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Journal of Physics B Atomic Molecular and Optical Physics

VUV resonance radiation trapping in an effusive He beam

Aldo Amodeo, V. Berardi, Roberta Capobianco, Giulia Pica, N Spinelli

Published Feb 14, 1997• 1 citation
Publisher

Abstract

We have characterized experimentally the trapping of resonance radiation in an effusive He beam produced by a needle injector. In order to take into account the influence of secondary effects, such as collisions, on the trapping process, the measurements were carried out by investigating the line intensity dependence on the atomic density of transitions , and in the visible and and in the vacuum ultraviolet region of the helium spectrum. The comparison between visible and vacuum ultraviolet spectra allowed us to characterize the excitation process and to evaluate the contribution of collisional effects. We have calculated the escape factor, g, as a function of the atomic density and of the distance from the needle injector, i.e. along the beam path. The results were also compared with the Holstein and Phelps approach describing the trapping process in terms of an effective radius, . Our results show that in the case of an effusive beam, the effective radius is of the order of the effusive beam radius, namely .

DOI
10.1088/0953-4075/30/3/007

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Effect of the Imprisonment of Resonance Radiation on Excitation Experiments

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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.

Physical Review•Jun 15, 1958•117 citations

[Radiation trapping effect and measurement of the Cs (6P3/2) level effective radiation rate in the vapor mixed with He].

Xiaoyan Shen, Kang Dai, Yifan Shen

The effective radiation rate for Cs (6P3/2) resonance level in the presence of helium was determined. A cell filled with Cs metal and He at pressure P(He) (0-500 Pa) was established at T = 300 K. The cell was heated in the temperature range between 330 and 370 K, which produced Cs number densities approximately in the range between 10(12) and 10(13) cm(-3). Cs atoms were excited to the 6P3/2 state using a single-mode diode laser(pump laser). The transmission of the medium at the center of the Doppler envelope of the strong h. f. component of the CsD2 line due to hyperfine pumping alone amounts to approximately 5%. The assumption that has been made is that the lower-state hyperfine levels are populated in a statistical ratio. The excited-atom density and spatial distribution were mapped by monitoring the absorption of a counterpropagating single-mode diode laser beam (probe laser) tuned to the 6P3/2 --> 8S1/2 transition which could be translated parallel to the pump beam. In the presence of radiation trapping, the spontaneous radiation rate is multiplied by the transmission factor T6P3/2 -->1/2, which describes the average probability that photons emitted within the fluorescence detection region can pass through the optically thick vapor without being absorbed. The T6P3/2 --> 6S1/2 is related to the frequency dependent absorption cross section and the density and spatial distribution of atoms at the level of the transition. Position dependent 6P3/2 state densities were combined with the collisional broadening rate of 6P3/2 <-- 6S1/2 line due to the perturbation of both helium and cesium to yield T6P3/2 --> 6S1/2. The effective radiation rates of the Cs D2 line as a function of the He pressure P(He) were obtained. The helium caused line broadening and therefore increased the effective radiation rate. The fluorescence intensity I852 of the 6P3/2 --> 6S1/2 emission was measured simultaneously. The measured fluorescence ratios determined the ratios of the effective radiation rates at different He density. These ratios are in agreement with theoretical evaluation.

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Radiation Trapping in Atomic Vapours

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Abstract Radiation from spectral lines can be absorbed and re- emitted many times in atomic vapours before it reaches the boundaries of the container encasing the vapour. This effect is known as radiation trapping. It plays an important role practically everywhere where atomic vapours occur, e.g. in spectroscopy, in gas lasers, in atomic line filters, in the determination of atomic lifetimes, in measurements of atomic interaction potentials, and in electric discharge lamps. This book for the first time assembles all the information necessary for a treatment of practical problems, emphasizing both physical insights and mathematical methods. After an introduction that reviews resonance radiation and collisional processes in atomic vapours, physical effects and mathematical methods for various types of problems (e.g. with or without saturation, particle diffusion, reflecting cell walls, etc.) are explained in detail. The last part of the book describes the applications of these methods to a variety of practical problems like cross-section measurements or the design of discharge lamps.Atoms can both absorb and emit electromagnetic radiation like visible light In an assembly of many atoms, e.g., in a vapour or in a gas, radiation emitted by one atom may be reabsorbed by one of its neighbours, just to be reemitted a little later. The game can go on for quite some time—until the photon manages somehow to escape from this prison. At first glance, quite easy to understand. On the other hand, there must be some reason for this voluminous book full of sums, integrals and matrices. Our interest in this subject originally stemmed from investigations on atomic line filters we did for the European Space Agency, ESA. We believed that radiation trapping would have some influence on the performance of these filters and were looking for a simple means to take it into account We started out the same way as probably anyone new to the field would have done when faced with the problem of trapping. We read the classical paper of Holstein, and thought that was all there was to it. We soon had to realize, however, that the assumptions made by Holstein were not fulfilled in our problem, and decided to give the whole matter a closer look. That ‘closer look’ obtained a momentum of its own, and trapping became the centre of our own research in the following years. As our overview of the subject increased. we found that trapping plays a role in a staggering variety of situations. Trapping appears to be important in most experimental setups and in most engineering applications where atomic vapours are involved.

