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Physical Review

Effect of the Imprisonment of Resonance Radiation on Excitation Experiments

A. V. Phelps

Published Jun 15, 1958• 117 citations
Publisher

Abstract

The theory of the imprisonment of resonance radiation developed by Holstein and by Bieberman is applied to the analysis of experimental measurements of excitation cross sections for the resonance ($n^{1}P$) states of helium. The transport equation for the density of atoms in the resonance state is solved numerically for the case of a thin sheet of exciting electrons between parallel plane electrodes. The fraction of the resonance atoms producing visible radiation is then calculated for parallel plane geometry and estimated to within five percent for cylindrical geometry with an axial electron beam. Predictions of the theory are compared with the available experimental data for helium. The theory shows that at the helium pressures commonly used (${10}^{\ensuremath{-}3}$ to ${10}^{\ensuremath{-}1}$ mm of Hg) the observed visible radiation may easily be a factor of ten greater than that expected when imprisonment effects are neglected. As a result, the cross sections for the excitation of the $n^{1}P$ states given in the literature are much too large. For example, our analysis of the available experimental data suggests that the cross section for excitation by electrons to the $3^{1}P$ state of helium at 100 electron volts is 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}18}$ ${\mathrm{cm}}^{2}$ instead of 4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ as given in the literature.

DOI
10.1103/physrev.110.1362

Related papers

Imprisonment of Resonance Radiation in a Gaseous Discharge

P. J. Walsh

Following the theory of Holstein, the density, ${N}_{r}$, and the imprisonment lifetime of resonance radiation, $T$, has been investigated for a gaseous discharge between parallel plates. A general solution is given. Two approximate solutions occur according as the number of electronic de-excitations of the resonance state during the imprisonment time of a photon is much less than or much greater than unity. When this number is much less than unity, ${N}_{r}$ can be given by a simple relation which compares well with computations based on the exact solution in the case of Doppler broadening. $T$ is then essentially equal to the decay time as calculated by Holstein for the decay of resonance radiation following optical excitation. For large numbers of de-excitations $T$ falls somewhat below the decay value and, as expected, ${N}_{r}$ is given by its thermodynamic equilibrium value at the temperature of the electrons.

Physical Review•Jul 15, 1957•45 citations

Isotope Effect in the Imprisonment of Resonance Radiation

Theodore D. Holstein, D. Alpert, A. O. McCoubrey

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 ${\mathrm{Hg}}^{198}$ (3 percent ${\mathrm{Hg}}^{199}$ and 0.1 percent ${\mathrm{Hg}}^{200}$). For vapor densities $N\ensuremath{\lesssim}\frac{{10}^{14}}{\mathrm{cc}}$, the predicted effect was verified. For $N>\frac{{10}^{14}}{\mathrm{cc}}$, the observed decay time drops below that predicted theoretically for pure ${\mathrm{Hg}}^{198}$. This secondary effect is here attributed to the transfer of excitation from ${\mathrm{Hg}}^{198}$ to ${\mathrm{Hg}}^{199}$ and ${\mathrm{Hg}}^{200}$ 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 ${10}^{\ensuremath{-}13}$ ${\mathrm{cm}}^{2}$, some twenty times the gas-kinetic cross section, and in order-of-magnitude agreement with theoretical expectations.

Physical Review•Mar 15, 1952•55 citations

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

Effect of Imprisonment of Radiation in Sodium Vapor on the Measured Lifetime of the 3 P2 States

B P Kibble, G. H. Copley, L. Krause

The effect of imprisonment of radiation in sodium vapor on the measured lifetime of the $3 ^{2}P$ states has been investigated in an experiment in which the atoms in the vapor were excited with 10-nsec pulses of resonance radiation and the elapsed times between the exciting and the fluorescent pulses were recorded using a time-to-amplitude converter and kicksorter. At vapor densities below ${10}^{10}$ atoms/${\mathrm{cm}}^{3}$, where there is no multiple scattering, the measured lifetime reaches a constant value of (1.63\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ sec, equal to the natural lifetime of the $3 ^{2}P$ states. In the density range ${10}^{9}$-${10}^{13}$ atoms/${\mathrm{cm}}^{3}$, the variation of the effective lifetime with the vapor density is in good agreement with the predictions of Milne's theory of radiation trapping; agreement with Holstein's theory is observed only in the range ${10}^{12}$-${10}^{13}$ atoms/${\mathrm{cm}}^{3}$. The results of a subsidiary Hanle experiment show that a multiply scattered photon of sodium resonance fluorescence loses its original polarization and that, at high sodium vapor pressure, coherence is not preserved.

