorption cross section and the density and spatial distribution of atoms at the level of the transition. Position dependent 6P3/2 state densities were combined with the collisional broadening rate of 6P3/2 <-- 6S1/2 line due to the perturbation of both helium and cesium to yield T6P3/2 --> 6S1/2. The effective radiation rates of the Cs D2 line as a function of the He pressure P(He) were obtained. The helium caused line broadening and therefore increased the effective radiation rate. The fluorescence intensity I852 of the 6P3/2 --> 6S1/2 emission was measured simultaneously. The measured fluorescence ratios determined the ratios of the effective radiation rates at different He density. These ratios are in agreement with theoretical evaluation.
Redistribution and depolarization of near-resonant radiation is studied for the He 2(1P)-3(1D) line (668 nm) and some data for H-alpha (656 nm) are also presented. A Nd:YAG pumped dye laser, with a bandwidth of 0.1/cm and a power density of 100 kW/sq cm, is used in the experiment. The transitions have lower levels with natural line widths that are large compared with their upper-level natural widths, and, under experimental conditions, their collisional widths are also small. The ratio of fluorescence to Rayleigh intensity is measured and the results indicate that while the Rayleigh emission has the same temporal development as the laser pulse (5 ns FWHM), the fluorescent intensity has a decay time determined by the radiative decay lifetime and by collisional quenching. The prediction that redistribution of radiation occurs in the absence of collisions for transitions having significant lower-level radiative widths is confirmed. Depolarization rates by collisions with helium are also inferred from the measurements.
The predictions of the incoherent scattering theory of the transport of resonance radiation developed by Holstein and by Biberman are shown to agree with laboratory measurements of the decay constants for the intensity of the mercury 2537 A resonance radiation following a period of optical excitation. Also, the relative importance of the diffusion of resonance atoms and the escape of resonance radiation as mechanisms for the destruction of mercury atoms in the 3P1^{3}P_{1}3P1​ or resonance state are determined from measurements of decay constants as a function of mercury density and cell radius. The experimental results show that diffusion of the resonance atoms is negligible and that the predictions of imprisonment theory are confirmed to within 15%. The experiment sets an upper limit to the diffusion coefficient at unit gas density for atoms in the 3P1^{3}P_{1}3P1​ state of 5\ifmmode\times\else\texttimes\fi{}1017{10}^{17}1017 ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ at 340\ifmmode^\circ\else\textdegree\fi{}K, which is consistent with a value of 4\ifmmode\times\else\texttimes\fi{}1016{10}^{16}1016 ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ predicted using the frequency of excitation transfer collisions calculated by Holstein. The success of the theories based on completely incoherent scattering of resonance radiation points to the desirability of including this feature in the treatment of those astrophysical problems in which the spectral line shape is determined by Doppler broadening or by collision broadening.