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Physical Review

Experimental Study of Resonance Radiation Transfer

H. Mochizuki, R. G. Fowler

Published Jan 4, 1965• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physrev.137.a17

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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 (\ensuremathω=2\ensuremathπf\ensuremath{\omega}=2\ensuremath{\pi}f\ensuremathω=2\ensuremathπf, 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 \ensuremathφ\ensuremath{\varphi}\ensuremathφ, \ensuremathφ=invtan\ensuremathωT\ensuremath{\varphi}=invtan\ensuremath{\omega}T\ensuremathφ=invtan\ensuremathωT. The relation T\ensuremath∝C2K2+C2T\ensuremath{\propto}\frac{{C}^{2}}{{K}^{2}}+{C}^{2}T\ensuremath∝K2C2​+C2), 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 lnT\ensuremath∝lnn\mathrm{ln}T\ensuremath{\propto}\mathrm{ln}nlnT\ensuremath∝lnn on the molecular density nnn. On the other hand, the transmitted radiation obeys a relation Tc\ensuremath∝(nA)12{T}_{c}\ensuremath{\propto}{(\mathrm{nA})}^{\frac{1}{2}}Tc​\ensuremath∝(nA)21​ 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 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.
When a mercury atom in the resonance 63P16^{3}P_{1}63P1​ state collides with a nitrogen molecule, it may be transferred to the metastable 63P06^{3}P_{0}63P0​ state. The cross section for this reaction has been measured by a new method. Mercury vapor, in the presence of a known pressure of nitrogen gas, is excited by 2537A radiation. After the source of the excitation is cut off, the decay time of the imprisoned radiation is observed. The quenching collision cross section ${\ensuremath{\sigma}}_{Q}$ is calculated from the measured decay time and the known value of the imprisonment time in the absence of the quenching gas. Measurements have been taken over the temperature range 325-525\ifmmode^\circ\else\textdegree\fi{}K; ${\ensuremath{\sigma}}_{Q}$ is found to increase from 5.0\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ cm2{\mathrm{cm}}^{2}cm2 at the lower temperature to 1.0\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ cm2{\mathrm{cm}}^{2}cm2 at the upper temperature.
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 description of the self-imprisonment of resonance radiation in gases or solids and of the density distribution of excited species depends upon a transmission coefficient $T(\ensuremath{\rho})$, the probability that a quantum of emitted radiation will traverse a thickness $\ensuremath{\rho}$ of material. This coefficient is shown to be given by the rapidly convergent series $T(\ensuremath{\rho})=\ensuremath{\Sigma}{n}^{}\frac{{(\ensuremath{-}{k}_{0}\ensuremath{\rho})}^{n}}{n!{(n+1)}^{\frac{1}{2}}}$, where k0{k}_{0}k0​ is a constant characteristic of the excited species and of the temperature. The above expression is used to give the first accurate discussion of resonance radiation confined between infinite parallel planes, and of radiation inside a sphere over a wide range of ${k}_{0}\ensuremath{\rho}$ values.