Physical Review•Jan 5, 1967•114 citations

Trapping and quenching of potassium resonance radiation

G. H. Copley, L. Krause

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.

Canadian Journal of Physics•Mar 1, 1969•45 citations

Collisional Destruction of the 63P1 State of Mercury

B. V. Waddell, G. S. Hurst

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.

The Journal of Chemical Physics•Nov 15, 1970•13 citations
The theory of the imprisonment of resonance radiation developed by Holstein and by Bieberman is applied to the analysis of experimental measurements of excitation cross sections for the resonance (n1Pn^{1}Pn1P) states of helium. The transport equation for the density of atoms in the resonance state is solved numerically for the case of a thin sheet of exciting electrons between parallel plane electrodes. The fraction of the resonance atoms producing visible radiation is then calculated for parallel plane geometry and estimated to within five percent for cylindrical geometry with an axial electron beam. Predictions of the theory are compared with the available experimental data for helium. The theory shows that at the helium pressures commonly used (10\ensuremath−3{10}^{\ensuremath{-}3}10\ensuremath−3 to 10\ensuremath−1{10}^{\ensuremath{-}1}10\ensuremath−1 mm of Hg) the observed visible radiation may easily be a factor of ten greater than that expected when imprisonment effects are neglected. As a result, the cross sections for the excitation of the n1Pn^{1}Pn1P states given in the literature are much too large. For example, our analysis of the available experimental data suggests that the cross section for excitation by electrons to the 31P3^{1}P31P state of helium at 100 electron volts is 3\ifmmode\times\else\texttimes\fi{}10\ensuremath−18{10}^{\ensuremath{-}18}10\ensuremath−18 cm2{\mathrm{cm}}^{2}cm2 instead of 4\ifmmode\times\else\texttimes\fi{}10\ensuremath−17{10}^{\ensuremath{-}17}10\ensuremath−17 cm2{\mathrm{cm}}^{2}cm2 as given in the literature.
Following the theory of Holstein, the density, Nr{N}_{r}Nr​, and the imprisonment lifetime of resonance radiation, TTT, has been investigated for a gaseous discharge between parallel plates. A general solution is given. Two approximate solutions occur according as the number of electronic de-excitations of the resonance state during the imprisonment time of a photon is much less than or much greater than unity. When this number is much less than unity, Nr{N}_{r}Nr​ can be given by a simple relation which compares well with computations based on the exact solution in the case of Doppler broadening. TTT is then essentially equal to the decay time as calculated by Holstein for the decay of resonance radiation following optical excitation. For large numbers of de-excitations TTT falls somewhat below the decay value and, as expected, Nr{N}_{r}Nr​ is given by its thermodynamic equilibrium value at the temperature of the electrons.
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.
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.
The effect of imprisonment of radiation in sodium vapor on the measured lifetime of the 32P3 ^{2}P32P states has been investigated in an experiment in which the atoms in the vapor were excited with 10-nsec pulses of resonance radiation and the elapsed times between the exciting and the fluorescent pulses were recorded using a time-to-amplitude converter and kicksorter. At vapor densities below 1010{10}^{10}1010 atoms/cm3{\mathrm{cm}}^{3}cm3, where there is no multiple scattering, the measured lifetime reaches a constant value of (1.63\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ sec, equal to the natural lifetime of the 32P3 ^{2}P32P states. In the density range 109{10}^{9}109-1013{10}^{13}1013 atoms/cm3{\mathrm{cm}}^{3}cm3, the variation of the effective lifetime with the vapor density is in good agreement with the predictions of Milne's theory of radiation trapping; agreement with Holstein's theory is observed only in the range 1012{10}^{12}1012-1013{10}^{13}1013 atoms/cm3{\mathrm{cm}}^{3}cm3. The results of a subsidiary Hanle experiment show that a multiply scattered photon of sodium resonance fluorescence loses its original polarization and that, at high sodium vapor pressure, coherence is not preserved.
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.
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.