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The Effects of a Finite Scattering Volume on the Determination of Electron Impact Coherence Parameters

P W Zetner, Sandor Trajmar, George Csanak

Published Jan 1, 1989• 0 citations
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Abstract

In this paper, we specifically examine the consequences of a finite scattering geometry on ''in-plane'' coherence experiments, i.e. polarization correlation or superelastic scattering experiments in which the incidence vector of the detected photon or the laser 'photon lies in the nominal scattering plane (/phi//nu/ = 0). The ''in-plane'' experimental configuration is adopted in order to give direct information about spin-orbit coupling effects. We show that a finite scattering geometry can give rise to severe distortion in the dependence of the coincidence or superelastic scattering signal intensity on the photon polarization and that this distorted behavior can be misinterpreted as arising from spin-orbit coupling effects. 11 refs., 3 figs.

Related papers

Influence of a finite scattering volume on the determination of electron-impact coherence parameters

P W Zetner, Sandor Trajmar, George Csanak

Superelastic electron scattering from laser-excited $^{138}\mathrm{Ba}$(. . .6s6p $^{1}$P) is investigated both theoretically and experimentally. The theoretical framework is developed and incorporated into a model of a realistic scattering geometry of finite spatial extent. Model calculations predict that the dependence of the superelastic scattering intensity on the linear polarization direction of the laser beam can be severely distorted due to the existence of a finite scattering volume. Our measurements confirm the presence of this distortion and are well described by the model calculations. Conclusions are drawn concerning the influence of this effect on the extraction of electron-impact coherence parameters.

Physical Review A•Jun 1, 1990•36 citations

Systematic errors in electron-photon coincidence measurements of the 31P state of helium

Ian Humphrey

The coherence parameters associated with the electron impact excitation of the He 3 1 P state are studied for a Monte Carlo simulation of an experiment consisting of crossed electron and atom beams. The effects of changes in gas pressure and interaction region geometry are monitored by a fixed polarimeter analysing radiation resulting from the 3 1 P to 1 1 S (53.7 nm) transition. This work extends the simulations of Humphrey with the incorporation of a finite electron detector, a region of background gas and angular dispersion in the electron beam. Humphrey found that with an infinitesimal electron detector, the measured polarizations were not strongly dependent on interaction region geometry. In this work, however, it is found that the coherence parameters are very strongly dependent on interaction region geometry, pressure and the solid angle of the electron detector. Even very small solid angles can adversely affect the measured parameters. While angular correlations are not specifically studied, there are indications from simulations of electron scattering angle integrated polarizations that it is most important that any measurements involving a rotation of the photon detector should rotate about a symmetry axis of the gas source.

Measurement Science and Technology•Feb 6, 2001•2 citations

Photon Vector Polarization and Coherence Parameters in an Electron-Photon Coincidence Experiment on Helium

M. C. Standage, Hans Kleinpoppen

We present linear and circular polarization measurements of $3^{1}P\ensuremath{-}2^{1}S$ (501.6 nm) photons detected in delayed coincidence with electrons inelastically scattered from the $3^{1}P$ level of helium. Vector polarization and coherence parameters of the coincident radiation provide direct experimental evidence of the coherent nature of the excitation process. Atomic orientation is obtained directly from the circular polarization measurements. Analysis of the data also yields $\ensuremath{\lambda}$ and $\ensuremath{\chi}$ parameters for $3^{1}P$ excitations, which are compared with previous data and theory.

Physical Review Letters•Mar 15, 1976•144 citations

Problems associated with the measurement of coherence parameters: Superelastic electron scattering by laser-excited Ba138 (...6s6p P11 ) atoms

P W Zetner, Sandor Trajmar, George Csanak +1 more

Measurements of superelastic scattering of electrons by laser-excited $^{138}\mathrm{Ba}$(. . .6s6p $^{1}P_{1}$) atoms were carried out. An asymmetry observed by us and previously by Register et al. [Phys. Rev. A 28, 151 (1983)] has been explained using a model of scattering from a target with finite dimensions. This model employed coherence parameters which we calculated in the distorted-wave approximation. The results indicated that the interpretation of coherence experiments in terms of scattering from a pointlike target can lead to serious errors in the deduction of coherence parameters at low scattering angles.

Physical Review A•Jun 1, 1989•22 citations

Coherence Measurements for Excited to Excited State Transitions in Barium

Sandor Trajmar, I. Kanik, V. Karaganov +2 more

Experimental studies concerning elastic and inelastic electron scattering by coherently ensembles of Ba (...6s6p (sub 1)P(sub 1)) atoms with various degrees of alignment will be described. An in-plane, linearly-polarized laser beam was utilized to prepare these target ensembles and the electron scattering signal as a function of polarization angle was measured for several laser geometries at fixed impact energies and scattering angles. From these measurements, we derived cross sections and electron-impact coherence parameters associated with the electron scattering process which is time reverse of the actual experimentally studied process. This interpretation of the experiment is based on the theory of Macek and Herte. The experimental results were also interpreted in terms of cross sections and collision parameters associated with the actual experimental processes. Results obtained so far will be presented and plans for further studies will be discussed.

•Jan 1, 2000•0 citations

Solid angle and lens corrections for light-polarization analysis in atomic scattering experiments

Ian Humphrey

Although it is a routine matter to correct for the systematic effects of a finite solid angle and the polarizing effects of a light-collection system in atomic collision studies, the methods for conducting such corrections are rarely (if at all) presented. It is the intention of the present work to present explicit formulae for the general case and explicit results for some popular experiments. No experimental results are presented. Integration over the solid angle of a conical light-collection system and the polarizing effect of a lens will be discussed. Three sample cases for which the solid-angle integration can be performed analytically are presented: a standard J = 1 J = 0 (or P S) electron-photon coincidence experiment; a laser-mediated stepwise coincidence experiment (laser-excited J = 1 J = 2 and spontaneous J = 2 J = 1); and an uncorrelated 3 P 0,1,2 3 S 1 light-polarization measurement (such as is commonly used to establish electron spin polarization). For most realistic cases, the total effect is very small and, furthermore, the lens, with some important exceptions, only marginally modifies the result of a pure solid-angle integration. The effect of internal absorption within the lens is considered and shown to be negligible. In-plane Stokes' measurements, such as of P 4 (or the stepwise P 190 parameter), are most seriously affected by these corrections.