•Nov 26, 1998•191 citations

Near-threshold excitation of the λ132.2 nm resonance line of the Tl+ ion by electron impact

Г. М. Гомонай, V Roman, Л. О. Бандуріна +3 more

Background : Among all processes of collision of electrons with atomic particles the study of the interaction between electrons and ions is extremely important and necessary for a better understanding of the basic collisional processes in plasma. In the processes of excitation, recombination, and ionization of ions by electron impact autoionization states play an important role. Their radiation decay makes an additional contribution to the photo-recombination process and leads to dielectronic recombination of an ion. Such contribution is most significant in the case of heavy many-electron ions such as the Tl + ion. Excitation of the Tl + ion by an electron impact at electron-ion collisions is practically not investigated up to date. Methods: Experiments were performed using a spectroscopic method in conditions of electron and ion beams intersecting at an angle of 90°. The ribbon electron beam (cross section 1×8 mm 2 , energy E e = 6–14 eV, current I e = (2–10)×10 –5 A) was formed by a low-energy three-electrode electron gun. The ion beam (cross section 2.5×2.5 mm 2 , energy E i = 800 eV, current I i = (5–7)×10 –7 A) was obtained using a low-voltage arc discharge source. The radiation due to decay of the ion states excited during the collisions was detected perpendicular to the plane of the beams intersection. Spectral separation of the radiation in a vacuum ultraviolet region was carried out by 70° vacuum monochromator based on the Seya-Namioka scheme. Results: Thorough measurements of the near-threshold region of the energy dependence of the effective cross section of the electron excitation of the resonance l 132.2 nm line (6 s 6 p 1 P o 1 → 6 s 2 1 S 0 ) of the Tl + ion in the 6–14 eV energy range revealed resonant features both after and before the excitation threshold of the line. The widths of the before-threshold peculiarities is defined by the dispersion of the excited electrons energy. This is indicative of their resonant nature, i.e., they are due to the formation and decay of the atoionization states (AIS) of the Tl atom. Most likely, they are related to the formation and decay of the AIS of the 6 s 6 pnp configuration ( n  ≥ 7) to the excited levels of the Tl atom. The nature of the after-threshold structure indicates that it is also the result of resonance processes and is due to the formation and decay of the AIS, most likely of the 5 d  9 6 s 2 6 p 2 configuration, in the electronic channel. The absolute values of the excitation cross sections of the dielectronic satellites were determined by comparison of their intensities with the intensity of the resonance l 132.2 nm line which effective excitation cross section was obtained by normalizing the experimental data on the theoretical calculation by the tight-binding method of two states of the excitation cross section of the 6 s 6 p  1 P o 1 level of the Tl + ion at the 100 eV energy. Conclusions: The energy dependence of the effective excitation cross section of the dielectronic satellites of the Tl + ion resonance line showed that the absolute values of their excitation cross sections are ~ 10 –16 cm 2 and are of the same order of magnitude with that for the resonance line. It is shown that the main excitation mechanism of the resonance line satellites is dielectronic recombination which effectiveness essentially depends on the ratio of the probabilities of the AIS radiation and electron decay. In the case of the relativistic Tl + ion a strong configuration mixing of levels leads to significant increase of the AIS radiation decay probability.

Scientific Herald of Uzhhorod University Series Physics•Dec 31, 2018•0 citations

The Effect of Collisions on the Resonance Fluorescence Spectrum of Three-Level Atoms with a V-Configuration of Levels

А. И. Пархоменко, Anatolii M. Shalagin

The effect of collisions on the resonance fluorescence spectrum of three-level atoms with a V-configuration of levels when excited by two monochromatic resonance fields has been theoretically investigated. The analysis has been carried out for the systems with a small Doppler broadening compared to the collision frequency (high buffer gas pressures) and for the general case of an arbitrary change (from complete failure to complete preservation) of the phase memory at any of the three transitions in the V-system. It has been shown that in the three-level V-type atoms excited by two monochromatic fields, the resonant fluorescence spectrum (the number of spectral lines and their widths) at one of the transitions strongly depends on the presence of resonant radiation at the adjacent transition. Under certain conditions, the line widths will be completely determined by the relaxation characteristics of the adjacent transition and, in particular, can be repeatedly narrowed with an increase in the radiation intensity at the adjacent transition. It has been shown that despite the homogeneous nature of the broadening of the absorption lines, the resonance fluorescence spectrum has a pronounced anisotropy with respect to the mutual orientation of the wave vectors of spontaneous and exciting radiation. It has been established that the line widths in the resonance fluorescence spectrum are proportional to the diffusion coefficient of the atoms interacting with radiation under certain conditions. This fact can serve as the basis for a spectroscopic method for measuring the transport frequencies of the collisions of the radiation-absorbing particles with the buffer ones. It has been shown that the effects of phase memory in the collisions lead to a strong qualitative and quantitative modification of the resonance fluorescence spectrum.

