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Physical Review A

Narrowing of Level-Crossing Signals by Radiative Transfer in Diffuse Reflection. II. Experiments on the 6P13 Level of Mercury

B. Dodsworth, J. C. Gay, A. Omont

Published Jun 1, 1971• 8 citations
Publisher

Abstract

We present experimental verification of a certain number of theoretical predictions given in the preceding paper. The narrowing of the different Hanle-effect signals by multiple diffusion is clearly weaker if observed using the light scattered in the backward direction than if observed using the laterally scattered light. This narrowing can become very small if the vapor is illuminated with light whose frequency is in the wings of the Doppler absorption width of the vapor. The values of the ratios of the widths and intensities of the different Hanle-effect signals that were measured are in good agreement with the values predicted by theory.

DOI
10.1103/physreva.3.1912

Related papers

Narrowing of Level-Crossing Signals by Radiative Transfer in Diffuse Reflection. I. Theory

B. Dodsworth, A. Omont

The multiple diffusion theory of Barrat has been extended by expanding the density matrix in irreducible tensors to calculate level-crossing signals arising from observation of the back-scattered light. In the framework of an approximation equivalent to the coherent scattering of radiative-transfer theory, we first calculate the different Hanle-effect signals, using, in particular, the results of Chandrasekhar which give light intensities in zero magnetic field. We then roughly evaluate the effect of the redistribution in frequency of the radiation and the variation of absorption with frequency. The narrowing predicted for the Hanle-effect curves is much less important than for lateral diffusion.

Physical Review A•Jun 1, 1971•5 citations

The forward scattering of resonance radiation, with special reference to double resonance and level-crossing experiments

Alan Corney, B P Kibble, George William Series

Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Jul 5, 1966•87 citations

Forward scattering of resonance radiation by mercury vapour in a magnetic field

Alan V. Durrant, B Landheer

The forward scattering of resonance radiation (2537 AA) from a 198-mercury lamp by 198-mercury vapour has been investigated as a function of magnetic field. The experiments have revealed two regions of interest; (i) in weak magnetic fields, certain features in the intensity against field (level crossing) curves shift to lower field strengths as the optical density is increased (coherence narrowing), (ii) in stronger magnetic fields, features shift to higher field values with increasing optical density. Over the range of densities investigated there is good agreement between theory and experiment.

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Resonant Broadening of Double-Resonance and Level-Crossing Signals: Application to the P13 State in Mercury

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A detailed calculation of the relaxation matrix of resonance atomic states by resonant collisions is carried out in the semiclassical impact theory. The validity of the different approximations is discussed. These results have been tested by observing self-broadening of level-crossing curves in high field and in zero field, in the $6^{3}P_{1}$ state in mercury. Observation of these signals at high pressures is very difficult with a pure isotope because of strong absorption and trapping of resonance light in the vapor; it is made very easy by observing level-crossing signals of one isotope in a very low concentration in the vapor of another isotope. Collisions between the different pairs of mercury isotopes have been thus systematically studied. Results are in excellent agreement (10%) with theory, both for the absolute value of cross sections and for the ratio of orientation broadening to alignment broadening.

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Dependence of Hanle signals on the spectral distribution of the exciting light

D. Lecler, R. Ostermann, Wulfhard K. Lange +1 more

The shape of Hanle (zero field level crossing) signals may be strongly distorted if the spectral profile of the exciting light varies rapidly on the scale of the natural linewidth, provided that the Doppler width in the scattering region is not very large compared with the natural width. A Hanle experiment has been performed at the resonance line of calcium. The exciting light had a spectral profile with a very narrow hole at the resonance frequency and was produced by a calcium hollow-cathode with an absorbing atomic beam of calcium inserted in its light path, The observed level crossing signals are in very good agreement with theoretical predictions.

Journal de physique•Jan 1, 1975•7 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
We present experimental verification of a certain number of theoretical predictions given in the preceding paper. The narrowing of the different Hanle-effect signals by multiple diffusion is clearly weaker if observed using the light scattered in the backward direction than if observed using the laterally scattered light. This narrowing can become very small if the vapor is illuminated with light whose frequency is in the wings of the Doppler absorption width of the vapor. The values of the ratios of the widths and intensities of the different Hanle-effect signals that were measured are in good agreement with the values predicted by theory.
The multiple diffusion theory of Barrat has been extended by expanding the density matrix in irreducible tensors to calculate level-crossing signals arising from observation of the back-scattered light. In the framework of an approximation equivalent to the coherent scattering of radiative-transfer theory, we first calculate the different Hanle-effect signals, using, in particular, the results of Chandrasekhar which give light intensities in zero magnetic field. We then roughly evaluate the effect of the redistribution in frequency of the radiation and the variation of absorption with frequency. The narrowing predicted for the Hanle-effect curves is much less important than for lateral diffusion.
Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.
The forward scattering of resonance radiation (2537 AA) from a 198-mercury lamp by 198-mercury vapour has been investigated as a function of magnetic field. The experiments have revealed two regions of interest; (i) in weak magnetic fields, certain features in the intensity against field (level crossing) curves shift to lower field strengths as the optical density is increased (coherence narrowing), (ii) in stronger magnetic fields, features shift to higher field values with increasing optical density. Over the range of densities investigated there is good agreement between theory and experiment.
A detailed calculation of the relaxation matrix of resonance atomic states by resonant collisions is carried out in the semiclassical impact theory. The validity of the different approximations is discussed. These results have been tested by observing self-broadening of level-crossing curves in high field and in zero field, in the 63P16^{3}P_{1}63P1​ state in mercury. Observation of these signals at high pressures is very difficult with a pure isotope because of strong absorption and trapping of resonance light in the vapor; it is made very easy by observing level-crossing signals of one isotope in a very low concentration in the vapor of another isotope. Collisions between the different pairs of mercury isotopes have been thus systematically studied. Results are in excellent agreement (10%) with theory, both for the absolute value of cross sections and for the ratio of orientation broadening to alignment broadening.
The shape of Hanle (zero field level crossing) signals may be strongly distorted if the spectral profile of the exciting light varies rapidly on the scale of the natural linewidth, provided that the Doppler width in the scattering region is not very large compared with the natural width. A Hanle experiment has been performed at the resonance line of calcium. The exciting light had a spectral profile with a very narrow hole at the resonance frequency and was produced by a calcium hollow-cathode with an absorbing atomic beam of calcium inserted in its light path, The observed level crossing signals are in very good agreement with theoretical predictions.
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.