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Physical Review

Imprisonment of Resonance Radiation in a Gaseous Discharge

P. J. Walsh

Published Jul 15, 1957• 45 citations
Publisher

Abstract

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.

DOI
10.1103/physrev.107.338

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Effect of the Imprisonment of Resonance Radiation on Excitation Experiments

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Imprisonment dynamics of resonance radiation in gases

Н. И. Косарев, N. Ya. Shaparev

Imprisonment of resonant radiation in gases on the basis of the numerical solution of the rate balance equation for the excited atoms and the transfer resonant radiation equation is investigated. Calculations of the escape factor for the slab, cylinder and sphere at Doppler and Lorentz forms of absorption and scattering profiles are executed. Calculation results of the escape factor for the cylinder and slab are compared with Holsten's asymptotical solutions. The numerical data for time dependence of a spectrum, the intensity of resonant radiation and the spatial distribution of the excited atomic concentration in a regime of afterglow are also considered.

Journal of Physics B Atomic Molecular and Optical Physics•Apr 28, 2011•8 citations
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.
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 (${10}^{\ensuremath{-}3}$ 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 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{}${10}^{\ensuremath{-}18}$ cm2{\mathrm{cm}}^{2}cm2 instead of 4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ cm2{\mathrm{cm}}^{2}cm2 as given in the literature.
The Holstein-Biberman integrodifferential equation for the transport of resonance radiation has been solved for a gas contained in a long cylindrical container. The solution involves the following assumptions: (i) The excited atoms are initially distributed uniformly along the axis of the cylinder; (ii) the pressure and temperature of the gas are such that the absorption coefficient has either a pure Doppler-broadened or a pure pressure-broadened profile; (iii) the radius of the cylinder corresponds to many optical depths at the frequency corresponding to the maximum of the absorption coefficient. It is also shown that steady-state solutions corresponding to a line source along the axis of the cylinder can be calculated by the same procedure. The geometry and the initial conditions considered here are of particular interest because the situation can be simulated experimentally. Hurst and Thonnard have pointed out that an approximate line of excited atoms can be produced by sending a well-collimated pulse of protons or electrons down the axis of a long cylinder containing the gas of interest. The present paper also considers the decay of resonance radiation from a steady state built up by a line source. The latter situation is even easier to arrange experimentally. All experimental work to date has concerned itself with situations where the initial distribution of excited atoms is not known, and theory and experiment can only be compared at times which are large enough so that the system has decayed to its lowest eigenmode.
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.
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.
Imprisonment of resonant radiation in gases on the basis of the numerical solution of the rate balance equation for the excited atoms and the transfer resonant radiation equation is investigated. Calculations of the escape factor for the slab, cylinder and sphere at Doppler and Lorentz forms of absorption and scattering profiles are executed. Calculation results of the escape factor for the cylinder and slab are compared with Holsten's asymptotical solutions. The numerical data for time dependence of a spectrum, the intensity of resonant radiation and the spatial distribution of the excited atomic concentration in a regime of afterglow are also considered.