Measurement Science and Technology•Jan 1, 1999•5 citations
In this paper, we specifically examine the consequences of a finite scattering geometry on ''in-plane'' coherence experiments, i.e. polarization correlation or superelastic scattering experiments in which the incidence vector of the detected photon or the laser 'photon lies in the nominal scattering plane (/phi//nu/ = 0). The ''in-plane'' experimental configuration is adopted in order to give direct information about spin-orbit coupling effects. We show that a finite scattering geometry can give rise to severe distortion in the dependence of the coincidence or superelastic scattering signal intensity on the photon polarization and that this distorted behavior can be misinterpreted as arising from spin-orbit coupling effects. 11 refs., 3 figs.
Superelastic electron scattering from laser-excited 138Ba^{138}\mathrm{Ba}138Ba(. . .6s6p 1^{1}1P) is investigated both theoretically and experimentally. The theoretical framework is developed and incorporated into a model of a realistic scattering geometry of finite spatial extent. Model calculations predict that the dependence of the superelastic scattering intensity on the linear polarization direction of the laser beam can be severely distorted due to the existence of a finite scattering volume. Our measurements confirm the presence of this distortion and are well described by the model calculations. Conclusions are drawn concerning the influence of this effect on the extraction of electron-impact coherence parameters.
The coherence parameters associated with the electron impact excitation of the He 3 1 P state are studied for a Monte Carlo simulation of an experiment consisting of crossed electron and atom beams. The effects of changes in gas pressure and interaction region geometry are monitored by a fixed polarimeter analysing radiation resulting from the 3 1 P to 1 1 S (53.7 nm) transition. This work extends the simulations of Humphrey with the incorporation of a finite electron detector, a region of background gas and angular dispersion in the electron beam. Humphrey found that with an infinitesimal electron detector, the measured polarizations were not strongly dependent on interaction region geometry. In this work, however, it is found that the coherence parameters are very strongly dependent on interaction region geometry, pressure and the solid angle of the electron detector. Even very small solid angles can adversely affect the measured parameters. While angular correlations are not specifically studied, there are indications from simulations of electron scattering angle integrated polarizations that it is most important that any measurements involving a rotation of the photon detector should rotate about a symmetry axis of the gas source.
We present linear and circular polarization measurements of $3^{1}P\ensuremath{-}2^{1}S$ (501.6 nm) photons detected in delayed coincidence with electrons inelastically scattered from the 31P3^{1}P31P level of helium. Vector polarization and coherence parameters of the coincident radiation provide direct experimental evidence of the coherent nature of the excitation process. Atomic orientation is obtained directly from the circular polarization measurements. Analysis of the data also yields $\ensuremath{\lambda}$ and $\ensuremath{\chi}$ parameters for 31P3^{1}P31P excitations, which are compared with previous data and theory.
Measurements of superelastic scattering of electrons by laser-excited 138Ba^{138}\mathrm{Ba}138Ba(. . .6s6p 1P1^{1}P_{1}1P1​) atoms were carried out. An asymmetry observed by us and previously by Register et al. [Phys. Rev. A 28, 151 (1983)] has been explained using a model of scattering from a target with finite dimensions. This model employed coherence parameters which we calculated in the distorted-wave approximation. The results indicated that the interpretation of coherence experiments in terms of scattering from a pointlike target can lead to serious errors in the deduction of coherence parameters at low scattering angles.
Experimental studies concerning elastic and inelastic electron scattering by coherently ensembles of Ba (...6s6p (sub 1)P(sub 1)) atoms with various degrees of alignment will be described. An in-plane, linearly-polarized laser beam was utilized to prepare these target ensembles and the electron scattering signal as a function of polarization angle was measured for several laser geometries at fixed impact energies and scattering angles. From these measurements, we derived cross sections and electron-impact coherence parameters associated with the electron scattering process which is time reverse of the actual experimentally studied process. This interpretation of the experiment is based on the theory of Macek and Herte. The experimental results were also interpreted in terms of cross sections and collision parameters associated with the actual experimental processes. Results obtained so far will be presented and plans for further studies will be discussed.
Although it is a routine matter to correct for the systematic effects of a finite solid angle and the polarizing effects of a light-collection system in atomic collision studies, the methods for conducting such corrections are rarely (if at all) presented. It is the intention of the present work to present explicit formulae for the general case and explicit results for some popular experiments. No experimental results are presented. Integration over the solid angle of a conical light-collection system and the polarizing effect of a lens will be discussed. Three sample cases for which the solid-angle integration can be performed analytically are presented: a standard J = 1 J = 0 (or P S) electron-photon coincidence experiment; a laser-mediated stepwise coincidence experiment (laser-excited J = 1 J = 2 and spontaneous J = 2 J = 1); and an uncorrelated 3 P 0,1,2 3 S 1 light-polarization measurement (such as is commonly used to establish electron spin polarization). For most realistic cases, the total effect is very small and, furthermore, the lens, with some important exceptions, only marginally modifies the result of a pure solid-angle integration. The effect of internal absorption within the lens is considered and shown to be negligible. In-plane Stokes' measurements, such as of P 4 (or the stepwise P 190 parameter), are most seriously affected by these corrections.