Optics and Spectroscopy•Dec 1, 2021•1 citation

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 have characterized experimentally the trapping of resonance radiation in an effusive He beam produced by a needle injector. In order to take into account the influence of secondary effects, such as collisions, on the trapping process, the measurements were carried out by investigating the line intensity dependence on the atomic density of transitions , and in the visible and and in the vacuum ultraviolet region of the helium spectrum. The comparison between visible and vacuum ultraviolet spectra allowed us to characterize the excitation process and to evaluate the contribution of collisional effects. We have calculated the escape factor, g, as a function of the atomic density and of the distance from the needle injector, i.e. along the beam path. The results were also compared with the Holstein and Phelps approach describing the trapping process in terms of an effective radius, . Our results show that in the case of an effusive beam, the effective radius is of the order of the effusive beam radius, namely .
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 effective radiation rate for Cs (6P3/2) resonance level in the presence of helium was determined. A cell filled with Cs metal and He at pressure P(He) (0-500 Pa) was established at T = 300 K. The cell was heated in the temperature range between 330 and 370 K, which produced Cs number densities approximately in the range between 10(12) and 10(13) cm(-3). Cs atoms were excited to the 6P3/2 state using a single-mode diode laser(pump laser). The transmission of the medium at the center of the Doppler envelope of the strong h. f. component of the CsD2 line due to hyperfine pumping alone amounts to approximately 5%. The assumption that has been made is that the lower-state hyperfine levels are populated in a statistical ratio. The excited-atom density and spatial distribution were mapped by monitoring the absorption of a counterpropagating single-mode diode laser beam (probe laser) tuned to the 6P3/2 --> 8S1/2 transition which could be translated parallel to the pump beam. In the presence of radiation trapping, the spontaneous radiation rate is multiplied by the transmission factor T6P3/2 -->1/2, which describes the average probability that photons emitted within the fluorescence detection region can pass through the optically thick vapor without being absorbed. The T6P3/2 --> 6S1/2 is related to the frequency dependent absorption cross section and the density and spatial distribution of atoms at the level of the transition. Position dependent 6P3/2 state densities were combined with the collisional broadening rate of 6P3/2 <-- 6S1/2 line due to the perturbation of both helium and cesium to yield T6P3/2 --> 6S1/2. The effective radiation rates of the Cs D2 line as a function of the He pressure P(He) were obtained. The helium caused line broadening and therefore increased the effective radiation rate. The fluorescence intensity I852 of the 6P3/2 --> 6S1/2 emission was measured simultaneously. The measured fluorescence ratios determined the ratios of the effective radiation rates at different He density. These ratios are in agreement with theoretical evaluation.
Abstract Radiation from spectral lines can be absorbed and re- emitted many times in atomic vapours before it reaches the boundaries of the container encasing the vapour. This effect is known as radiation trapping. It plays an important role practically everywhere where atomic vapours occur, e.g. in spectroscopy, in gas lasers, in atomic line filters, in the determination of atomic lifetimes, in measurements of atomic interaction potentials, and in electric discharge lamps. This book for the first time assembles all the information necessary for a treatment of practical problems, emphasizing both physical insights and mathematical methods. After an introduction that reviews resonance radiation and collisional processes in atomic vapours, physical effects and mathematical methods for various types of problems (e.g. with or without saturation, particle diffusion, reflecting cell walls, etc.) are explained in detail. The last part of the book describes the applications of these methods to a variety of practical problems like cross-section measurements or the design of discharge lamps.Atoms can both absorb and emit electromagnetic radiation like visible light In an assembly of many atoms, e.g., in a vapour or in a gas, radiation emitted by one atom may be reabsorbed by one of its neighbours, just to be reemitted a little later. The game can go on for quite some time—until the photon manages somehow to escape from this prison. At first glance, quite easy to understand. On the other hand, there must be some reason for this voluminous book full of sums, integrals and matrices. Our interest in this subject originally stemmed from investigations on atomic line filters we did for the European Space Agency, ESA. We believed that radiation trapping would have some influence on the performance of these filters and were looking for a simple means to take it into account We started out the same way as probably anyone new to the field would have done when faced with the problem of trapping. We read the classical paper of Holstein, and thought that was all there was to it. We soon had to realize, however, that the assumptions made by Holstein were not fulfilled in our problem, and decided to give the whole matter a closer look. That ‘closer look’ obtained a momentum of its own, and trapping became the centre of our own research in the following years. As our overview of the subject increased. we found that trapping plays a role in a staggering variety of situations. Trapping appears to be important in most experimental setups and in most engineering applications where atomic vapours are involved.
