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Physical Review

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

A. V. Phelps, A. O. McCoubrey

Published Jun 15, 1960• 48 citations
Publisher

Abstract

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.

DOI
10.1103/physrev.118.1561

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Collisional Destruction of the 63P1 State of Mercury

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Inclusion of collisional destruction mechanisms as sink terms in the theory of imprisonment of resonance radiation appears to have been neglected in the case of the 2537-Å mercury line. In this paper, the Holstein photon transport equation is employed to determine the effect of destructive or self-quenching collisions between resonance state and ground state atoms, processes in which the resonance state is converted to another excited state with the release of kinetic energy. These mechanisms seem to explain experimental work in which the decay constant of the 2537-Å mercury line reaches a minimum and then increases with density. Comparison of theory with experimental data yields a cross section between 3.0 and 10.0 × 10−18 for the conversion of Hg(3P1) to metastable Hg(3P0) by two-body collisions with Hg(1S0). The sharp increase at high density of the decay constant of the 2537-Å mercury line has not been predicted by previous theories but is a general consequence of the inclusion of collisional destruction mechanisms.

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Experimental Study of Resonance Radiation Transfer

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Experimental investigations have been made of the transfer of mercury 2537-\AA{} radiation through a slab of natural mercury gas of various densities and dimensions, using a sinusoidally modulated ($\ensuremath{\omega}=2\ensuremath{\pi}f$, $f=5 \mathrm{to} 50$ kc/sec) radio-frequency-excited (50-Mc/sec) source of 2537-\AA{} radiation. Transmitted radiation has been found to gain in phase relative to the source wave, while that which is scattered at 90\ifmmode^\circ\else\textdegree\fi{} loses phase. From the radiation scattered at 90\ifmmode^\circ\else\textdegree\fi{}, decay time constants of the imprisoned photons have been calculated by using the relation between the time constant $T$ and the phase shift $\ensuremath{\varphi}$, $\ensuremath{\varphi}=invtan\ensuremath{\omega}T$. The relation $T\ensuremath{\propto}\frac{{C}^{2}}{{K}^{2}}+{C}^{2}$), where $K$ is a constant, has been found for the dependence on the breadth $C$ of the resonance tube as well as the well known dependence $\mathrm{ln}T\ensuremath{\propto}\mathrm{ln}n$ on the molecular density $n$. On the other hand, the transmitted radiation obeys a relation ${T}_{c}\ensuremath{\propto}{(\mathrm{nA})}^{\frac{1}{2}}$ between the time constant ${T}_{c}$ corresponding to the advanced phase shift, the thickness $A$ of the resonance tube, and $n$. The dependences on other factors have also been examined.

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

H. A. Post, Peter van de Weijer, R. M. M. Cremers

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.

Physical Review A•Mar 1, 1986•33 citations
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 cm\ensuremath−1{\mathrm{cm}}^{\ensuremath{-}1}cm\ensuremath−1 sec\ensuremath−1{\mathrm{sec}}^{\ensuremath{-}1}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 cm\ensuremath−1{\mathrm{cm}}^{\ensuremath{-}1}cm\ensuremath−1 sec\ensuremath−1{\mathrm{sec}}^{\ensuremath{-}1}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.
Inclusion of collisional destruction mechanisms as sink terms in the theory of imprisonment of resonance radiation appears to have been neglected in the case of the 2537-Å mercury line. In this paper, the Holstein photon transport equation is employed to determine the effect of destructive or self-quenching collisions between resonance state and ground state atoms, processes in which the resonance state is converted to another excited state with the release of kinetic energy. These mechanisms seem to explain experimental work in which the decay constant of the 2537-Å mercury line reaches a minimum and then increases with density. Comparison of theory with experimental data yields a cross section between 3.0 and 10.0 × 10−18 for the conversion of Hg(3P1) to metastable Hg(3P0) by two-body collisions with Hg(1S0). The sharp increase at high density of the decay constant of the 2537-Å mercury line has not been predicted by previous theories but is a general consequence of the inclusion of collisional destruction mechanisms.
Experimental investigations have been made of the transfer of mercury 2537-\AA{} radiation through a slab of natural mercury gas of various densities and dimensions, using a sinusoidally modulated ($\ensuremath{\omega}=2\ensuremath{\pi}f$, f=5to50f=5 \mathrm{to} 50f=5to50 kc/sec) radio-frequency-excited (50-Mc/sec) source of 2537-\AA{} radiation. Transmitted radiation has been found to gain in phase relative to the source wave, while that which is scattered at 90\ifmmode^\circ\else\textdegree\fi{} loses phase. From the radiation scattered at 90\ifmmode^\circ\else\textdegree\fi{}, decay time constants of the imprisoned photons have been calculated by using the relation between the time constant TTT and the phase shift $\ensuremath{\varphi}$, $\ensuremath{\varphi}=invtan\ensuremath{\omega}T$. The relation $T\ensuremath{\propto}\frac{{C}^{2}}{{K}^{2}}+{C}^{2}$), where KKK is a constant, has been found for the dependence on the breadth CCC of the resonance tube as well as the well known dependence $\mathrm{ln}T\ensuremath{\propto}\mathrm{ln}n$ on the molecular density nnn. On the other hand, the transmitted radiation obeys a relation ${T}_{c}\ensuremath{\propto}{(\mathrm{nA})}^{\frac{1}{2}}$ between the time constant Tc{T}_{c}Tc​ corresponding to the advanced phase shift, the thickness AAA of the resonance tube, and nnn. The dependences on other factors have also been examined.
The decay of imprisoned resonance radiation in mercury has been studied using delayed-coincidence techniques. It is characterized by two exponentially decaying components, whose relative amplitudes depend on the direction of linear polarization of the incident radiation. When this direction makes an angle of 54.7° to the direction of observation, only one component is observed. Classical and quantum-mechanical theories are presented which show that the geometry of the scattering cell plays an important role at low atomic densities. Experimental values are presented for the average degree of coherence transferred in the scattering process and for the natural lifetime of the 63P1 state of mercury.
On theoretical grounds it is expected that the decay time of imprisoned resonance radiation in the vapor of a single even isotope of mercury should be some six times larger than that observed with the natural samples of mixed isotopic constitution. To investigate this effect experimentally, decay measurements were carried out with samples of Hg198{\mathrm{Hg}}^{198}Hg198 (3 percent Hg199{\mathrm{Hg}}^{199}Hg199 and 0.1 percent Hg200{\mathrm{Hg}}^{200}Hg200). For vapor densities $N\ensuremath{\lesssim}\frac{{10}^{14}}{\mathrm{cc}}$, the predicted effect was verified. For N>1014ccN>\frac{{10}^{14}}{\mathrm{cc}}N>cc1014​, the observed decay time drops below that predicted theoretically for pure Hg198{\mathrm{Hg}}^{198}Hg198. This secondary effect is here attributed to the transfer of excitation from Hg198{\mathrm{Hg}}^{198}Hg198 to Hg199{\mathrm{Hg}}^{199}Hg199 and Hg200{\mathrm{Hg}}^{200}Hg200 by collisions of the second kind. Comparison of experimental data with an appropriately generalized theory permits estimation of the cross section for such collisions. The value so obtained is ${10}^{\ensuremath{-}13}$ cm2{\mathrm{cm}}^{2}cm2, some twenty times the gas-kinetic cross section, and in order-of-magnitude agreement with theoretical expectations.
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.