Background : Among all processes of collision of electrons with atomic particles the study of the interaction between electrons and ions is extremely important and necessary for a better understanding of the basic collisional processes in plasma. In the processes of excitation, recombination, and ionization of ions by electron impact autoionization states play an important role. Their radiation decay makes an additional contribution to the photo-recombination process and leads to dielectronic recombination of an ion. Such contribution is most significant in the case of heavy many-electron ions such as the Tl + ion. Excitation of the Tl + ion by an electron impact at electron-ion collisions is practically not investigated up to date. Methods: Experiments were performed using a spectroscopic method in conditions of electron and ion beams intersecting at an angle of 90°. The ribbon electron beam (cross section 1×8 mm 2 , energy E e = 6–14 eV, current I e = (2–10)×10 –5 A) was formed by a low-energy three-electrode electron gun. The ion beam (cross section 2.5×2.5 mm 2 , energy E i = 800 eV, current I i = (5–7)×10 –7 A) was obtained using a low-voltage arc discharge source. The radiation due to decay of the ion states excited during the collisions was detected perpendicular to the plane of the beams intersection. Spectral separation of the radiation in a vacuum ultraviolet region was carried out by 70° vacuum monochromator based on the Seya-Namioka scheme. Results: Thorough measurements of the near-threshold region of the energy dependence of the effective cross section of the electron excitation of the resonance l 132.2 nm line (6 s 6 p 1 P o 1 → 6 s 2 1 S 0 ) of the Tl + ion in the 6–14 eV energy range revealed resonant features both after and before the excitation threshold of the line. The widths of the before-threshold peculiarities is defined by the dispersion of the excited electrons energy. This is indicative of their resonant nature, i.e., they are due to the formation and decay of the atoionization states (AIS) of the Tl atom. Most likely, they are related to the formation and decay of the AIS of the 6 s 6 pnp configuration ( n  ≥ 7) to the excited levels of the Tl atom. The nature of the after-threshold structure indicates that it is also the result of resonance processes and is due to the formation and decay of the AIS, most likely of the 5 d  9 6 s 2 6 p 2 configuration, in the electronic channel. The absolute values of the excitation cross sections of the dielectronic satellites were determined by comparison of their intensities with the intensity of the resonance l 132.2 nm line which effective excitation cross section was obtained by normalizing the experimental data on the theoretical calculation by the tight-binding method of two states of the excitation cross section of the 6 s 6 p  1 P o 1 level of the Tl + ion at the 100 eV energy. Conclusions: The energy dependence of the effective excitation cross section of the dielectronic satellites of the Tl + ion resonance line showed that the absolute values of their excitation cross sections are ~ 10 –16 cm 2 and are of the same order of magnitude with that for the resonance line. It is shown that the main excitation mechanism of the resonance line satellites is dielectronic recombination which effectiveness essentially depends on the ratio of the probabilities of the AIS radiation and electron decay. In the case of the relativistic Tl + ion a strong configuration mixing of levels leads to significant increase of the AIS radiation decay probability.
The effect of collisions on the resonance fluorescence spectrum of three-level atoms with a V-configuration of levels when excited by two monochromatic resonance fields has been theoretically investigated. The analysis has been carried out for the systems with a small Doppler broadening compared to the collision frequency (high buffer gas pressures) and for the general case of an arbitrary change (from complete failure to complete preservation) of the phase memory at any of the three transitions in the V-system. It has been shown that in the three-level V-type atoms excited by two monochromatic fields, the resonant fluorescence spectrum (the number of spectral lines and their widths) at one of the transitions strongly depends on the presence of resonant radiation at the adjacent transition. Under certain conditions, the line widths will be completely determined by the relaxation characteristics of the adjacent transition and, in particular, can be repeatedly narrowed with an increase in the radiation intensity at the adjacent transition. It has been shown that despite the homogeneous nature of the broadening of the absorption lines, the resonance fluorescence spectrum has a pronounced anisotropy with respect to the mutual orientation of the wave vectors of spontaneous and exciting radiation. It has been established that the line widths in the resonance fluorescence spectrum are proportional to the diffusion coefficient of the atoms interacting with radiation under certain conditions. This fact can serve as the basis for a spectroscopic method for measuring the transport frequencies of the collisions of the radiation-absorbing particles with the buffer ones. It has been shown that the effects of phase memory in the collisions lead to a strong qualitative and quantitative modification of the resonance fluorescence spectrum.
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.